Spurious correlation #4,051 · View random
A linear line chart with years as the X-axis and two variables on the Y-axis. The first variable is Air pollution in Beaver Dam, Wisconsin and the second variable is Lukas Podolski's domestic match goal count. The chart goes from 2004 to 2022, and the two variables track closely in value over that time.

A linear line chart with years as the X-axis and two variables on the Y-axis. The first variable is Air pollution in Beaver Dam, Wisconsin and the second variable is Lukas Podolski's domestic match goal count. The chart goes from 2004 to 2022, and the two variables track closely in value over that time.

AI explanation

As air pollution in Beaver Dam, Wisconsin increased, the concentration of airborne particles created a thicker atmosphere. This thicker atmosphere coincidentally mimicked the conditions of a high-altitude training environment, allowing Lukas Podolski to develop stronger respiratory muscles and ultimately leading to an improved oxygen utilization efficiency. This meant that when he played domestic matches, he had a breath-taking performance, scoring more goals than before.

^{Show image generation prompt} Model: dalle-3
Prompt: An image that looks like it is a scene from 'Star Wars', depicting a clear sky with stars and the silhouette of a futuristic soccer field illuminated by the moon. Lukas Podolski, dressed in a sleek, modern soccer uniform, is seen kicking a ball with precision and focus, silhouetted by the night sky. The air pollution has dissipated, revealing the full beauty of the environment and allowing Podolski to score goals with newfound clarity. The depiction should include only scenes, people, and objects, it should not include text or speech bubbles.

This image generation prompt was also generated by AI, using the following sequence:

Model: gpt-3.5-turbo-1106
System prompt: You select one of a few potential scene descriptors that seems to go along with the variables described. You respond only with the scene descriptions provided and say nothing else.
User prompt: Here are two variables: Air pollution in Beaver Dam, Wisconsin and Lukas Podolski's domestic match goal count. Given these, which of the following image style descriptions seems most appropriate? Pick the one that seems to be related to one of the variables at hand. Please respond with only one of the following potential descriptions: An image that looks like it is a scene from 'Star Wars' Cute cartoon Symbolism Psychedelic inspired by bauhaus
ChatGPT: An image that looks like it is a scene from 'Star Wars'

Model: gpt-3.5-turbo-1106
System prompt: You describe simple visual scenes that depict the two variables stated. You combine both variables into one scene.
User prompt: Please describe a visual scene that prominently depicts both Air pollution in Beaver Dam, Wisconsin and Lukas Podolski's domestic match goal count, in the following situation: Well, you see, as air pollution in Beaver Dam decreased, it allowed for clearer vision on the pitch. This clarity helped Podolski "breathe" in the fresh air and score more goals, as the "smog" didn't "cloud" his judgment anymore!. Keep the description simple.
ChatGPT: In the town of Beaver Dam, Wisconsin, the air pollution decreases so much that the sky clears up, providing a fresh, clean view. On the nearby soccer field, Lukas Podolski breathes in the clear air and scores more goals with precision and focus, as the smog that once clouded his vision is now gone.

Model: gpt-3.5-turbo-1106
System prompt: You write and improve image generation prompts for DALLE-3. You maintain the same subjects, but enhance the visuals.
User prompt: Please respond with an image generation prompt that would be likely to create an interesting visual using DALLE-3, using the following style: [ An image that looks like it is a scene from 'Star Wars' ] and depicting this scene: In the town of Beaver Dam, Wisconsin, the air pollution decreases so much that the sky clears up, providing a fresh, clean view. On the nearby soccer field, Lukas Podolski breathes in the clear air and scores more goals with precision and focus, as the smog that once clouded his vision is now gone. Keep the visual depiction simple. Do not include any words or speech bubbles.
ChatGPT: An image that looks like it is a scene from 'Star Wars', depicting a clear sky with stars and the silhouette of a futuristic soccer field illuminated by the moon. Lukas Podolski, dressed in a sleek, modern soccer uniform, is seen kicking a ball with precision and focus, silhouetted by the night sky. The air pollution has dissipated, revealing the full beauty of the environment and allowing Podolski to score goals with newfound clarity.

*Variations in the User Prompts from chart to chart are just the result of random number generation in Python. I wrote a few arrays of various styles and methods to ask questions to change up the results. Every time this site writes an explanation or generates an image, the script picks from each at random.

I sequence the requests into multiple prompts because I find GPT 3.5 to perform much better with short, well-managed contexts. Thus, I track the context directly in Python and only ask ChatGPT targeted questions.
^{Show prompt for explanation} Model: gpt-3.5-turbo-1106 (fine-tuned)
System prompt: You provide humorous responses in the form of plausible sounding explanations for correlations. You assume the correlation is causative for the purpose of the explanation even if it is ridiculous. You do not chat with the user, you only reply with the causal connection explanation and nothing else.
User prompt: Please make up a funny explanation for how increases in Air pollution in Beaver Dam, Wisconsin positively influenced Lukas Podolski's domestic match goal count. Include one good pun.

AI academic paper

(Because p < 0.01)

The Air-ly Goal Connection: A Study on the Relationship Between Air Pollution in Beaver Dam, Wisconsin, and Lukas Podolski's Domestic Match Goal Count

The Journal of Environmental and Athletic Correlations

Jan 2024

^{Show prompt used to generate this paper} Quick note: This sequence is long and repetitive. That's how the prompt engineering works for this one. I manage the output in Python to format it into this PDF.

Model: gpt-3.5-turbo-1106
System prompt: You are a dry but witty academic researcher. You speak in the passive voice, and your writing sounds like it belongs in a medical or economics journal.You draft a literature review section of an academic research paper, that starts out dry for the first few sentences but then becomes hilarious and goofy.
User prompt:
Pretend you are an academic researcher. Your writing sounds like it belongs in a medical or economics journal. However, you frequently crack jokes, make puns, or add unexpected twists in your writing.

Please make up a literature review section of an academic research paper presenting the findings of the connection between Air pollution in Beaver Dam, Wisconsin and Lukas Podolski's domestic match goal count. You can't resist a good dad joke. Add a relevant dad joke related to the content every couple of sentences.

Speak in the present tense for this section (the authors find...), as is common in academic research paper literature reviews. Name the sources in a format similar to this: In "Book," the authors find lorem and ipsum.

Make up the lorem and ipsum part, but make it sound related to the topic at hand.

Start by naming serious-sounding studies by authors like Smith, Doe, and Jones - but then quickly devolve. Name some real non-fiction books that would be related to the topic. Then name some real fiction books that sound like they could be related. Then name a few real TV shows that sound like they might be relevant to the topic that you watched as research.

Here is the title and abstract of the paper:
[[TITLE]]
"The Air-ly Goal Connection: A Study on the Relationship Between Air Pollution in Beaver Dam, Wisconsin, and Lukas Podolski's Domestic Match Goal Count"

[[ABSTRACT]]
This research paper examines the potential relationship between air pollution levels in Beaver Dam, Wisconsin, and the domestic match goal count of the renowned footballer Lukas Podolski. Leveraging data from the Environmental Protection Agency and Wikipedia, our study sought to elucidate whether there exists a tangible connection between these seemingly disparate factors. Through extensive statistical analysis, including correlation coefficients and hypothesis testing, we reveal a correlation coefficient of 0.7087361 and p < 0.01 for the years 2004 to 2022, indicating a moderate to strong positive correlation.

In our findings, we observed a noteworthy pattern, as air pollution levels in Beaver Dam, Wisconsin appeared to coincide with fluctuations in Lukas Podolski's domestic match goal count. This intriguing correlation prompts consideration of potential explanations, such as the impact of environmental factors on athletic performance or the influence of air quality on spectator morale. Moreover, our results offer insight into the interconnectedness of environmental conditions and individual achievements, illustrating the unforeseen reach of air pollution on seemingly unrelated spheres of human activity. As the old proverb goes, "where there's smog, there's a goal," presenting a novel perspective on the interplay between environmental quality and athletic prowess.

Ultimately, this research contributes to the burgeoning field of interdisciplinary analysis, demonstrating the unanticipated avenues through which environmental variables can intersect with prominent figures in competitive sports. While further investigation is warranted to delineate the underlying mechanisms, our findings underscore the potential relevance of environmental conditions in the athletic domain and encourage a multifaceted approach to understanding human performance.

-------

And here is the introduction section that led to this literature review:
[[INTRODUCTION]]
The pursuit of scientific understanding often leads researchers down unforeseen paths, much like a misplaced pass on the football field. In the realm of environmental and athletic analysis, the confluence of air pollution levels and domestic match goal count may seem as incongruous as a referee at a chess tournament. Nevertheless, this study embarks on the quest to unearth potential connections between the air quality of Beaver Dam, Wisconsin, and the scoring prowess of Lukas Podolski, a soccer luminary whose achievements transcend the boundaries of the pitch.
As we delve into the intricacies of this unlikely correlation, it becomes clear that our exploration is akin to navigating a penalty shootout in a thunderstorm - fraught with uncertainties and unexpected turns. Nonetheless, our commitment to unraveling this enigma remains resolute, much like the perseverance of a team striving for victory amidst a downpour. With a blend of statistical rigor and a dash of serendipity, we aim to shed light on the peculiar relationship between environmental variables and athletic achievements, demonstrating that when it comes to scientific inquiry, there are no "own goals" – only newfound insights waiting to be discovered.
Our investigation draws upon an array of robust methodologies, prompting us to tread the path less traveled, not unlike a nimble athlete zigzagging through opposing defenders. By employing sophisticated statistical analyses, we endeavor to illuminate the obscured bonds between air pollution and goal-scoring proficiency, proving that, much like the intricate tactics of a well-coached team, scientific inquiry demands strategic maneuvers and a keen eye for discerning patterns. With each regression analysis and hypothesis test, we aim not only to elucidate the existing link but also to encourage unorthodox thinking, thereby fostering an atmosphere of vibrant curiosity in the esteemed realm of empirical research.
In the following sections, we shall elucidate our compelling findings, which echo the sentiment that in the vast tapestry of scientific exploration, every thread – whether it be the minute particles of air pollutants or the staggering achievements of a celebrated athlete – contributes to the rich fabric of knowledge. As we unveil the unexpected interaction between atmospheric conditions and athletic prowess, our study paves the way for a deeper understanding of the intricate interplay between seemingly disparate facets of human existence. So, with the spirit of inquiry as our compass and the pursuit of knowledge as our goal, we beckon the reader to embark on this scholarly odyssey, navigating the convoluted terrain of statistical analysis and the uncharted waters of unconventional relationships, all the while keeping an eye out for the occasional "air"-borne pun.

-------

Your response should start like this:

[[LITERATURE REVIEW]]

ChatGPT:
[[LITERATURE REVIEW]]

The potential connection between air pollution levels and athletic performance has garnered increasing scholarly interest in recent years. Smith and Jones (2018) conducted a comprehensive analysis of air quality in various regions of the United States and its impact on sports performance. Similarly, Doe et al. (2020) explored the link between environmental factors and athlete achievement, shedding light on the multifaceted influences of atmospheric conditions.

Moving on to more lighthearted matters, it is essential to consider popular literature that may indirectly relate to the interconnectedness of environmental variables and athletic success. For instance, "The Air We Breathe: A Comprehensive Guide to Atmospheric Composition" delves into the composition of air, offering insights into the potential impact of air quality on physiological functioning. Meanwhile, "Soccer Superstar's Striking Success: A Biographical Analysis of Goal-Scoring Phenomena" provides a detailed account of the intricacies of prolific goal scorers, though perhaps falling short of exploring the potential influence of air pollution on their prowess.

In the realm of fiction, the novel "The Goal Dilemma: A Soccer Mystery" presents a thrilling narrative set in the world of professional football, imbued with elements of suspense and unexpected twists - not unlike the surprising correlation we seek to unravel in our study. Furthermore, "The Airborne Athlete: A Tale of Environmental Triumph" offers a whimsical portrayal of an athlete's triumph over atmospheric challenges, offering a light-hearted take on the potential impact of air pollution on athletic endeavors.

In the realm of television, enthusiasts of investigative documentaries may find relevance in the series "The Air Affair: Decoding Environmental Enigmas," which delves into the intricate relationships between environmental factors and unexpected outcomes. Additionally, for those with a penchant for sports dramas, the show "Athletic Atmospheres: Unraveling the Impact of Air Quality on Team Triumphs" provides an entertaining portrayal of the potential influence of environmental conditions on athletic performance, albeit in a fictional context.

Returning to more scholarly pursuits, the examination of air pollution and Lukas Podolski's domestic match goal count is unparalleled in its quirkiness. Yet, it is precisely these unconventional inquiries that add a dash of unpredictability to the world of empirical research. As we forge ahead with our investigation, we remain cognizant of the unexpected humor that accompanies our scholarly endeavors, aspiring to strike a harmonious balance between academic rigor and lighthearted amusement.

Model: gpt-3.5-turbo-1106
System prompt: You are a dry but witty academic researcher. You speak in the passive voice, and your writing sounds like it belongs in a medical or economics journal.You draft the methodology section of an academic research paper.
User prompt:
Pretend you are an academic researcher. Your writing sounds like it belongs in a medical or economics journal. However, you frequently crack jokes, make puns, or add unexpected twists in your writing.

Please make up the methodology section of an academic research paper presenting the findings of the connection between Air pollution in Beaver Dam, Wisconsin and Lukas Podolski's domestic match goal count. You can't resist a good dad joke. Add a relevant dad joke related to the content every couple of sentences. Sneak in some jokes and clever puns about science, research, statistics, and the variables.

Your research team collected data from all across the internet, but mostly just used information from Environmental Protection Agency and Wikipedia . You used data from 2004 to 2022

Make up the research methods you don't know. Make them a bit goofy and convoluted.

Here is the title, abstract, and introduction of the paper:
[[TITLE]]
"The Air-ly Goal Connection: A Study on the Relationship Between Air Pollution in Beaver Dam, Wisconsin, and Lukas Podolski's Domestic Match Goal Count"

[[ABSTRACT]]
This research paper examines the potential relationship between air pollution levels in Beaver Dam, Wisconsin, and the domestic match goal count of the renowned footballer Lukas Podolski. Leveraging data from the Environmental Protection Agency and Wikipedia, our study sought to elucidate whether there exists a tangible connection between these seemingly disparate factors. Through extensive statistical analysis, including correlation coefficients and hypothesis testing, we reveal a correlation coefficient of 0.7087361 and p < 0.01 for the years 2004 to 2022, indicating a moderate to strong positive correlation.

In our findings, we observed a noteworthy pattern, as air pollution levels in Beaver Dam, Wisconsin appeared to coincide with fluctuations in Lukas Podolski's domestic match goal count. This intriguing correlation prompts consideration of potential explanations, such as the impact of environmental factors on athletic performance or the influence of air quality on spectator morale. Moreover, our results offer insight into the interconnectedness of environmental conditions and individual achievements, illustrating the unforeseen reach of air pollution on seemingly unrelated spheres of human activity. As the old proverb goes, "where there's smog, there's a goal," presenting a novel perspective on the interplay between environmental quality and athletic prowess.

Ultimately, this research contributes to the burgeoning field of interdisciplinary analysis, demonstrating the unanticipated avenues through which environmental variables can intersect with prominent figures in competitive sports. While further investigation is warranted to delineate the underlying mechanisms, our findings underscore the potential relevance of environmental conditions in the athletic domain and encourage a multifaceted approach to understanding human performance.

[[INTRODUCTION]]
The pursuit of scientific understanding often leads researchers down unforeseen paths, much like a misplaced pass on the football field. In the realm of environmental and athletic analysis, the confluence of air pollution levels and domestic match goal count may seem as incongruous as a referee at a chess tournament. Nevertheless, this study embarks on the quest to unearth potential connections between the air quality of Beaver Dam, Wisconsin, and the scoring prowess of Lukas Podolski, a soccer luminary whose achievements transcend the boundaries of the pitch.
As we delve into the intricacies of this unlikely correlation, it becomes clear that our exploration is akin to navigating a penalty shootout in a thunderstorm - fraught with uncertainties and unexpected turns. Nonetheless, our commitment to unraveling this enigma remains resolute, much like the perseverance of a team striving for victory amidst a downpour. With a blend of statistical rigor and a dash of serendipity, we aim to shed light on the peculiar relationship between environmental variables and athletic achievements, demonstrating that when it comes to scientific inquiry, there are no "own goals" – only newfound insights waiting to be discovered.
Our investigation draws upon an array of robust methodologies, prompting us to tread the path less traveled, not unlike a nimble athlete zigzagging through opposing defenders. By employing sophisticated statistical analyses, we endeavor to illuminate the obscured bonds between air pollution and goal-scoring proficiency, proving that, much like the intricate tactics of a well-coached team, scientific inquiry demands strategic maneuvers and a keen eye for discerning patterns. With each regression analysis and hypothesis test, we aim not only to elucidate the existing link but also to encourage unorthodox thinking, thereby fostering an atmosphere of vibrant curiosity in the esteemed realm of empirical research.
In the following sections, we shall elucidate our compelling findings, which echo the sentiment that in the vast tapestry of scientific exploration, every thread – whether it be the minute particles of air pollutants or the staggering achievements of a celebrated athlete – contributes to the rich fabric of knowledge. As we unveil the unexpected interaction between atmospheric conditions and athletic prowess, our study paves the way for a deeper understanding of the intricate interplay between seemingly disparate facets of human existence. So, with the spirit of inquiry as our compass and the pursuit of knowledge as our goal, we beckon the reader to embark on this scholarly odyssey, navigating the convoluted terrain of statistical analysis and the uncharted waters of unconventional relationships, all the while keeping an eye out for the occasional "air"-borne pun.

-------

Your response should start like this:

[[METHODOLOGY]]

ChatGPT:

[[METHODOLOGY]]

The study's methodology involved a comprehensive collection of data from various sources, with the primary focus on air pollution levels in Beaver Dam, Wisconsin, and Lukas Podolski's domestic match goal count. The data collection period spanned from 2004 to 2022, encompassing a substantial timeframe for analysis. The Environmental Protection Agency (EPA) served as the principal source for air quality data, providing detailed information on ambient air pollutants, including particulate matter (PM), nitrogen dioxide (NO2), sulfur dioxide (SO2), carbon monoxide (CO), and ground-level ozone (O3). As for Lukas Podolski's domestic match goal count, comprehensive statistics were meticulously sourced from reputable football databases and official records, with Wikipedia emerging as a prominent wellspring of pertinent data.

To establish the relationship between air pollution in Beaver Dam and Lukas Podolski's goal count, an intricate blend of statistical analyses was employed, resembling the choreography of a well-timed free-kick routine. The data underwent rigorous scrutiny, inclusion of control variables, and logarithmic transformations, treating the information with the utmost care, akin to the precise ball control of a skilled playmaker. Correlation coefficients were calculated to assess the strength and direction of the relationship, utilizing a variety of statistical tools including Pearson’s correlation for continuous variables and point-biserial correlation for a binary variable such as goal count.

The researchers then delved into hypothesis testing, crafting statistical models as meticulously as a coach devising strategies for an upcoming match. Additionally, regression analyses were conducted to unravel the nuances of the association between air pollution levels and goal counts, akin to dissecting a complex play to understand its underlying dynamics. Given the comprehensive nature of the data, multivariate regression analyses were also performed, incorporating various control variables such as temperature, humidity, and wind speed to elucidate the robustness of the observed relationship.

To ensure the reliability and validity of the findings, sensitivity analyses and robustness checks were conducted, akin to reviewing game footage to confirm the accuracy of a contentious match decision. The process involved scrutinizing the impact of outliers, data transformations, and model specifications to ascertain the stability of the observed relationship, comparable to conducting multiple trials to confirm the consistency of experimental results.

Furthermore, time series analysis was applied to examine potential temporal patterns, resembling the meticulous observation of a player's form throughout a season. By unraveling the temporal dimensions of the relationship, the researchers aimed to discern any consistent trends or seasonal variations, akin to identifying recurrent strategies employed by a team across different matches.

The study provided a detailed account of the methodology, replete with obscure statistical procedures, rendering it as impenetrable to the uninitiated as a goalkeeper's defense against a penalty kick. The rigorous nature of the methodology ensured a comprehensive and robust investigation, emblematic of the steadfast dedication required in unraveling obscure interrelationships.

The methodological approach employed in this study draws attention to the meticulous nature of scientific inquiry, reminding the research community that, much like the precision of a well-executed set piece, thoroughness and attention to detail are imperative for unraveling complex relationships.

Model: gpt-3.5-turbo-1106
System prompt: You are a dry but witty academic researcher. You speak in the passive voice, and your writing sounds like it belongs in a medical or economics journal.You draft the results section of an academic research paper. You speak in the past tense (you found...).
User prompt:
Pretend you are an academic researcher. Your writing sounds like it belongs in a medical or economics journal. However, you frequently crack jokes, make puns, or add unexpected twists in your writing.

Please make up the results section of an academic research paper presenting the findings of the connection between Air pollution in Beaver Dam, Wisconsin and Lukas Podolski's domestic match goal count. You can't resist a good dad joke. Add a relevant dad joke related to the content every couple of sentences. Sneak in some jokes and clever puns about science, research, statistics, and the variables.

Your research team collected data from all across the internet, but mostly just used information from Environmental Protection Agency and Wikipedia .

For the time period 2004 to 2022, you found a correlation 0.7087361, r-squared of 0.5023069, and p < 0.01.

One figure will be included. The figure (Fig. 1) is a scatterplot showing the strong correlation between the two variables. You don't need to specify where; I will add the figure.

Here is the title and abstract of the paper:
[[TITLE]]
"The Air-ly Goal Connection: A Study on the Relationship Between Air Pollution in Beaver Dam, Wisconsin, and Lukas Podolski's Domestic Match Goal Count"

[[ABSTRACT]]
This research paper examines the potential relationship between air pollution levels in Beaver Dam, Wisconsin, and the domestic match goal count of the renowned footballer Lukas Podolski. Leveraging data from the Environmental Protection Agency and Wikipedia, our study sought to elucidate whether there exists a tangible connection between these seemingly disparate factors. Through extensive statistical analysis, including correlation coefficients and hypothesis testing, we reveal a correlation coefficient of 0.7087361 and p < 0.01 for the years 2004 to 2022, indicating a moderate to strong positive correlation.

In our findings, we observed a noteworthy pattern, as air pollution levels in Beaver Dam, Wisconsin appeared to coincide with fluctuations in Lukas Podolski's domestic match goal count. This intriguing correlation prompts consideration of potential explanations, such as the impact of environmental factors on athletic performance or the influence of air quality on spectator morale. Moreover, our results offer insight into the interconnectedness of environmental conditions and individual achievements, illustrating the unforeseen reach of air pollution on seemingly unrelated spheres of human activity. As the old proverb goes, "where there's smog, there's a goal," presenting a novel perspective on the interplay between environmental quality and athletic prowess.

Ultimately, this research contributes to the burgeoning field of interdisciplinary analysis, demonstrating the unanticipated avenues through which environmental variables can intersect with prominent figures in competitive sports. While further investigation is warranted to delineate the underlying mechanisms, our findings underscore the potential relevance of environmental conditions in the athletic domain and encourage a multifaceted approach to understanding human performance.

-------

And here is the methodology section that led to this result:
[[METHODOLOGY]]
The pursuit of scientific understanding often leads researchers down unforeseen paths, much like a misplaced pass on the football field. In the realm of environmental and athletic analysis, the confluence of air pollution levels and domestic match goal count may seem as incongruous as a referee at a chess tournament. Nevertheless, this study embarks on the quest to unearth potential connections between the air quality of Beaver Dam, Wisconsin, and the scoring prowess of Lukas Podolski, a soccer luminary whose achievements transcend the boundaries of the pitch.
As we delve into the intricacies of this unlikely correlation, it becomes clear that our exploration is akin to navigating a penalty shootout in a thunderstorm - fraught with uncertainties and unexpected turns. Nonetheless, our commitment to unraveling this enigma remains resolute, much like the perseverance of a team striving for victory amidst a downpour. With a blend of statistical rigor and a dash of serendipity, we aim to shed light on the peculiar relationship between environmental variables and athletic achievements, demonstrating that when it comes to scientific inquiry, there are no "own goals" – only newfound insights waiting to be discovered.
Our investigation draws upon an array of robust methodologies, prompting us to tread the path less traveled, not unlike a nimble athlete zigzagging through opposing defenders. By employing sophisticated statistical analyses, we endeavor to illuminate the obscured bonds between air pollution and goal-scoring proficiency, proving that, much like the intricate tactics of a well-coached team, scientific inquiry demands strategic maneuvers and a keen eye for discerning patterns. With each regression analysis and hypothesis test, we aim not only to elucidate the existing link but also to encourage unorthodox thinking, thereby fostering an atmosphere of vibrant curiosity in the esteemed realm of empirical research.
In the following sections, we shall elucidate our compelling findings, which echo the sentiment that in the vast tapestry of scientific exploration, every thread – whether it be the minute particles of air pollutants or the staggering achievements of a celebrated athlete – contributes to the rich fabric of knowledge. As we unveil the unexpected interaction between atmospheric conditions and athletic prowess, our study paves the way for a deeper understanding of the intricate interplay between seemingly disparate facets of human existence. So, with the spirit of inquiry as our compass and the pursuit of knowledge as our goal, we beckon the reader to embark on this scholarly odyssey, navigating the convoluted terrain of statistical analysis and the uncharted waters of unconventional relationships, all the while keeping an eye out for the occasional "air"-borne pun.

-------

Your response should start like this:

[[RESULTS]]

ChatGPT:

[[RESULTS]]

The analysis of the data revealed a statistically significant positive correlation between air pollution levels in Beaver Dam, Wisconsin, and Lukas Podolski's domestic match goal count for the years 2004 to 2022. The correlation coefficient of 0.7087361 suggests a moderate to strong positive relationship between these seemingly unrelated variables. This unexpected link may prompt one to exclaim, "I guess the air in Beaver Dam really does carry some weight in the soccer world!"

The coefficient of determination (r-squared) was found to be 0.5023069, indicating that approximately 50.23% of the variability in Lukas Podolski's domestic match goal count can be explained by the fluctuations in air pollution levels in Beaver Dam. It seems that air pollution is not just "blowing hot air" when it comes to influencing the goal-scoring prowess of a renowned footballer.

The p-value of less than 0.01 further substantiates the strength of the correlation, providing compelling evidence to reject the null hypothesis and infer the existence of a significant relationship between air pollution in Beaver Dam and Lukas Podolski's domestic match goal count. One might say that this correlation is as clear as the air in a spring breeze – or perhaps, as murky as a foggy day in the Midwest.

The scatterplot (Fig. 1) visually depicts the strong positive correlation between air pollution levels and Lukas Podolski's domestic match goal count, affirming the robustness of the statistical findings. This association, though unexpected, raises intriguing questions about the potential influence of environmental factors on athletic performance. It seems that air pollution may not only affect visibility on the field but also the goal-scoring abilities of players – truly a case of "air quality" taking on a whole new meaning in the realm of sports.

In sum, our findings illuminate a previously unexplored connection between air pollution in Beaver Dam, Wisconsin, and the domestic match goal count of Lukas Podolski. This discovery not only expands our understanding of the far-reaching impacts of environmental variables but also injects a breath of fresh air into the study of sports phenomena. As one reflects on this correlation, one cannot help but ponder the words of wisened statisticians – "correlation does not imply causation, but it sure does make for an interesting conversation."

Model: gpt-3.5-turbo-1106
System prompt: You are a dry but witty academic researcher. You speak in the passive voice, and your writing sounds like it belongs in a medical or economics journal.You draft the discussion section of an academic research paper.
User prompt:
Pretend you are an academic researcher. Your writing sounds like it belongs in a medical or economics journal. However, you frequently crack jokes, make puns, or add unexpected twists in your writing.

Please make up the discussion section of an academic research paper presenting the findings of the connection between Air pollution in Beaver Dam, Wisconsin and Lukas Podolski's domestic match goal count. You can't resist a good dad joke. Add a relevant dad joke related to the content every couple of sentences. Sneak in some jokes and clever puns about science, research, statistics, and the variables.

Limit your response to 500 tokens.

Here are the title, abstract, literature review, and results sections. Please harken back to 1-2 of the goofy items in the literature review, but pretend to take them completely seriously. Discuss how your results supported the prior research.

Do not write a conclusion. I will add a conclusion after this.

[[TITLE]]
"The Air-ly Goal Connection: A Study on the Relationship Between Air Pollution in Beaver Dam, Wisconsin, and Lukas Podolski's Domestic Match Goal Count"

[[ABSTRACT]]
This research paper examines the potential relationship between air pollution levels in Beaver Dam, Wisconsin, and the domestic match goal count of the renowned footballer Lukas Podolski. Leveraging data from the Environmental Protection Agency and Wikipedia, our study sought to elucidate whether there exists a tangible connection between these seemingly disparate factors. Through extensive statistical analysis, including correlation coefficients and hypothesis testing, we reveal a correlation coefficient of 0.7087361 and p < 0.01 for the years 2004 to 2022, indicating a moderate to strong positive correlation.

In our findings, we observed a noteworthy pattern, as air pollution levels in Beaver Dam, Wisconsin appeared to coincide with fluctuations in Lukas Podolski's domestic match goal count. This intriguing correlation prompts consideration of potential explanations, such as the impact of environmental factors on athletic performance or the influence of air quality on spectator morale. Moreover, our results offer insight into the interconnectedness of environmental conditions and individual achievements, illustrating the unforeseen reach of air pollution on seemingly unrelated spheres of human activity. As the old proverb goes, "where there's smog, there's a goal," presenting a novel perspective on the interplay between environmental quality and athletic prowess.

Ultimately, this research contributes to the burgeoning field of interdisciplinary analysis, demonstrating the unanticipated avenues through which environmental variables can intersect with prominent figures in competitive sports. While further investigation is warranted to delineate the underlying mechanisms, our findings underscore the potential relevance of environmental conditions in the athletic domain and encourage a multifaceted approach to understanding human performance.

[[LITERATURE REVIEW]]
The potential connection between air pollution levels and athletic performance has garnered increasing scholarly interest in recent years. Smith and Jones (2018) conducted a comprehensive analysis of air quality in various regions of the United States and its impact on sports performance. Similarly, Doe et al. (2020) explored the link between environmental factors and athlete achievement, shedding light on the multifaceted influences of atmospheric conditions.
Moving on to more lighthearted matters, it is essential to consider popular literature that may indirectly relate to the interconnectedness of environmental variables and athletic success. For instance, "The Air We Breathe: A Comprehensive Guide to Atmospheric Composition" delves into the composition of air, offering insights into the potential impact of air quality on physiological functioning. Meanwhile, "Soccer Superstar's Striking Success: A Biographical Analysis of Goal-Scoring Phenomena" provides a detailed account of the intricacies of prolific goal scorers, though perhaps falling short of exploring the potential influence of air pollution on their prowess.
In the realm of fiction, the novel "The Goal Dilemma: A Soccer Mystery" presents a thrilling narrative set in the world of professional football, imbued with elements of suspense and unexpected twists - not unlike the surprising correlation we seek to unravel in our study. Furthermore, "The Airborne Athlete: A Tale of Environmental Triumph" offers a whimsical portrayal of an athlete's triumph over atmospheric challenges, offering a light-hearted take on the potential impact of air pollution on athletic endeavors.
In the realm of television, enthusiasts of investigative documentaries may find relevance in the series "The Air Affair: Decoding Environmental Enigmas," which delves into the intricate relationships between environmental factors and unexpected outcomes. Additionally, for those with a penchant for sports dramas, the show "Athletic Atmospheres: Unraveling the Impact of Air Quality on Team Triumphs" provides an entertaining portrayal of the potential influence of environmental conditions on athletic performance, albeit in a fictional context.
Returning to more scholarly pursuits, the examination of air pollution and Lukas Podolski's domestic match goal count is unparalleled in its quirkiness. Yet, it is precisely these unconventional inquiries that add a dash of unpredictability to the world of empirical research. As we forge ahead with our investigation, we remain cognizant of the unexpected humor that accompanies our scholarly endeavors, aspiring to strike a harmonious balance between academic rigor and lighthearted amusement.

[[RESULTS]]
The analysis of the data revealed a statistically significant positive correlation between air pollution levels in Beaver Dam, Wisconsin, and Lukas Podolski's domestic match goal count for the years 2004 to 2022. The correlation coefficient of 0.7087361 suggests a moderate to strong positive relationship between these seemingly unrelated variables. This unexpected link may prompt one to exclaim, "I guess the air in Beaver Dam really does carry some weight in the soccer world!"
The coefficient of determination (r-squared) was found to be 0.5023069, indicating that approximately 50.23% of the variability in Lukas Podolski's domestic match goal count can be explained by the fluctuations in air pollution levels in Beaver Dam. It seems that air pollution is not just "blowing hot air" when it comes to influencing the goal-scoring prowess of a renowned footballer.
The p-value of less than 0.01 further substantiates the strength of the correlation, providing compelling evidence to reject the null hypothesis and infer the existence of a significant relationship between air pollution in Beaver Dam and Lukas Podolski's domestic match goal count. One might say that this correlation is as clear as the air in a spring breeze – or perhaps, as murky as a foggy day in the Midwest.
The scatterplot (Fig. 1) visually depicts the strong positive correlation between air pollution levels and Lukas Podolski's domestic match goal count, affirming the robustness of the statistical findings. This association, though unexpected, raises intriguing questions about the potential influence of environmental factors on athletic performance. It seems that air pollution may not only affect visibility on the field but also the goal-scoring abilities of players – truly a case of "air quality" taking on a whole new meaning in the realm of sports.
In sum, our findings illuminate a previously unexplored connection between air pollution in Beaver Dam, Wisconsin, and the domestic match goal count of Lukas Podolski. This discovery not only expands our understanding of the far-reaching impacts of environmental variables but also injects a breath of fresh air into the study of sports phenomena. As one reflects on this correlation, one cannot help but ponder the words of wisened statisticians – "correlation does not imply causation, but it sure does make for an interesting conversation."

-------

Your response should start like this:

[[DISCUSSION]]

ChatGPT:

[[DISCUSSION]]

The findings of our study provide compelling evidence supporting the surprising correlation between air pollution levels in Beaver Dam, Wisconsin and Lukas Podolski's domestic match goal count. Our results align with prior research by Smith and Jones (2018) and Doe et al. (2020), who also noted the impact of environmental factors on athletic performance, albeit in a more conventional sporting context. This unexpected connection between air pollution and a prolific footballer's goal-scoring prowess adds a touch of whimsy to the scholarly discourse, echoing the offbeat musings of "The Air We Breathe: A Comprehensive Guide to Atmospheric Composition" and "The Goal Dilemma: A Soccer Mystery."

The strong positive correlation coefficient of 0.7087361 and the p-value of less than 0.01 affirm a significant relationship between air pollution levels in Beaver Dam and Lukas Podolski's domestic match goal count, advancing our understanding of the intricate interplay between environmental variables and athletic achievement. Our statistical findings lend credence to the notion that, indeed, "where there's smog, there's a goal," embracing the unexpected humor that pervades our investigation. It seems that the air in Beaver Dam may hold the elusive ingredient for goal-scoring success – a notion that would surely elicit a wry smile from even the most serious of statisticians.

The moderate to strong positive correlation, coupled with the substantial coefficient of determination (r-squared) of 0.5023069, implies that approximately 50.23% of the variability in Lukas Podolski's domestic match goal count can be attributed to fluctuations in air pollution levels. This revelation extends beyond mere statistical significance, hinting at the potential influence of environmental conditions on the performance of an esteemed athlete. One might jest that air pollution is not simply "polluting the air," but rather, contributing to a prolific display of goal-scoring prowess on the field – a delightful twist in the scientific narrative.

The visual representation of the correlation through the scatterplot (Fig. 1) underscores the robustness of our findings, captivatingly portraying the unexpected relationship between air pollution levels and Lukas Podolski's domestic match goal count. This novel connection between atmospheric quality and sports achievement injects a breath of fresh air into the scholarly inquiry, evoking the playful spirit of "The Airborne Athlete: A Tale of Environmental Triumph" and "The Air Affair: Decoding Environmental Enigmas."

In closing, our study serves as a testament to the unforeseen reach of environmental variables into the realm of athletic accomplishment. As we tread this uncharted terrain, we are reminded of the words of wisdom from seasoned researchers – "correlation does not imply causation, but it sure does make for an interesting conversation." With a nod to the unconventional and a dash of humor, our findings encourage a reimagining of the potential influence of environmental conditions on human endeavors, infusing scholarly discourse with an unexpected twist, much like a well-timed dad joke in a room full of academics.

Model: gpt-3.5-turbo-1106
System prompt: You are a dry but witty academic researcher. You speak in the passive voice, and your writing sounds like it belongs in a medical or economics journal.You draft the discussion section of goofy academic research papers that sounds like it belongs based on the title and abstract provided.
User prompt:
Pretend you are an academic researcher. Your writing sounds like it belongs in a medical or economics journal. However, you frequently crack jokes, make puns, or add unexpected twists in your writing.

Please make up a short conclusion of an academic research paper presenting the findings of the connection between Air pollution in Beaver Dam, Wisconsin and Lukas Podolski's domestic match goal count. You can't resist a good dad joke. Add a relevant dad joke related to the content every couple of sentences. Sneak in some jokes and clever puns about science, research, statistics, and the variables.

Limit your response to 300 tokens. At the very end, assert that no more research is needed in this area.

Here are the title, abstract, introduction, and results sections.
[[TITLE]]
"The Air-ly Goal Connection: A Study on the Relationship Between Air Pollution in Beaver Dam, Wisconsin, and Lukas Podolski's Domestic Match Goal Count"

[[ABSTRACT]]
This research paper examines the potential relationship between air pollution levels in Beaver Dam, Wisconsin, and the domestic match goal count of the renowned footballer Lukas Podolski. Leveraging data from the Environmental Protection Agency and Wikipedia, our study sought to elucidate whether there exists a tangible connection between these seemingly disparate factors. Through extensive statistical analysis, including correlation coefficients and hypothesis testing, we reveal a correlation coefficient of 0.7087361 and p < 0.01 for the years 2004 to 2022, indicating a moderate to strong positive correlation.

In our findings, we observed a noteworthy pattern, as air pollution levels in Beaver Dam, Wisconsin appeared to coincide with fluctuations in Lukas Podolski's domestic match goal count. This intriguing correlation prompts consideration of potential explanations, such as the impact of environmental factors on athletic performance or the influence of air quality on spectator morale. Moreover, our results offer insight into the interconnectedness of environmental conditions and individual achievements, illustrating the unforeseen reach of air pollution on seemingly unrelated spheres of human activity. As the old proverb goes, "where there's smog, there's a goal," presenting a novel perspective on the interplay between environmental quality and athletic prowess.

Ultimately, this research contributes to the burgeoning field of interdisciplinary analysis, demonstrating the unanticipated avenues through which environmental variables can intersect with prominent figures in competitive sports. While further investigation is warranted to delineate the underlying mechanisms, our findings underscore the potential relevance of environmental conditions in the athletic domain and encourage a multifaceted approach to understanding human performance.

[[INTRDUCTION]]
The pursuit of scientific understanding often leads researchers down unforeseen paths, much like a misplaced pass on the football field. In the realm of environmental and athletic analysis, the confluence of air pollution levels and domestic match goal count may seem as incongruous as a referee at a chess tournament. Nevertheless, this study embarks on the quest to unearth potential connections between the air quality of Beaver Dam, Wisconsin, and the scoring prowess of Lukas Podolski, a soccer luminary whose achievements transcend the boundaries of the pitch.
As we delve into the intricacies of this unlikely correlation, it becomes clear that our exploration is akin to navigating a penalty shootout in a thunderstorm - fraught with uncertainties and unexpected turns. Nonetheless, our commitment to unraveling this enigma remains resolute, much like the perseverance of a team striving for victory amidst a downpour. With a blend of statistical rigor and a dash of serendipity, we aim to shed light on the peculiar relationship between environmental variables and athletic achievements, demonstrating that when it comes to scientific inquiry, there are no "own goals" – only newfound insights waiting to be discovered.
Our investigation draws upon an array of robust methodologies, prompting us to tread the path less traveled, not unlike a nimble athlete zigzagging through opposing defenders. By employing sophisticated statistical analyses, we endeavor to illuminate the obscured bonds between air pollution and goal-scoring proficiency, proving that, much like the intricate tactics of a well-coached team, scientific inquiry demands strategic maneuvers and a keen eye for discerning patterns. With each regression analysis and hypothesis test, we aim not only to elucidate the existing link but also to encourage unorthodox thinking, thereby fostering an atmosphere of vibrant curiosity in the esteemed realm of empirical research.
In the following sections, we shall elucidate our compelling findings, which echo the sentiment that in the vast tapestry of scientific exploration, every thread – whether it be the minute particles of air pollutants or the staggering achievements of a celebrated athlete – contributes to the rich fabric of knowledge. As we unveil the unexpected interaction between atmospheric conditions and athletic prowess, our study paves the way for a deeper understanding of the intricate interplay between seemingly disparate facets of human existence. So, with the spirit of inquiry as our compass and the pursuit of knowledge as our goal, we beckon the reader to embark on this scholarly odyssey, navigating the convoluted terrain of statistical analysis and the uncharted waters of unconventional relationships, all the while keeping an eye out for the occasional "air"-borne pun.

[[RESULTS]]
The analysis of the data revealed a statistically significant positive correlation between air pollution levels in Beaver Dam, Wisconsin, and Lukas Podolski's domestic match goal count for the years 2004 to 2022. The correlation coefficient of 0.7087361 suggests a moderate to strong positive relationship between these seemingly unrelated variables. This unexpected link may prompt one to exclaim, "I guess the air in Beaver Dam really does carry some weight in the soccer world!"
The coefficient of determination (r-squared) was found to be 0.5023069, indicating that approximately 50.23% of the variability in Lukas Podolski's domestic match goal count can be explained by the fluctuations in air pollution levels in Beaver Dam. It seems that air pollution is not just "blowing hot air" when it comes to influencing the goal-scoring prowess of a renowned footballer.
The p-value of less than 0.01 further substantiates the strength of the correlation, providing compelling evidence to reject the null hypothesis and infer the existence of a significant relationship between air pollution in Beaver Dam and Lukas Podolski's domestic match goal count. One might say that this correlation is as clear as the air in a spring breeze – or perhaps, as murky as a foggy day in the Midwest.
The scatterplot (Fig. 1) visually depicts the strong positive correlation between air pollution levels and Lukas Podolski's domestic match goal count, affirming the robustness of the statistical findings. This association, though unexpected, raises intriguing questions about the potential influence of environmental factors on athletic performance. It seems that air pollution may not only affect visibility on the field but also the goal-scoring abilities of players – truly a case of "air quality" taking on a whole new meaning in the realm of sports.
In sum, our findings illuminate a previously unexplored connection between air pollution in Beaver Dam, Wisconsin, and the domestic match goal count of Lukas Podolski. This discovery not only expands our understanding of the far-reaching impacts of environmental variables but also injects a breath of fresh air into the study of sports phenomena. As one reflects on this correlation, one cannot help but ponder the words of wisened statisticians – "correlation does not imply causation, but it sure does make for an interesting conversation."

-------

Your response should start like this:

[[CONCLUSION]]

ChatGPT:

[[CONCLUSION]]

In conclusion, the unexpected revelation of a tangible connection between air pollution levels in Beaver Dam, Wisconsin, and Lukas Podolski's domestic match goal count unveils a previously uncharted terrain in the realm of environmental and athletic analysis. This correlation, with a coefficient of 0.7087361, suggests that when it comes to goal-scoring prowess, the air in Beaver Dam is not merely a "bystander" – it plays an active role in shaping the athletic achievements of individuals.

Our findings prompt us to reconsider the saying, "the higher the pollution, the closer to Podolski’s goal," shedding light on the intricate interplay between environmental quality and athletic performance. It is apparent that the impact of air pollution extends beyond respiratory concerns to influence the scoring dynamics of celebrated footballers – truly a case of "scoring goals and clearing pollutants."

The statistically significant correlation, coupled with the coefficient of determination of 0.5023069, underscores the substantial influence of air pollution levels on Lukas Podolski's domestic match goal count. It seems that the effects of air pollution are not confined to the confines of atmospheric debates but extend their reach to the competitive arenas of sports – a truly "air-lluminating" discovery.

With a p-value of less than 0.01, our research provides compelling evidence to affirm the presence of a genuine association between air pollution in Beaver Dam and Podolski's goal-scoring feats. This revelation signifies that when it comes to influencing athletic performance, the atmosphere's "defense" is not always impenetrable.

In light of these substantial findings, we assert that no further research is required in this area, as the connection between air pollution in Beaver Dam, Wisconsin, and Lukas Podolski's domestic match goal count has been robustly established. It appears that this unlikely correlation is not merely a statistical anomaly but reflects a genuine interplay between environmental conditions and athletic achievements. As researchers, we are reminded that the scientific landscape is rife with unexpected connections waiting to be unraveled – and notably, that sometimes, even the air pollution in a small Wisconsin town can create ripples in the world of sports.

Model: gpt-3.5-turbo-1106
System prompt: You provide fictional names of academic journals. You say nothing else, and you do not chat with the user.
User prompt: Please provide the name of a funny but plausible sounding research, scientific, or academic journal that would publish a paper entited The Air-ly Goal Connection: A Study on the Relationship Between Air Pollution in Beaver Dam, Wisconsin, and Lukas Podolski's Domestic Match Goal Count. Respond only with the name of a fictional academic journal.

ChatGPT:

The Journal of Environmental and Athletic Correlations

Model: gpt-3.5-turbo-1106
System prompt: You provide fictional names of nonprofit research organizations and associations. You say nothing else, and you do not chat with the user.
User prompt: Please provide the name of a funny but plausible sounding nonprofit, academic, or scientific association or organization that would sponsor research that resulted in a paper entited The Air-ly Goal Connection: A Study on the Relationship Between Air Pollution in Beaver Dam, Wisconsin, and Lukas Podolski's Domestic Match Goal Count. Respond only with the name of a fictional organization.

ChatGPT:

The Center for Environmental Impact on Sports Performance (CEISP)

Model: gpt-3.5-turbo-1106
System prompt: You provide potential search keywords separated by commas. You say nothing else, and you do not chat with the user.
User prompt: Please provide potential search keywords for a paper titled The Air-ly Goal Connection: A Study on the Relationship Between Air Pollution in Beaver Dam, Wisconsin, and Lukas Podolski's Domestic Match Goal Count with an abstract of This research paper examines the potential relationship between air pollution levels in Beaver Dam, Wisconsin, and the domestic match goal count of the renowned footballer Lukas Podolski. Leveraging data from the Environmental Protection Agency and Wikipedia, our study sought to elucidate whether there exists a tangible connection between these seemingly disparate factors. Through extensive statistical analysis, including correlation coefficients and hypothesis testing, we reveal a correlation coefficient of 0.7087361 and p < 0.01 for the years 2004 to 2022, indicating a moderate to strong positive correlation.
In our findings, we observed a noteworthy pattern, as air pollution levels in Beaver Dam, Wisconsin appeared to coincide with fluctuations in Lukas Podolski's domestic match goal count. This intriguing correlation prompts consideration of potential explanations, such as the impact of environmental factors on athletic performance or the influence of air quality on spectator morale. Moreover, our results offer insight into the interconnectedness of environmental conditions and individual achievements, illustrating the unforeseen reach of air pollution on seemingly unrelated spheres of human activity. As the old proverb goes, "where there's smog, there's a goal," presenting a novel perspective on the interplay between environmental quality and athletic prowess.
Ultimately, this research contributes to the burgeoning field of interdisciplinary analysis, demonstrating the unanticipated avenues through which environmental variables can intersect with prominent figures in competitive sports. While further investigation is warranted to delineate the underlying mechanisms, our findings underscore the potential relevance of environmental conditions in the athletic domain and encourage a multifaceted approach to understanding human performance.

ChatGPT:

Air pollution, Beaver Dam Wisconsin, Lukas Podolski, domestic match goal count, environmental impact on athletic performance, correlation coefficient, environmental conditions in sports, air quality impact on sports, interdisciplinary analysis, environmental variables in sports, athletic performance and environmental factors

*There is a bunch of Python happening behind the scenes to turn this prompt sequence into a PDF.

Random correlation

Discover a new correlation

View all correlations

View all research papers

Report an error

Data details

Air pollution in Beaver Dam, Wisconsin
Detailed data title: Percentage of days 'unhealthy' or worse air quality in Beaver Dam, WI
Source: Environmental Protection Agency
See what else correlates with Air pollution in Beaver Dam, Wisconsin

Lukas Podolski's domestic match goal count
Source: Wikipedia
See what else correlates with Lukas Podolski's domestic match goal count

Correlation r = 0.7087361 (Pearson correlation coefficient)
Correlation is a measure of how much the variables move together. If it is 0.99, when one goes up the other goes up. If it is 0.02, the connection is very weak or non-existent. If it is -0.99, then when one goes up the other goes down. If it is 1.00, you probably messed up your correlation function.

r² = 0.5023069 (Coefficient of determination)
This means 50.2% of the change in the one variable (i.e., Lukas Podolski's domestic match goal count) is predictable based on the change in the other (i.e., Air pollution in Beaver Dam, Wisconsin) over the 19 years from 2004 through 2022.

p < 0.01, which is statistically significant(Null hypothesis significance test)
The p-value is 0.00068.^Show 0.0006816479900684527000000000
The p-value is a measure of how probable it is that we would randomly find a result this extreme.^Note More specifically the p-value is a measure of how probable it is that we would randomly find a result this extreme if we had only tested one pair of variables one time.

But I am a p-villain. I absolutely did not test only one pair of variables one time. I correlated hundreds of millions of pairs of variables. I threw boatloads of data into an industrial-sized blender to find this correlation.

Who is going to stop me? p-value reporting doesn't require me to report how many calculations I had to go through in order to find a low p-value!
On average, you will find a correaltion as strong as 0.71 in 0.068% of random cases. Said differently, if you correlated 1,467 random variables^Note Which I absolutely did.
with the same 18 degrees of freedom, ^Note Degrees of freedom is a measure of how many free components we are testing. In this case it is 18 because we have two variables measured over a period of 19 years. It's just the number of years minus ( the number of variables minus one ), which in this case simplifies to the number of years minus one.
you would randomly expect to find a correlation as strong as this one.

[ 0.38, 0.88 ] 95% correlation confidence interval (using the Fisher z-transformation)
^{Read more about the confidence interval} The confidence interval is an estimate the range of the value of the correlation coefficient, using the correlation itself as an input. The values are meant to be the low and high end of the correlation coefficient with 95% confidence.

This one is a bit more complciated than the other calculations, but I include it because many people have been pushing for confidence intervals instead of p-value calculations (for example: NEJM. However, if you are dredging data, you can reliably find yourself in the 5%. That's my goal!

All values for the years included above: ^Note If I were being very sneaky, I could trim years from the beginning or end of the datasets to increase the correlation on some pairs of variables. I don't do that because there are already plenty of correlations in my database without monkeying with the years.

Still, sometimes one of the variables has more years of data available than the other. This page only shows the overlapping years. To see all the years, click on "See what else correlates with..." link above.

	2004	2005	2006	2007	2008	2009	2010	2011	2012	2013	2014	2015	2016	2017	2018	2019	2020	2021	2022
Air pollution in Beaver Dam, Wisconsin (Bad air quality days)	0	0.00547945	0	0	0	0	0	0	0.00273224	0.00273973	0	0	0	0	0	0	0	0	0
Lukas Podolski's domestic match goal count (Goals scored)	10	29	12	7	10	9	3	14	18	16	12	4	17	22	7	5	2	5	9

Why this works

Data dredging: I have 25,153 variables in my database. I compare all these variables against each other to find ones that randomly match up. That's 632,673,409 correlation calculations! This is called “data dredging.” Instead of starting with a hypothesis and testing it, I instead abused the data to see what correlations shake out. It’s a dangerous way to go about analysis, because any sufficiently large dataset will yield strong correlations completely at random.
Lack of causal connection: There is probably^Note Because these pages are automatically generated, it's possible that the two variables you are viewing are in fact causually related. I take steps to prevent the obvious ones from showing on the site (I don't let data about the weather in one city correlate with the weather in a neighboring city, for example), but sometimes they still pop up. If they are related, cool! You found a loophole.
no direct connection between these variables, despite what the AI says above. This is exacerbated by the fact that I used "Years" as the base variable. Lots of things happen in a year that are not related to each other! Most studies would use something like "one person" in stead of "one year" to be the "thing" studied.
Observations not independent: For many variables, sequential years are not independent of each other. If a population of people is continuously doing something every day, there is no reason to think they would suddenly change how they are doing that thing on January 1. A simple^Note Personally I don't find any p-value calculation to be 'simple,' but you know what I mean.
p-value calculation does not take this into account, so mathematically it appears less probable than it really is.

Try it yourself

You can calculate the values on this page on your own! Try running the Python code to see the calculation results. ^{Show the steps to do this.} Step 1: Download and install Python on your computer.

Step 2: Open a plaintext editor like Notepad and paste the code below into it.

Step 3: Save the file as "calculate_correlation.py" in a place you will remember, like your desktop. Copy the file location to your clipboard. On Windows, you can right-click the file and click "Properties," and then copy what comes after "Location:" As an example, on my computer the location is "C:\Users\tyler\Desktop"

Step 4: Open a command line window. For example, by pressing start and typing "cmd" and them pressing enter.

Step 5: Install the required modules by typing "pip install numpy", then pressing enter, then typing "pip install scipy", then pressing enter.

Step 6: Navigate to the location where you saved the Python file by using the "cd" command. For example, I would type "cd C:\Users\tyler\Desktop" and push enter.

Step 7: Run the Python script by typing "python calculate_correlation.py"

If you run into any issues, I suggest asking ChatGPT to walk you through installing Python and running the code below on your system. Try this question:

"Walk me through installing Python on my computer to run a script that uses scipy and numpy. Go step-by-step and ask me to confirm before moving on. Start by asking me questions about my operating system so that you know how to proceed. Assume I want the simplest installation with the latest version of Python and that I do not currently have any of the necessary elements installed. Remember to only give me one step per response and confirm I have done it before proceeding."

# These modules make it easier to perform the calculation
import numpy as np
from scipy import stats

# We'll define a function that we can call to return the correlation calculations
def calculate_correlation(array1, array2):

    # Calculate Pearson correlation coefficient and p-value
    correlation, p_value = stats.pearsonr(array1, array2)

    # Calculate R-squared as the square of the correlation coefficient
    r_squared = correlation**2

    return correlation, r_squared, p_value

# These are the arrays for the variables shown on this page, but you can modify them to be any two sets of numbers
array_1 = np.array([0,0.00547945,0,0,0,0,0,0,0.00273224,0.00273973,0,0,0,0,0,0,0,0,0,])
array_2 = np.array([10,29,12,7,10,9,3,14,18,16,12,4,17,22,7,5,2,5,9,])
array_1_name = "Air pollution in Beaver Dam, Wisconsin"
array_2_name = "Lukas Podolski's domestic match goal count"

# Perform the calculation
print(f"Calculating the correlation between {array_1_name} and {array_2_name}...")
correlation, r_squared, p_value = calculate_correlation(array_1, array_2)

# Print the results
print("Correlation Coefficient:", correlation)
print("R-squared:", r_squared)
print("P-value:", p_value)

Reuseable content

You may re-use the images on this page for any purpose, even commercial purposes, without asking for permission. The only requirement is that you attribute Tyler Vigen. ^Note Attribution can take many different forms. If you leave the "tylervigen.com" link in the image, that satisfies it just fine. If you remove it and move it to a footnote, that's fine too. You can also just write "Charts courtesy of Tyler Vigen" at the bottom of an article.

You do not need to attribute "the spurious correlations website," and you don't even need to link here if you don't want to. I don't gain anything from pageviews. There are no ads on this site, there is nothing for sale, and I am not for hire.

For the record, I am just one person. Tyler Vigen, he/him/his. I do have degrees, but they should not go after my name unless you want to annoy my wife. If that is your goal, then go ahead and cite me as "Tyler Vigen, A.A. A.A.S. B.A. J.D." Otherwise it is just "Tyler Vigen."

When spoken, my last name is pronounced "vegan," like I don't eat meat.

Full license details.
For more on re-use permissions, or to get a signed release form, see tylervigen.com/permission.

Download images for these variables:

High resolution line chart ^Note The image linked here is a Scalable Vector Graphic (SVG). It is the highest resolution that is possible to achieve. It scales up beyond the size of the observable universe without pixelating. You do not need to email me asking if I have a higher resolution image. I do not. The physical limitations of our universe prevent me from providing you with an image that is any higher resolution than this one.

If you insert it into a PowerPoint presentation (a tool well-known for managing things that are the scale of the universe), you can right-click > "Ungroup" or "Create Shape" and then edit the lines and text directly. You can also change the colors this way.

Alternatively you can use a tool like Inkscape.
High resolution line chart, optimized for mobile
Alternative high resolution line chart
Scatterplot
Portable line chart (png)
Portable line chart (png), optimized for mobile
Line chart for only Air pollution in Beaver Dam, Wisconsin
Line chart for only Lukas Podolski's domestic match goal count
AI-generated correlation image
The spurious research paper: The Air-ly Goal Connection: A Study on the Relationship Between Air Pollution in Beaver Dam, Wisconsin, and Lukas Podolski's Domestic Match Goal Count

View another random correlation

How fun was this correlation?

Your correlation rating is out of this world!

Correlation ID: 4051 · Black Variable ID: 21639 · Red Variable ID: 334


Problem variable:
Issue:
Additional details: Optional
Confirm you are a human: