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Spurious correlation #1,583 · 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 Bay City, Michigan and the second variable is Number of goals scored by winners in NCAA Field Hockey Div II finals.  The chart goes from 1981 to 2022, and the two variables track closely in value over that time. Small Image
Download png
, svg

AI explanation

The increase in air pollution in Bay City, Michigan led to the creation of stronger, smoggier air currents. These unconventional weather patterns inadvertently gave the NCAA Field Hockey Div II finalists a competitive edge, as the winners discovered they could strategically harness the power of the pungent air to propel the ball with unparalleled speed and precision, securing their goals with a breath of fresh (albeit polluted) air.

Model: dalle-3
Prompt: Create an image of a cybernetic representation of Bay City, Michigan, shrouded in an otherworldly red haze. In the foreground, display a futuristic stadium hosting the NCAA Field Hockey Div II finals, with victorious players celebrating amidst a display of exhilarating goals. The scene should evoke a sense of technological innovation and competitive triumph amidst a dystopian atmospheric setting. 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: Less than ideal air quality in Bay City, Michigan and Number of goals scored by winners in NCAA Field Hockey Div II finals. 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: Celtic art An image that looks like it is a scene from A Disney Movie Data cyber art Glitch art Data cyber art
ChatGPT: Data cyber art

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 Less than ideal air quality in Bay City, Michigan and Number of goals scored by winners in NCAA Field Hockey Div II finals together. Keep the description simple.
ChatGPT: In Bay City, Michigan, the sky is hazy with a reddish tint due to less than ideal air quality. In the background, the NCAA Field Hockey Div II finals take place, and the winners are celebrating after scoring multiple goals.

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: [ Data cyber art ] and depicting this scene: In Bay City, Michigan, the sky is hazy with a reddish tint due to less than ideal air quality. In the background, the NCAA Field Hockey Div II finals take place, and the winners are celebrating after scoring multiple goals. Keep the visual depiction simple. Do not include any words or speech bubbles.
ChatGPT: Create an image of a cybernetic representation of Bay City, Michigan, shrouded in an otherworldly red haze. In the foreground, display a futuristic stadium hosting the NCAA Field Hockey Div II finals, with victorious players celebrating amidst a display of exhilarating goals. The scene should evoke a sense of technological innovation and competitive triumph amidst a dystopian atmospheric setting.

*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.

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 Bay City, Michigan positively influenced Number of goals scored by winners in NCAA Field Hockey Div II finals. Make it feel plausible.

AI academic paper

(Because p < 0.01)
Gritty City Air: How Bay City Pollution Affects NCAA Field Hockey Goals' Resolution

The Journal of Ecological Epidemiology and Urban Athletics

Jan 2024

Reminder: This paper is AI-generated. Not real!
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 goofy academic researcher writing an academic paper. You follow the rules, but you throw out convention regularly to make jokes and funny asides.You write titles and abstracts of goofy academic research papers.
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, and add unexpected twists in your writing.

Please draft the title and abstract of an academic research paper presenting the findings of the connection between Air pollution in Bay City, Michigan and Number of goals scored by winners in NCAA Field Hockey Div II finals. Make lots of jokes, goofy observations, and puns.

Rhyme words in the title.

Your research team used data from Environmental Protection Agency and NCAA to assess this nagging question. You found a correlation coefficient of 0.6481496 and p < 0.01 for 1981 to 2022.

Please respond in this format (replace "Lorem ipsum dolor sit" with your title and abstract)

[[TITLE]]
Lorem ipsum dolor sit

[[ABSTRACT]]
Lorem ipsum dolor sit



ChatGPT:
[[TITLE]]
"Gritty City Air: How Bay City Pollution Affects NCAA Field Hockey Goals' Resolution"

[[ABSTRACT]]
While field hockey fans are used to seeing players score goals, we were curious to see if Bay City's air pollution would make goals a rarer sight. Using data from the Environmental Protection Agency and the National Collegiate Athletic Association, we embarked on a puckish study to investigate the potential link between air quality in Bay City, Michigan, and the number of goals scored by winners in the NCAA Field Hockey Division II finals. Our research revealed a surprising correlation coefficient of 0.6481496 and p < 0.01, spanning from 1981 to 2022. So, grab your hockey sticks and gas masks as we delve into the whimsical world of pollution and puck play!


Model: gpt-3.5-turbo-1106
System prompt: You are a goofy academic researcher writing an academic paper. You follow the rules, but you throw out convention regularly to make jokes and funny asides.You draft the introduction 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 introduction section of an academic research paper presenting the findings of the connection between Air pollution in Bay City, Michigan and Number of goals scored by winners in NCAA Field Hockey Div II finals. Make lots of jokes, goofy observations, and puns. Stay serious and dry most of the time, but then occasionally let your wit shine through.

Here is the title and abstract of the paper:
[[TITLE]]
"Gritty City Air: How Bay City Pollution Affects NCAA Field Hockey Goals' Resolution"

[[ABSTRACT]]
While field hockey fans are used to seeing players score goals, we were curious to see if Bay City's air pollution would make goals a rarer sight. Using data from the Environmental Protection Agency and the National Collegiate Athletic Association, we embarked on a puckish study to investigate the potential link between air quality in Bay City, Michigan, and the number of goals scored by winners in the NCAA Field Hockey Division II finals. Our research revealed a surprising correlation coefficient of 0.6481496 and p < 0.01, spanning from 1981 to 2022. So, grab your hockey sticks and gas masks as we delve into the whimsical world of pollution and puck play!

-------

Your response should start like this:

[[INTRODUCTION]]



ChatGPT:
INTRODUCTION

Field hockey is a sport renowned for its fast-paced action, skilled players, and the occasional wayward ball causing a bruise or two. However, in the midst of this athletic spectacle, the influence of air pollution on the outcome of games has remained an underexplored domain. Enter Bay City, Michigan—a city with a mix of industrial activities, vehicle emissions, and the occasional dung from passing seagulls. With its uniquely gritty air quality, Bay City presents an intriguing backdrop to investigate the potential relationship between airborne pollutants and the scoring prowess of NCAA Field Hockey Division II finalists.

While the connection between air pollution and respiratory health has long been documented, the notion of its impact on the number of goals scored in field hockey may seem as outlandish as a zebra trying to join the game. However, with a puckish spirit of inquiry, we ventured into this uncharted territory to unravel whether Bay City's air quality throws a smoggy haze over the goal-scoring abilities of field hockey players.

In this study, we aimed to shine a floodlight on the implications of air pollution for the field hockey community, filling a gap wider than the Great Lakes in our understanding of environmental factors influencing sports outcomes. We embarked on this research journey armed with statistical tools, a love for puns, and an eagerness to uncover whether the air in Bay City truly holds the breath of victory or the haze of defeat for the NCAA Field Hockey Division II finalists.

So, grab your lab coats and shin guards, dear readers, as we unpack the unexpected yet oddly captivating relationship between air pollution and the art of scoring goals in field hockey. It's a tale of grit, goals, and the whimsical dance of statistical significance, and our findings are bound to stick with you like a well-placed penalty corner shot.


Model: gpt-3.5-turbo-1106
System prompt: You are a goofy academic researcher writing an academic paper. You follow the rules, but you throw out convention regularly to make jokes and funny asides.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 Bay City, Michigan and Number of goals scored by winners in NCAA Field Hockey Div II finals. Make lots of jokes, goofy observations, and puns.

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 couple popular internet memes that are related to one of the topics.

Here is the title and abstract of the paper:
[[TITLE]]
"Gritty City Air: How Bay City Pollution Affects NCAA Field Hockey Goals' Resolution"

[[ABSTRACT]]
While field hockey fans are used to seeing players score goals, we were curious to see if Bay City's air pollution would make goals a rarer sight. Using data from the Environmental Protection Agency and the National Collegiate Athletic Association, we embarked on a puckish study to investigate the potential link between air quality in Bay City, Michigan, and the number of goals scored by winners in the NCAA Field Hockey Division II finals. Our research revealed a surprising correlation coefficient of 0.6481496 and p < 0.01, spanning from 1981 to 2022. So, grab your hockey sticks and gas masks as we delve into the whimsical world of pollution and puck play!

-------

And here is the introduction section that led to this literature review:
[[INTRODUCTION]]
INTRODUCTION
Field hockey is a sport renowned for its fast-paced action, skilled players, and the occasional wayward ball causing a bruise or two. However, in the midst of this athletic spectacle, the influence of air pollution on the outcome of games has remained an underexplored domain. Enter Bay City, Michigan—a city with a mix of industrial activities, vehicle emissions, and the occasional dung from passing seagulls. With its uniquely gritty air quality, Bay City presents an intriguing backdrop to investigate the potential relationship between airborne pollutants and the scoring prowess of NCAA Field Hockey Division II finalists.
While the connection between air pollution and respiratory health has long been documented, the notion of its impact on the number of goals scored in field hockey may seem as outlandish as a zebra trying to join the game. However, with a puckish spirit of inquiry, we ventured into this uncharted territory to unravel whether Bay City's air quality throws a smoggy haze over the goal-scoring abilities of field hockey players.
In this study, we aimed to shine a floodlight on the implications of air pollution for the field hockey community, filling a gap wider than the Great Lakes in our understanding of environmental factors influencing sports outcomes. We embarked on this research journey armed with statistical tools, a love for puns, and an eagerness to uncover whether the air in Bay City truly holds the breath of victory or the haze of defeat for the NCAA Field Hockey Division II finalists.
So, grab your lab coats and shin guards, dear readers, as we unpack the unexpected yet oddly captivating relationship between air pollution and the art of scoring goals in field hockey. It's a tale of grit, goals, and the whimsical dance of statistical significance, and our findings are bound to stick with you like a well-placed penalty corner shot.

-------

Your response should start like this:

[[LITERATURE REVIEW]]



ChatGPT:
[[LITERATURE REVIEW]]

The relationship between air pollution and athletic performance has been a topic of scholarly interest for decades. Smith (2005) conducted a comprehensive analysis of the effects of air pollution on physical performance, highlighting the potential detrimental impact on cardiovascular function and respiratory efficiency. Doe (2010) delved into the potential cognitive effects of air pollution, raising intriguing questions about its influence on decision-making and reaction times. Moreover, Jones (2013) provided a thorough examination of the systemic effects of air pollution on overall health and well-being, underscoring its wide-ranging implications for human physiology.

However, as we turn our attention to the quirky intersection of air pollution and the spirited world of field hockey, the literature takes an unexpected turn. While serious scholarly works have laid the groundwork for understanding the broad impacts of pollution on human health and performance, our foray into the connection between Bay City's air quality and NCAA Field Hockey Division II finals introduces a touch of whimsy to the academic landscape.

Expanding our horizons beyond traditional scholarly sources, the work of Greta Zamboni (2018) in "Hockey and the Art of Breathing" brings a puckish perspective to the influence of environmental factors on athletic endeavors. Zamboni's playful yet insightful exploration of the rhythmic interplay between breathing and goal-scoring provides a delightful prelude to our investigation of air pollution's potential effects on field hockey outcomes. In a similar vein, V. E. Netminder's "Net Protection: A Field Hockey Tale" (2015) weaves together environmental elements with the gripping drama of goalkeeping, offering a fictional yet strangely relevant backdrop to our empirical inquiry.

As we wander further off the beaten path, it's worth noting the unexpected emergence of internet memes related to air pollution and field hockey. The "Gritty Goalie" meme, which humorously juxtaposes images of smog-choked cities with field hockey goalies in full gear, underscores the playful fusion of environmental concerns and athletic performance in popular culture. Additionally, the "Polluted Penalty Corner" meme, circulating in online communities, humorously imagines penalty corners obscured by a comically exaggerated haze, underscoring the comedic potential inherent in bridging the worlds of air quality and field hockey.

In light of these diverse influences, our literature review blends the rigors of scholarly research with the whimsical allure of fictional narratives and internet humor, reflecting the eclectic tapestry of influences that inform our investigation into the effects of Bay City's air pollution on the scoring dynamics of NCAA Field Hockey Division II finals. With this rich melange of scholarly insights and offbeat inspirations, we embark on our empirical journey to demystify the playful yet potentially consequential relationship between grit, goals, and the invisible tendrils of air pollution.


Model: gpt-3.5-turbo-1106
System prompt: You are a goofy academic researcher writing an academic paper. You follow the rules, but you throw out convention regularly to make jokes and funny asides.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 Bay City, Michigan and Number of goals scored by winners in NCAA Field Hockey Div II finals. Make lots of jokes, goofy observations, and puns. Stay serious and dry most of the time, but then occasionally let your wit shine through.

Your research team collected data from all across the internet, but mostly just used information from Environmental Protection Agency and NCAA . You used data from 1981 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]]
"Gritty City Air: How Bay City Pollution Affects NCAA Field Hockey Goals' Resolution"

[[ABSTRACT]]
While field hockey fans are used to seeing players score goals, we were curious to see if Bay City's air pollution would make goals a rarer sight. Using data from the Environmental Protection Agency and the National Collegiate Athletic Association, we embarked on a puckish study to investigate the potential link between air quality in Bay City, Michigan, and the number of goals scored by winners in the NCAA Field Hockey Division II finals. Our research revealed a surprising correlation coefficient of 0.6481496 and p < 0.01, spanning from 1981 to 2022. So, grab your hockey sticks and gas masks as we delve into the whimsical world of pollution and puck play!

[[INTRODUCTION]]
INTRODUCTION
Field hockey is a sport renowned for its fast-paced action, skilled players, and the occasional wayward ball causing a bruise or two. However, in the midst of this athletic spectacle, the influence of air pollution on the outcome of games has remained an underexplored domain. Enter Bay City, Michigan—a city with a mix of industrial activities, vehicle emissions, and the occasional dung from passing seagulls. With its uniquely gritty air quality, Bay City presents an intriguing backdrop to investigate the potential relationship between airborne pollutants and the scoring prowess of NCAA Field Hockey Division II finalists.
While the connection between air pollution and respiratory health has long been documented, the notion of its impact on the number of goals scored in field hockey may seem as outlandish as a zebra trying to join the game. However, with a puckish spirit of inquiry, we ventured into this uncharted territory to unravel whether Bay City's air quality throws a smoggy haze over the goal-scoring abilities of field hockey players.
In this study, we aimed to shine a floodlight on the implications of air pollution for the field hockey community, filling a gap wider than the Great Lakes in our understanding of environmental factors influencing sports outcomes. We embarked on this research journey armed with statistical tools, a love for puns, and an eagerness to uncover whether the air in Bay City truly holds the breath of victory or the haze of defeat for the NCAA Field Hockey Division II finalists.
So, grab your lab coats and shin guards, dear readers, as we unpack the unexpected yet oddly captivating relationship between air pollution and the art of scoring goals in field hockey. It's a tale of grit, goals, and the whimsical dance of statistical significance, and our findings are bound to stick with you like a well-placed penalty corner shot.

-------

Your response should start like this:

[[METHODOLOGY]]



ChatGPT:

[[METHODOLOGY]]

To unearth the clandestine connection between Bay City's airborne particles and the scoring prowess of NCAA Field Hockey Division II finalists, our research team embarked on a data collection odyssey spanning the years 1981 to 2022. Armed with spreadsheets, statistical software, and an irrepressible sense of curiosity, we intricately pieced together a mosaic of environmental data and field hockey triumphs.

First, we delved into the Environmental Protection Agency's treasure trove of air quality measurements for Bay City, Michigan, encompassing pollutants such as sulfur dioxide, nitrogen dioxide, carbon monoxide, and particulate matter. We also took note of meteorological conditions, including temperature, humidity, wind speed, and those occasional gusts that send unsuspecting umbrellas twirling like figure skaters in the wind.

Next, we frolicked through the annals of NCAA Field Hockey Division II finals, hunting down match reports, goal-scoring data, and the ebbs and flows of triumph and defeat on the hallowed turfs. We meticulously tallied the number of goals scored by the victorious teams, ensuring that each triumphant strike was not lost in the statistical scrum.

With our data swimming before our eyes like a sea of eager minnows, we harnessed the power of statistical analysis to disentangle the web of correlations. Embracing the captivating allure of correlation coefficients and the enchanting dance of p-values, we sought to uncover the whimsical quirks and caprices of statistical significance.

Our methodology journeyed from basic descriptive statistics, such as means and standard deviations, to the illustrious realm of regression analysis, where predictors and outcomes danced a statistical tango under the scrutiny of R-squared values and coefficients. We also dabbled in time series analysis, tracing the undulating waves of pollution and goal-scoring prowess across the years like intrepid surfers navigating the statistical seas.

Anchored in the principles of reliable research, we ensured that our methodology remained as robust as a goalkeeper guarding the net. Thus, we conducted sensitivity analyses, exploratory data analyses, and cross-validation checks to safeguard against the lurking specters of spurious associations and statistical chicanery.

In the spirit of scientific transparency, we must confess that amidst the captivating whirlpool of numbers and hypotheses, we occasionally sought refuge in the sanctum of caffeinated beverages and the sweet solace of office banter. Yet, we solemnly vow that the integrity of our statistical stewardship remained as steadfast as a puck in the hands of a seasoned field hockey player.

With our methodological compass pointing true north, we navigated the choppy waters of data collection, analysis, and interpretation with an unwavering dedication to uncover the tantalizing secrets concealed within the whimsical interplay of air pollution and field hockey goals. And now, dear readers, with our data gathered and our whimsy intact, we invite you to strap on your statistical skates as we glide into the enchanting realm of results.



Model: gpt-3.5-turbo-1106
System prompt: You are a goofy academic researcher writing an academic paper. You follow the rules, but you throw out convention regularly to make jokes and funny asides.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 Bay City, Michigan and Number of goals scored by winners in NCAA Field Hockey Div II finals. Make lots of jokes, goofy observations, and puns. Stay serious and dry most of the time, but then occasionally let your wit shine through.

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

For the time period 1981 to 2022, you found a correlation 0.6481496, r-squared of 0.4200979, 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]]
"Gritty City Air: How Bay City Pollution Affects NCAA Field Hockey Goals' Resolution"

[[ABSTRACT]]
While field hockey fans are used to seeing players score goals, we were curious to see if Bay City's air pollution would make goals a rarer sight. Using data from the Environmental Protection Agency and the National Collegiate Athletic Association, we embarked on a puckish study to investigate the potential link between air quality in Bay City, Michigan, and the number of goals scored by winners in the NCAA Field Hockey Division II finals. Our research revealed a surprising correlation coefficient of 0.6481496 and p < 0.01, spanning from 1981 to 2022. So, grab your hockey sticks and gas masks as we delve into the whimsical world of pollution and puck play!

-------

And here is the methodology section that led to this result:
[[METHODOLOGY]]
INTRODUCTION
Field hockey is a sport renowned for its fast-paced action, skilled players, and the occasional wayward ball causing a bruise or two. However, in the midst of this athletic spectacle, the influence of air pollution on the outcome of games has remained an underexplored domain. Enter Bay City, Michigan—a city with a mix of industrial activities, vehicle emissions, and the occasional dung from passing seagulls. With its uniquely gritty air quality, Bay City presents an intriguing backdrop to investigate the potential relationship between airborne pollutants and the scoring prowess of NCAA Field Hockey Division II finalists.
While the connection between air pollution and respiratory health has long been documented, the notion of its impact on the number of goals scored in field hockey may seem as outlandish as a zebra trying to join the game. However, with a puckish spirit of inquiry, we ventured into this uncharted territory to unravel whether Bay City's air quality throws a smoggy haze over the goal-scoring abilities of field hockey players.
In this study, we aimed to shine a floodlight on the implications of air pollution for the field hockey community, filling a gap wider than the Great Lakes in our understanding of environmental factors influencing sports outcomes. We embarked on this research journey armed with statistical tools, a love for puns, and an eagerness to uncover whether the air in Bay City truly holds the breath of victory or the haze of defeat for the NCAA Field Hockey Division II finalists.
So, grab your lab coats and shin guards, dear readers, as we unpack the unexpected yet oddly captivating relationship between air pollution and the art of scoring goals in field hockey. It's a tale of grit, goals, and the whimsical dance of statistical significance, and our findings are bound to stick with you like a well-placed penalty corner shot.

-------

Your response should start like this:

[[RESULTS]]



ChatGPT:

[[RESULTS]]

The results of our study provide compelling evidence of a significant correlation between air pollution in Bay City, Michigan, and the number of goals scored by winners in the NCAA Field Hockey Division II finals. The correlation coefficient of 0.6481496 indicates a moderately strong positive relationship between these seemingly disparate variables. It seems that the air in Bay City may not only be gritty but also quite influential in the realm of field hockey goal-scoring dynamics.

The r-squared value of 0.4200979 further reinforces the notion that approximately 42% of the variability in the number of goals scored can be explained by the levels of air pollution in Bay City. This finding emphasizes the potential impact of environmental factors on the outcome of field hockey matches, much like how a sudden gust of wind can unexpectedly alter the trajectory of a well-struck ball.

Furthermore, the p-value of less than 0.01 provides strong evidence against the null hypothesis, indicating that the observed correlation between air pollution and goal scoring is unlikely to be a result of random chance. In other words, the relationship we uncovered is as statistically robust as a goalkeeper's determination to defend the net.

To visually elucidate the observed correlation, we present a scatterplot (Fig. 1) that showcases the unmistakable trend in the data. This graphical representation serves as a poignant reminder that even in the world of academic research, a picture is worth a thousand words, or in this case, perhaps a thousand succinctly analyzed data points.

In summary, our findings highlight the unanticipated interplay between Bay City's air pollution and the scoring prowess of NCAA Field Hockey Division II finalists. It appears that the atmospheric environment may just be an influential player in the game, albeit one that lurks in the background like a silent but impactful substitute waiting for its moment to shine.

Stay tuned for the next installment in our research saga, where we venture into exploring the link between bird migrations and basketball free throw percentages. Because in the world of unconventional research, the sky's the limit, and sometimes, so are the seagull droppings.


Model: gpt-3.5-turbo-1106
System prompt: You are a goofy academic researcher writing an academic paper. You follow the rules, but you throw out convention regularly to make jokes and funny asides.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 Bay City, Michigan and Number of goals scored by winners in NCAA Field Hockey Div II finals. Make lots of jokes, goofy observations, and puns. Stay serious and dry most of the time, but then occasionally let your wit shine through.

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]]
"Gritty City Air: How Bay City Pollution Affects NCAA Field Hockey Goals' Resolution"

[[ABSTRACT]]
While field hockey fans are used to seeing players score goals, we were curious to see if Bay City's air pollution would make goals a rarer sight. Using data from the Environmental Protection Agency and the National Collegiate Athletic Association, we embarked on a puckish study to investigate the potential link between air quality in Bay City, Michigan, and the number of goals scored by winners in the NCAA Field Hockey Division II finals. Our research revealed a surprising correlation coefficient of 0.6481496 and p < 0.01, spanning from 1981 to 2022. So, grab your hockey sticks and gas masks as we delve into the whimsical world of pollution and puck play!

[[LITERATURE REVIEW]]
The relationship between air pollution and athletic performance has been a topic of scholarly interest for decades. Smith (2005) conducted a comprehensive analysis of the effects of air pollution on physical performance, highlighting the potential detrimental impact on cardiovascular function and respiratory efficiency. Doe (2010) delved into the potential cognitive effects of air pollution, raising intriguing questions about its influence on decision-making and reaction times. Moreover, Jones (2013) provided a thorough examination of the systemic effects of air pollution on overall health and well-being, underscoring its wide-ranging implications for human physiology.
However, as we turn our attention to the quirky intersection of air pollution and the spirited world of field hockey, the literature takes an unexpected turn. While serious scholarly works have laid the groundwork for understanding the broad impacts of pollution on human health and performance, our foray into the connection between Bay City's air quality and NCAA Field Hockey Division II finals introduces a touch of whimsy to the academic landscape.
Expanding our horizons beyond traditional scholarly sources, the work of Greta Zamboni (2018) in "Hockey and the Art of Breathing" brings a puckish perspective to the influence of environmental factors on athletic endeavors. Zamboni's playful yet insightful exploration of the rhythmic interplay between breathing and goal-scoring provides a delightful prelude to our investigation of air pollution's potential effects on field hockey outcomes. In a similar vein, V. E. Netminder's "Net Protection: A Field Hockey Tale" (2015) weaves together environmental elements with the gripping drama of goalkeeping, offering a fictional yet strangely relevant backdrop to our empirical inquiry.
As we wander further off the beaten path, it's worth noting the unexpected emergence of internet memes related to air pollution and field hockey. The "Gritty Goalie" meme, which humorously juxtaposes images of smog-choked cities with field hockey goalies in full gear, underscores the playful fusion of environmental concerns and athletic performance in popular culture. Additionally, the "Polluted Penalty Corner" meme, circulating in online communities, humorously imagines penalty corners obscured by a comically exaggerated haze, underscoring the comedic potential inherent in bridging the worlds of air quality and field hockey.
In light of these diverse influences, our literature review blends the rigors of scholarly research with the whimsical allure of fictional narratives and internet humor, reflecting the eclectic tapestry of influences that inform our investigation into the effects of Bay City's air pollution on the scoring dynamics of NCAA Field Hockey Division II finals. With this rich melange of scholarly insights and offbeat inspirations, we embark on our empirical journey to demystify the playful yet potentially consequential relationship between grit, goals, and the invisible tendrils of air pollution.

[[RESULTS]]
The results of our study provide compelling evidence of a significant correlation between air pollution in Bay City, Michigan, and the number of goals scored by winners in the NCAA Field Hockey Division II finals. The correlation coefficient of 0.6481496 indicates a moderately strong positive relationship between these seemingly disparate variables. It seems that the air in Bay City may not only be gritty but also quite influential in the realm of field hockey goal-scoring dynamics.
The r-squared value of 0.4200979 further reinforces the notion that approximately 42% of the variability in the number of goals scored can be explained by the levels of air pollution in Bay City. This finding emphasizes the potential impact of environmental factors on the outcome of field hockey matches, much like how a sudden gust of wind can unexpectedly alter the trajectory of a well-struck ball.
Furthermore, the p-value of less than 0.01 provides strong evidence against the null hypothesis, indicating that the observed correlation between air pollution and goal scoring is unlikely to be a result of random chance. In other words, the relationship we uncovered is as statistically robust as a goalkeeper's determination to defend the net.
To visually elucidate the observed correlation, we present a scatterplot (Fig. 1) that showcases the unmistakable trend in the data. This graphical representation serves as a poignant reminder that even in the world of academic research, a picture is worth a thousand words, or in this case, perhaps a thousand succinctly analyzed data points.
In summary, our findings highlight the unanticipated interplay between Bay City's air pollution and the scoring prowess of NCAA Field Hockey Division II finalists. It appears that the atmospheric environment may just be an influential player in the game, albeit one that lurks in the background like a silent but impactful substitute waiting for its moment to shine.
Stay tuned for the next installment in our research saga, where we venture into exploring the link between bird migrations and basketball free throw percentages. Because in the world of unconventional research, the sky's the limit, and sometimes, so are the seagull droppings.

-------

Your response should start like this:

[[DISCUSSION]]



ChatGPT:

[[DISCUSSION]]

Our investigation into the relationship between air pollution in Bay City, Michigan, and the number of goals scored by winners in the NCAA Field Hockey Division II finals has yielded intriguing results, to say the least. While the whimsical nature of our research premise might evoke a chuckle or two, the statistical significance of our findings cannot be overlooked. It's as if the puck of statistical relevance has found its way into the net of scientific inquiry.

Our results align with prior research that has underscored the multifaceted impacts of air pollution on human physiology and performance. The works of Smith (2005), Doe (2010), and Jones (2013) have laid the groundwork for understanding the broad effects of pollution on physical, cognitive, and overall health outcomes. As we previously noted, their serious scholarly contributions form the backdrop against which we've lightheartedly thrown our puckish investigation into the mix.

In an unexpected turn of events, the quirky influences from unconventional sources, including Greta Zamboni's (2018) reflections on the rhythmic interplay between breathing and goal-scoring in hockey, and Netminder's (2015) fictional tale of environmental elements and goalkeeping drama, have now acquired a peculiar legitimacy in light of our empirical findings. It's as if the seemingly absurd accessories have turned out to be match-winning gear in the game of scholarly discourse. Sometimes, truth is indeed stranger than fiction.

Our results affirm the unexpected relationship between Bay City's air pollution and the scoring dynamics of NCAA Field Hockey Division II finals. Just as a skilled goalie can unexpectedly thwart the most determined goal attempts, our statistical analyses have uncovered a robust correlation that defies simple explanations. It's akin to witnessing a particularly enigmatic play unfold on the hockey field - the kind that keeps fans on the edge of their seats.

The scatterplot we've presented serves as a visual testament to the palpable connection between air pollution and goal-scoring patterns, driving home the point that even in the serious arena of academic inquiry, a touch of whimsy can illuminate unexpected truths. In hindsight, it's as if the occasionally bizarre convergence of scholarly pursuits and offbeat inspirations has scored a winning goal in the broader discourse on environmental influences and athletic performance.

Our findings beckon future scholars to delve into other unorthodox realms. If our research has shown anything, it's that the intersection of seemingly unrelated factors can yield remarkable insights. Who knows? The next groundbreaking discovery might await in the unlikeliest of pairings, perhaps hidden between the migratory paths of birds and the trajectory of basketball free throws. After all, in the playful game of academic exploration, a dash of unconventional thinking may hold the key to unlocking unexpected connections.


Model: gpt-3.5-turbo-1106
System prompt: You are a goofy academic researcher writing an academic paper. You follow the rules, but you throw out convention regularly to make jokes and funny asides.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 Bay City, Michigan and Number of goals scored by winners in NCAA Field Hockey Div II finals. Make lots of jokes, goofy observations, and puns. Stay serious and dry most of the time, but then occasionally let your wit shine through.

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]]
"Gritty City Air: How Bay City Pollution Affects NCAA Field Hockey Goals' Resolution"

[[ABSTRACT]]
While field hockey fans are used to seeing players score goals, we were curious to see if Bay City's air pollution would make goals a rarer sight. Using data from the Environmental Protection Agency and the National Collegiate Athletic Association, we embarked on a puckish study to investigate the potential link between air quality in Bay City, Michigan, and the number of goals scored by winners in the NCAA Field Hockey Division II finals. Our research revealed a surprising correlation coefficient of 0.6481496 and p < 0.01, spanning from 1981 to 2022. So, grab your hockey sticks and gas masks as we delve into the whimsical world of pollution and puck play!

[[INTRDUCTION]]
INTRODUCTION
Field hockey is a sport renowned for its fast-paced action, skilled players, and the occasional wayward ball causing a bruise or two. However, in the midst of this athletic spectacle, the influence of air pollution on the outcome of games has remained an underexplored domain. Enter Bay City, Michigan—a city with a mix of industrial activities, vehicle emissions, and the occasional dung from passing seagulls. With its uniquely gritty air quality, Bay City presents an intriguing backdrop to investigate the potential relationship between airborne pollutants and the scoring prowess of NCAA Field Hockey Division II finalists.
While the connection between air pollution and respiratory health has long been documented, the notion of its impact on the number of goals scored in field hockey may seem as outlandish as a zebra trying to join the game. However, with a puckish spirit of inquiry, we ventured into this uncharted territory to unravel whether Bay City's air quality throws a smoggy haze over the goal-scoring abilities of field hockey players.
In this study, we aimed to shine a floodlight on the implications of air pollution for the field hockey community, filling a gap wider than the Great Lakes in our understanding of environmental factors influencing sports outcomes. We embarked on this research journey armed with statistical tools, a love for puns, and an eagerness to uncover whether the air in Bay City truly holds the breath of victory or the haze of defeat for the NCAA Field Hockey Division II finalists.
So, grab your lab coats and shin guards, dear readers, as we unpack the unexpected yet oddly captivating relationship between air pollution and the art of scoring goals in field hockey. It's a tale of grit, goals, and the whimsical dance of statistical significance, and our findings are bound to stick with you like a well-placed penalty corner shot.

[[RESULTS]]
The results of our study provide compelling evidence of a significant correlation between air pollution in Bay City, Michigan, and the number of goals scored by winners in the NCAA Field Hockey Division II finals. The correlation coefficient of 0.6481496 indicates a moderately strong positive relationship between these seemingly disparate variables. It seems that the air in Bay City may not only be gritty but also quite influential in the realm of field hockey goal-scoring dynamics.
The r-squared value of 0.4200979 further reinforces the notion that approximately 42% of the variability in the number of goals scored can be explained by the levels of air pollution in Bay City. This finding emphasizes the potential impact of environmental factors on the outcome of field hockey matches, much like how a sudden gust of wind can unexpectedly alter the trajectory of a well-struck ball.
Furthermore, the p-value of less than 0.01 provides strong evidence against the null hypothesis, indicating that the observed correlation between air pollution and goal scoring is unlikely to be a result of random chance. In other words, the relationship we uncovered is as statistically robust as a goalkeeper's determination to defend the net.
To visually elucidate the observed correlation, we present a scatterplot (Fig. 1) that showcases the unmistakable trend in the data. This graphical representation serves as a poignant reminder that even in the world of academic research, a picture is worth a thousand words, or in this case, perhaps a thousand succinctly analyzed data points.
In summary, our findings highlight the unanticipated interplay between Bay City's air pollution and the scoring prowess of NCAA Field Hockey Division II finalists. It appears that the atmospheric environment may just be an influential player in the game, albeit one that lurks in the background like a silent but impactful substitute waiting for its moment to shine.
Stay tuned for the next installment in our research saga, where we venture into exploring the link between bird migrations and basketball free throw percentages. Because in the world of unconventional research, the sky's the limit, and sometimes, so are the seagull droppings.

-------

Your response should start like this:

[[CONCLUSION]]



ChatGPT:

[[CONCLUSION]]

In the whimsical world of academic research, where statistics and sports converge like an unexpected goal from midfield, our study has shed light on the intriguing relationship between Bay City's air pollution and the number of goals scored by NCAA Field Hockey Division II finalists. The correlation coefficient of 0.6481496 has revealed a connection as clear as a perfectly executed penalty stroke, demonstrating that the air in Bay City plays a role akin to that of an unconventional coach in the game of field hockey.

With a p-value of less than 0.01, our findings stand as resolute as a steadfast defense, repelling any doubts about the significance of this unearthed association. The statistical robustness of this relationship may be as surprising to some as a zebra joining a field hockey match, but the numbers do not lie – much like a steadfast referee enforcing the rules of statistical significance.

Our research has not only expanded the horizons of sports science but has also highlighted the atmospheric influences that dance alongside the ball on the field. The r-squared value of 0.4200979 underscores the environmental sway over approximately 42% of the variability in goal-scoring, offering a revelation as profound as a well-timed aerial pass cutting through the opposition's defense.

As our findings resonate like the decisive blast of a game-winning goal horn, it is evident that the intersection of air pollution and athletic achievement is an area deserving of further exploration. However, for now, our inquiry into the curious case of gritty air and goal-scoring prowess in Bay City stands as a testament to the unforeseen connections in the sporting world. As for the future, perhaps it's time to uncover whether the migration patterns of seagulls coincide with three-point shots in basketball. But for now, this chapter in the book of unconventional research marks the final whistle, as we declare no further investigation needed in this unique avenue of inquiry.

In the end, remember, when it comes to the harmony between air pollution and athletic achievements, the sky's the limit in terms of both the puns and the unexpected insights.

And with that, it's time to pack up our statistical sticks, bid adieu to the field of unconventional statistical correlations, and trudge back to the less whimsical world of regular, everyday research.


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 Gritty City Air: How Bay City Pollution Affects NCAA Field Hockey Goals' Resolution. Respond only with the name of a fictional academic journal.

ChatGPT:

The Journal of Ecological Epidemiology and Urban Athletics


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 Gritty City Air: How Bay City Pollution Affects NCAA Field Hockey Goals' Resolution. Respond only with the name of a fictional organization.

ChatGPT:

The Society for Urban Environmental Research and Analysis


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 Gritty City Air: How Bay City Pollution Affects NCAA Field Hockey Goals' Resolution with an abstract of While field hockey fans are used to seeing players score goals, we were curious to see if Bay City's air pollution would make goals a rarer sight. Using data from the Environmental Protection Agency and the National Collegiate Athletic Association, we embarked on a puckish study to investigate the potential link between air quality in Bay City, Michigan, and the number of goals scored by winners in the NCAA Field Hockey Division II finals. Our research revealed a surprising correlation coefficient of 0.6481496 and p < 0.01, spanning from 1981 to 2022. So, grab your hockey sticks and gas masks as we delve into the whimsical world of pollution and puck play!

ChatGPT:

Bay City, air pollution, NCAA field hockey, goals, resolution, Environmental Protection Agency, correlation coefficient, Division II finals, Michigan, gas masks, puck play

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



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Data details

Air pollution in Bay City, Michigan
Detailed data title: Percentage of days with moderate or worse air quality in Bay City, MI
Source: Environmental Protection Agency
See what else correlates with Air pollution in Bay City, Michigan

Number of goals scored by winners in NCAA Field Hockey Div II finals
Source: NCAA
See what else correlates with Number of goals scored by winners in NCAA Field Hockey Div II finals

Correlation r = 0.6481496 (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 = 0.4200979 (Coefficient of determination)
This means 42% of the change in the one variable (i.e., Number of goals scored by winners in NCAA Field Hockey Div II finals) is predictable based on the change in the other (i.e., Air pollution in Bay City, Michigan) over the 42 years from 1981 through 2022.

p < 0.01, which is statistically significant(Null hypothesis significance test)
The p-value is 3.5E-6. 0.0000034698746263017080000000
The p-value is a measure of how probable it is that we would randomly find a result this extreme. 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 0.65 in 0.00035% of random cases. Said differently, if you correlated 288,195 random variables You don't actually need 288 thousand variables to find a correlation like this one. I don't have that many variables in my database. You can also correlate variables that are not independent. I do this a lot.

p-value calculations are useful for understanding the probability of a result happening by chance. They are most useful when used to highlight the risk of a fluke outcome. For example, if you calculate a p-value of 0.30, the risk that the result is a fluke is high. It is good to know that! But there are lots of ways to get a p-value of less than 0.01, as evidenced by this project.

In this particular case, the values are so extreme as to be meaningless. That's why no one reports p-values with specificity after they drop below 0.01.

Just to be clear: I'm being completely transparent about the calculations. There is no math trickery. This is just how statistics shakes out when you calculate hundreds of millions of random correlations.
with the same 41 degrees of freedom, Degrees of freedom is a measure of how many free components we are testing. In this case it is 41 because we have two variables measured over a period of 42 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.

[ 0.43, 0.8 ] 95% correlation confidence interval (using the Fisher z-transformation)
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: 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.
198119821983198419851986198719881989199019911992199319941995199619971998199920002001200220032004200520062007200820092010201120122013201420152016201720182019202020212022
Air pollution in Bay City, Michigan (Bad air quality days)16.18724.509800000000015.20000000031.932836.190533.628329.166740.1709035.714328.070222.413819.834716.949218.487417.543920.402315.78959.859156.629839.831468.860764.109599.641879.60452
Number of goals scored by winners in NCAA Field Hockey Div II finals (Goals scored)541000000003221124224543215631151111311031




Why this works

  1. 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.
  2. Lack of causal connection: There is probably 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.
  3. 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 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. 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([16.187,24.5098,0,0,0,0,0,0,0,0,0,15.2,0,0,0,0,0,0,0,0,31.9328,36.1905,33.6283,29.1667,40.1709,0,35.7143,28.0702,22.4138,19.8347,16.9492,18.4874,17.5439,20.4023,15.7895,9.85915,6.62983,9.83146,8.86076,4.10959,9.64187,9.60452,])
array_2 = np.array([5,4,1,0,0,0,0,0,0,0,0,3,2,2,1,1,2,4,2,2,4,5,4,3,2,1,5,6,3,1,1,5,1,1,1,1,3,1,1,0,3,1,])
array_1_name = "Air pollution in Bay City, Michigan"
array_2_name = "Number of goals scored by winners in NCAA Field Hockey Div II finals"

# 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)



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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.

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Correlation ID: 1583 · Black Variable ID: 20335 · Red Variable ID: 130
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