Spurious correlation #2,881 · 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 Sacramento and the second variable is Physical album shipment volume in the United States. The chart goes from 1999 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 Sacramento and the second variable is Physical album shipment volume in the United States. The chart goes from 1999 to 2022, and the two variables track closely in value over that time.

Download png, svg

AI explanation

As Sacramento's air got cleaner, it became too pure for the outdated tunes, leading to a nationwide dip in physical album shipments. Maybe the albums just wanted to go green and travel by air with less emissions!

^{Show image generation prompt} Model: dalle-3
Prompt: [ A photo-realistic image ] of a clear and vibrant sky over Sacramento, with a flock of colorful birds gracefully soaring through the air, alongside physical album shipments being gently carried by ambitious birds. The scene conveys the harmony and natural balance of reducing air pollution, allowing birds to soar, while also capturing the whimsical notion of birds being drawn to physical album shipments, leading to a change in their distribution patterns. 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 Sacramento and Physical album shipment volume in the United States. 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: A photo-realistic image Futuristic Scalar art Cubism Macabre
ChatGPT: A photo-realistic image

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 Sacramento and Physical album shipment volume in the United States, in the following situation: As air pollution decreased in Sacramento, birds were able to fly more freely, leading to a higher rate of bird attacks on physical album shipments, ultimately causing a decrease in volume.. Keep the description simple.
ChatGPT: As the air pollution in Sacramento decreased, the skies cleared, allowing birds to soar more easily. In the United States, a higher number of physical album shipments were being attacked by ambitious birds, leading to a decrease in volume.

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: [ A photo-realistic image ] and depicting this scene: As the air pollution in Sacramento decreased, the skies cleared, allowing birds to soar more easily. In the United States, a higher number of physical album shipments were being attacked by ambitious birds, leading to a decrease in volume. Keep the visual depiction simple. Do not include any words or speech bubbles.
ChatGPT: [ A photo-realistic image ] of a clear and vibrant sky over Sacramento, with a flock of colorful birds gracefully soaring through the air, alongside physical album shipments being gently carried by ambitious birds. The scene conveys the harmony and natural balance of reducing air pollution, allowing birds to soar, while also capturing the whimsical notion of birds being drawn to physical album shipments, leading to a change in their distribution patterns.

*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 a decrease in Air pollution in Sacramento caused Physical album shipment volume in the United States to decrease. Add a funny one-liner at the end.

AI academic paper

(Because p < 0.01)

A Breath of Fresh Vinyl: Exploring the Correlation Between Air Pollution in Sacramento and Physical Album Shipment Volume in the United States

Journal of Ecological Harmonies

Jan 2024

Reminder: This paper is AI-generated. Not real!

^{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 Sacramento and Physical album shipment volume in the United States. Make it seem dry like academic research paper, but with lots of subtle hidden offhand remarks, 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 devolve ever further, and mention something completely ridiculous, like you conducted literature review by reading the backs of shampoo bottles.

Here is the title and abstract of the paper:
[[TITLE]]
A Breath of Fresh Vinyl: Exploring the Correlation Between Air Pollution in Sacramento and Physical Album Shipment Volume in the United States

[[ABSTRACT]]
This study exudes a thorough exploration of the potential link between air pollution levels in Sacramento and the volume of physical album shipments across the United States. Drawing upon data meticulously collected from the Environmental Protection Agency and Statista, our research team conducted an in-depth analysis spanning the years 1999 to 2022. The findings unearth a remarkably high correlation coefficient of 0.9039559, with a p-value of less than 0.01, indicating a statistically significant relationship between the two variables. The implications of this correlation are not to be sniffed at, as they convey a possible intertwining of environmental factors with the music industry's physical product distribution. This offbeat connection sheds new light on the dynamic interplay of seemingly disparate domains and inspires further exploration into the whimsical dance of air quality and record shipments.

-------

And here is the introduction section that led to this literature review:
[[INTRODUCTION]]
INTRODUCTION
The intersection of environmental factors and economic trends has long captivated researchers seeking to unpack the interconnected web of influences shaping society. In this vein, our study delves into the unexpected coupling of air pollution levels in Sacramento with the shipment volume of physical albums in the United States. While the connection may seem as elusive as a rare vinyl pressing, our rigorous analysis uncovers a compelling correlation that may just hit the high note of serendipitous discovery.
As anyone with a discerning ear for statistics knows, uncovering a correlation is akin to striking gold in the data mines. Our journey began with a meticulous gathering of data from the Environmental Protection Agency and Statista, capturing the intricate dance of air pollution levels and physical album shipments from the year 1999 to 2022. The numbers, much like a tight harmony, revealed a striking correlation coefficient of 0.9039559, accompanied by a p-value that induced a nod of statistical significance falling below the hallowed threshold of 0.01. This eloquent synchronization speaks volumes, confirming the tantalizing connection between Sacramento's air quality and the beat of album shipments reverberating across the nation.
This correlation, like a catchy tune, resounds with implications that stretch far beyond mere statistical curiosity. The seemingly disparate realms of environmental quality and the music industry intersect in an unexpected medley, prompting us to ponder the strings of causality weaving through this colorful tapestry of variables. The discovery of such an unlikely synergy compels us to harmonize our understanding of the intricate relationship between environmental conditions and consumer behaviors, offering a new riff to the symphony of interdisciplinary inquiry.

-------

Your response should start like this:

[[LITERATURE REVIEW]]

ChatGPT:
[[LITERATURE REVIEW]]

In "The Impact of Air Pollution on Economic Growth," Smith and Jones elucidate the multifaceted ways in which air pollution can influence various economic indicators. The authors find that higher levels of air pollution are associated with decreased economic activity, posing a myriad of challenges for policymakers and businesses alike.

Doe's study, "The Environmental Consequences of Industrial Development," delves into the environmental repercussions of industrial activity, shedding light on the intricate linkages between economic advancement and ecological degradation. The findings underscore the need for sustainable development practices to mitigate the adverse effects of industrial growth on air quality.

Turning our attention to scholarly works that traverse the realms of music and commerce, "The Business of Music" by Davis et al. offers a comprehensive examination of the music industry's evolution in the digital age. The authors expound upon the shifting landscape of physical album sales and distribution, providing valuable insights for understanding the factors that may influence album shipment volume.

In a similar vein, "The Soundtrack of Our Lives: A Cultural History of Music" by Author illuminates the rich tapestry of music's influence on societal trends and consumer behaviors. The book provides a nuanced perspective on the interplay of cultural, economic, and environmental forces that shape the music industry's dynamics.

Stepping into the realm of fiction, the classic novel "High Fidelity" by Nick Hornby offers a whimsical exploration of vinyl records and the idiosyncrasies of music enthusiasts. While a work of fiction, the book's portrayal of the music retail business and its eccentric clientele provides a lighthearted glimpse into the world of physical album consumption.

Now, veering into the more unconventional sources of insight, the researchers stumbled upon a trove of unexpected wisdom while perusing the backs of shampoo bottles. The cryptic yet oddly captivating prose adorning these humble containers offered a curious blend of hygiene advice and existential musings, providing a peculiar lens through which to contemplate the enigmatic relationship between air pollution and album shipments. Although not a conventional scholarly source, the shampoo bottle snippets added a dash of whimsy to the research endeavor, reminding the researchers that unconventional inspirations can sometimes yield unexpected insights.

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 Sacramento and Physical album shipment volume in the United States. Make it seem dry like academic research paper, but with lots of subtle hidden offhand remarks, jokes, goofy observations, and puns.

Your research team collected data from all across the internet, but mostly just used information from Environmental Protection Agency and Statista . You used data from 1999 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]]
A Breath of Fresh Vinyl: Exploring the Correlation Between Air Pollution in Sacramento and Physical Album Shipment Volume in the United States

[[ABSTRACT]]
This study exudes a thorough exploration of the potential link between air pollution levels in Sacramento and the volume of physical album shipments across the United States. Drawing upon data meticulously collected from the Environmental Protection Agency and Statista, our research team conducted an in-depth analysis spanning the years 1999 to 2022. The findings unearth a remarkably high correlation coefficient of 0.9039559, with a p-value of less than 0.01, indicating a statistically significant relationship between the two variables. The implications of this correlation are not to be sniffed at, as they convey a possible intertwining of environmental factors with the music industry's physical product distribution. This offbeat connection sheds new light on the dynamic interplay of seemingly disparate domains and inspires further exploration into the whimsical dance of air quality and record shipments.

[[INTRODUCTION]]
INTRODUCTION
The intersection of environmental factors and economic trends has long captivated researchers seeking to unpack the interconnected web of influences shaping society. In this vein, our study delves into the unexpected coupling of air pollution levels in Sacramento with the shipment volume of physical albums in the United States. While the connection may seem as elusive as a rare vinyl pressing, our rigorous analysis uncovers a compelling correlation that may just hit the high note of serendipitous discovery.
As anyone with a discerning ear for statistics knows, uncovering a correlation is akin to striking gold in the data mines. Our journey began with a meticulous gathering of data from the Environmental Protection Agency and Statista, capturing the intricate dance of air pollution levels and physical album shipments from the year 1999 to 2022. The numbers, much like a tight harmony, revealed a striking correlation coefficient of 0.9039559, accompanied by a p-value that induced a nod of statistical significance falling below the hallowed threshold of 0.01. This eloquent synchronization speaks volumes, confirming the tantalizing connection between Sacramento's air quality and the beat of album shipments reverberating across the nation.
This correlation, like a catchy tune, resounds with implications that stretch far beyond mere statistical curiosity. The seemingly disparate realms of environmental quality and the music industry intersect in an unexpected medley, prompting us to ponder the strings of causality weaving through this colorful tapestry of variables. The discovery of such an unlikely synergy compels us to harmonize our understanding of the intricate relationship between environmental conditions and consumer behaviors, offering a new riff to the symphony of interdisciplinary inquiry.

-------

Your response should start like this:

[[METHODOLOGY]]

ChatGPT:

[[METHODOLOGY]]

Data Collection:
The data for air pollution levels in Sacramento was obtained from the Environmental Protection Agency's Air Quality System database. This dataset, much like a forgotten gem in a dusty record store, provided hourly measurements of various air pollutants including particulate matter, nitrogen dioxide, and ozone from monitoring stations across Sacramento. The physical album shipment volume data, on the other hand, was sourced from Statista; much like a well-used vinyl, it offered a comprehensive collection of information on the annual shipment of physical albums in the United States from 1999 to 2022.

Data Screening:
Before embarking on the statistical waltz, the collected data underwent rigorous screening and cleaning. Outliers and missing values were scrutinized with the precision of a discerning audiophile, ensuring the integrity of the dataset and maintaining the harmonious rhythm of the analysis.

Variable Transformation:
In order to orchestrate a seamless interplay of data, logarithmic transformation was applied to the air pollution levels and album shipment volumes. This transformation, akin to tuning an instrument, aimed to achieve a normalized distribution and enhance the symmetry of the variables, enabling a more melodious statistical analysis.

Statistical Analysis:
The empirical investigation of the potential correlation between air pollution in Sacramento and physical album shipment volume in the United States was conducted using Pearson's correlation coefficient. This method, like a conductor guiding a symphony, elucidated the strength and direction of the relationship between these seemingly unrelated variables. The statistical significance of the correlation coefficient was assessed using a two-tailed hypothesis test with a level of significance set at α = 0.01, ensuring a judicious evaluation of the findings.

Interpretation and Limitations:
The results of the statistical analysis were interpreted with an inclination towards cautious optimism, recognizing that correlation does not imply causation. While our findings reveal a robust correlation between air pollution levels in Sacramento and physical album shipment volume in the United States, the study is not without its limitations. Factors such as regional variations in music preferences and technological advancements in music consumption may compose a counter-melody to our proposed correlation, warranting further exploration and refinement of the research harmony.

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 Sacramento and Physical album shipment volume in the United States. Make it seem dry like academic research paper, but with lots of subtle hidden offhand remarks, jokes, goofy observations, and puns.

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]]
A Breath of Fresh Vinyl: Exploring the Correlation Between Air Pollution in Sacramento and Physical Album Shipment Volume in the United States

[[ABSTRACT]]
This study exudes a thorough exploration of the potential link between air pollution levels in Sacramento and the volume of physical album shipments across the United States. Drawing upon data meticulously collected from the Environmental Protection Agency and Statista, our research team conducted an in-depth analysis spanning the years 1999 to 2022. The findings unearth a remarkably high correlation coefficient of 0.9039559, with a p-value of less than 0.01, indicating a statistically significant relationship between the two variables. The implications of this correlation are not to be sniffed at, as they convey a possible intertwining of environmental factors with the music industry's physical product distribution. This offbeat connection sheds new light on the dynamic interplay of seemingly disparate domains and inspires further exploration into the whimsical dance of air quality and record shipments.

[[LITERATURE REVIEW]]
In "The Impact of Air Pollution on Economic Growth," Smith and Jones elucidate the multifaceted ways in which air pollution can influence various economic indicators. The authors find that higher levels of air pollution are associated with decreased economic activity, posing a myriad of challenges for policymakers and businesses alike.
Doe's study, "The Environmental Consequences of Industrial Development," delves into the environmental repercussions of industrial activity, shedding light on the intricate linkages between economic advancement and ecological degradation. The findings underscore the need for sustainable development practices to mitigate the adverse effects of industrial growth on air quality.
Turning our attention to scholarly works that traverse the realms of music and commerce, "The Business of Music" by Davis et al. offers a comprehensive examination of the music industry's evolution in the digital age. The authors expound upon the shifting landscape of physical album sales and distribution, providing valuable insights for understanding the factors that may influence album shipment volume.
In a similar vein, "The Soundtrack of Our Lives: A Cultural History of Music" by Author illuminates the rich tapestry of music's influence on societal trends and consumer behaviors. The book provides a nuanced perspective on the interplay of cultural, economic, and environmental forces that shape the music industry's dynamics.
Stepping into the realm of fiction, the classic novel "High Fidelity" by Nick Hornby offers a whimsical exploration of vinyl records and the idiosyncrasies of music enthusiasts. While a work of fiction, the book's portrayal of the music retail business and its eccentric clientele provides a lighthearted glimpse into the world of physical album consumption.
Now, veering into the more unconventional sources of insight, the researchers stumbled upon a trove of unexpected wisdom while perusing the backs of shampoo bottles. The cryptic yet oddly captivating prose adorning these humble containers offered a curious blend of hygiene advice and existential musings, providing a peculiar lens through which to contemplate the enigmatic relationship between air pollution and album shipments. Although not a conventional scholarly source, the shampoo bottle snippets added a dash of whimsy to the research endeavor, reminding the researchers that unconventional inspirations can sometimes yield unexpected insights.

[[RESULTS]]
The analysis of the data revealed a striking correlation coefficient of 0.9039559 between air pollution levels in Sacramento and the volume of physical album shipments across the United States from 1999 to 2022. This robust correlation, akin to a well-orchestrated duet, suggests a strong linear relationship between these seemingly incongruous variables. The coefficient of determination (r-squared) of 0.8171363 further accentuates the harmonious nature of this correlation, explaining approximately 81.7% of the variability in physical album shipment volume through its association with air pollution levels.
The p-value of less than 0.01 adds an air of statistical significance to this melodic connection, affirming the resonance of the relationship beyond mere chance. This p-value, much like a rare vinyl find, substantiates the presence of a meaningful association between air pollution in Sacramento and the level of physical album shipments in the broader United States market.
The scatterplot (Fig. 1) visually portrays the compelling correlation between the variables, providing a harmonious visualization of this unexpected connection. This graphical representation underscores the clear trend in the data and accentuates the robustness of the statistical findings.
The results of this analysis resonate with the profound implications of this unlikely pairing, illustrating the intricate harmony between environmental quality and consumer behaviors. The synergy uncovered in this study invites further exploration into the intricate interplay of environmental factors and economic trends, offering a unique chord in the symphony of interdisciplinary research.

-------

Your response should start like this:

[[DISCUSSION]]

ChatGPT:

[[DISCUSSION]]

The findings of this study corroborate and extend upon prior research that has examined the impact of air pollution on economic activities. Smith and Jones, in their enlightening work, revealed a negative relationship between air pollution and economic growth, painting a rather bleak picture of the repercussions of environmental degradation. Our study, however, adds a melodious twist to this narrative by demonstrating a positive correlation between air pollution levels in Sacramento and physical album shipment volume in the United States. While their findings may sound like a discordant note in the orchestra of economic literature, our results harmoniously resonate with the notion that environmental factors can indeed influence consumer behaviors in unexpected ways.

Similarly, Doe's investigation into the environmental consequences of industrial development provided key insights into the interplay between economic stimuli and environmental stresses. Our study builds upon this theme by dancing into uncharted territory, revealing the enchanted waltz of air quality and record shipments. The serendipitous discovery of this unlikely pairing demonstrates that, much like a well-composed symphony, the forces influencing consumer behaviors are rich and multifaceted, playing in concert with environmental factors to produce a dynamic and nuanced melody of market dynamics.

The unconventional sources of insight highlighted in our literature review, such as the whimsical inspiration found on the backs of shampoo bottles, may initially seem like a lighthearted detour from the gravitas of scholarly discourse. However, this offhand yet oddly captivating source of inspiration underscores the importance of staying open to unexpected avenues of insight. Just as a chance encounter with an obscure vinyl album can lead to the discovery of a hidden gem, our unconventional sources of inspiration have illuminated a unique connection between air pollution and album shipments, adding a distinctive timbre to the chorus of existing research.

In summary, our findings lend empirical support to the notion that environmental quality can harmonize with consumer behaviors in delightful and surprising ways, with potentially far-reaching implications for understanding the interplay of environmental, economic, and cultural forces. This study urges further exploration into the quirky cadence of air pollution's influence on market dynamics, inviting researchers to listen for the subtler, more nuanced melodies that may be lurking beneath the surface of seemingly disparate domains.

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 Sacramento and Physical album shipment volume in the United States. Make it seem dry like academic research paper, but with lots of subtle hidden offhand remarks, jokes, goofy observations, and puns.

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]]
A Breath of Fresh Vinyl: Exploring the Correlation Between Air Pollution in Sacramento and Physical Album Shipment Volume in the United States

[[ABSTRACT]]
This study exudes a thorough exploration of the potential link between air pollution levels in Sacramento and the volume of physical album shipments across the United States. Drawing upon data meticulously collected from the Environmental Protection Agency and Statista, our research team conducted an in-depth analysis spanning the years 1999 to 2022. The findings unearth a remarkably high correlation coefficient of 0.9039559, with a p-value of less than 0.01, indicating a statistically significant relationship between the two variables. The implications of this correlation are not to be sniffed at, as they convey a possible intertwining of environmental factors with the music industry's physical product distribution. This offbeat connection sheds new light on the dynamic interplay of seemingly disparate domains and inspires further exploration into the whimsical dance of air quality and record shipments.

[[INTRDUCTION]]
INTRODUCTION
The intersection of environmental factors and economic trends has long captivated researchers seeking to unpack the interconnected web of influences shaping society. In this vein, our study delves into the unexpected coupling of air pollution levels in Sacramento with the shipment volume of physical albums in the United States. While the connection may seem as elusive as a rare vinyl pressing, our rigorous analysis uncovers a compelling correlation that may just hit the high note of serendipitous discovery.
As anyone with a discerning ear for statistics knows, uncovering a correlation is akin to striking gold in the data mines. Our journey began with a meticulous gathering of data from the Environmental Protection Agency and Statista, capturing the intricate dance of air pollution levels and physical album shipments from the year 1999 to 2022. The numbers, much like a tight harmony, revealed a striking correlation coefficient of 0.9039559, accompanied by a p-value that induced a nod of statistical significance falling below the hallowed threshold of 0.01. This eloquent synchronization speaks volumes, confirming the tantalizing connection between Sacramento's air quality and the beat of album shipments reverberating across the nation.
This correlation, like a catchy tune, resounds with implications that stretch far beyond mere statistical curiosity. The seemingly disparate realms of environmental quality and the music industry intersect in an unexpected medley, prompting us to ponder the strings of causality weaving through this colorful tapestry of variables. The discovery of such an unlikely synergy compels us to harmonize our understanding of the intricate relationship between environmental conditions and consumer behaviors, offering a new riff to the symphony of interdisciplinary inquiry.

[[RESULTS]]
The analysis of the data revealed a striking correlation coefficient of 0.9039559 between air pollution levels in Sacramento and the volume of physical album shipments across the United States from 1999 to 2022. This robust correlation, akin to a well-orchestrated duet, suggests a strong linear relationship between these seemingly incongruous variables. The coefficient of determination (r-squared) of 0.8171363 further accentuates the harmonious nature of this correlation, explaining approximately 81.7% of the variability in physical album shipment volume through its association with air pollution levels.
The p-value of less than 0.01 adds an air of statistical significance to this melodic connection, affirming the resonance of the relationship beyond mere chance. This p-value, much like a rare vinyl find, substantiates the presence of a meaningful association between air pollution in Sacramento and the level of physical album shipments in the broader United States market.
The scatterplot (Fig. 1) visually portrays the compelling correlation between the variables, providing a harmonious visualization of this unexpected connection. This graphical representation underscores the clear trend in the data and accentuates the robustness of the statistical findings.
The results of this analysis resonate with the profound implications of this unlikely pairing, illustrating the intricate harmony between environmental quality and consumer behaviors. The synergy uncovered in this study invites further exploration into the intricate interplay of environmental factors and economic trends, offering a unique chord in the symphony of interdisciplinary research.

-------

Your response should start like this:

[[CONCLUSION]]

ChatGPT:

[[CONCLUSION]]

In conclusion, our study has diligently peeled back the layers of this unexpected melodic harmony between Sacramento's air pollution and the shipment volume of physical albums in the United States. The striking correlation coefficient of 0.9039559, resembling a perfectly pitched chorus, alongside a p-value less than 0.01, akin to a rare gem in the statistical treasure trove, strongly supports the existence of a meaningful association between these seemingly dissonant variables. The strong linear relationship, much like a well-composed symphony, suggests that as air pollution levels in Sacramento rise and fall, so too does the volume of physical albums distributed across the nation.

This curious concerto of environmental quality and consumer music preferences holds intriguing implications for the interplay of diverse domains. The whimsical dance of air quality and record shipments highlights the interconnectedness of seemingly unrelated spheres, much like a surprising duet between musicians from vastly different genres. As we reflect on the resonance of this unlikely pairing, we are reminded of the unpredictable harmonies that echo through the tapestry of human activity.

While this study has struck a resounding chord in uncovering this unexpected connection, it is important to acknowledge the limitations inherent in correlational research. Further studies may consider the influence of other environmental and socio-economic factors on album shipment volume, as well as delve into the underlying mechanisms driving this peculiar relationship. However, for now, this research provides a captivating overture to the waltz of environmental conditions and consumer behaviors, offering a fresh note in the symphony of interdisciplinary inquiry.

In light of these findings, we assert that no more research is needed in this area, as our study has riffed on this harmonious correlation and struck a resounding final chord.

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 A Breath of Fresh Vinyl: Exploring the Correlation Between Air Pollution in Sacramento and Physical Album Shipment Volume in the United States. Respond only with the name of a fictional academic journal.

ChatGPT:

Journal of Ecological Harmonies

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 A Breath of Fresh Vinyl: Exploring the Correlation Between Air Pollution in Sacramento and Physical Album Shipment Volume in the United States. Respond only with the name of a fictional organization.

ChatGPT:

The Society for Airborne Audiophile Research

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 A Breath of Fresh Vinyl: Exploring the Correlation Between Air Pollution in Sacramento and Physical Album Shipment Volume in the United States with an abstract of This study exudes a thorough exploration of the potential link between air pollution levels in Sacramento and the volume of physical album shipments across the United States. Drawing upon data meticulously collected from the Environmental Protection Agency and Statista, our research team conducted an in-depth analysis spanning the years 1999 to 2022. The findings unearth a remarkably high correlation coefficient of 0.9039559, with a p-value of less than 0.01, indicating a statistically significant relationship between the two variables. The implications of this correlation are not to be sniffed at, as they convey a possible intertwining of environmental factors with the music industry's physical product distribution. This offbeat connection sheds new light on the dynamic interplay of seemingly disparate domains and inspires further exploration into the whimsical dance of air quality and record shipments.

ChatGPT:

air pollution, Sacramento, physical album shipment, correlation, United States, Environmental Protection Agency, Statista, correlation coefficient, p-value, music industry, distribution, environmental factors

*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 Sacramento
Detailed data title: Percentage of days with air quality at 'unhealthy for sensitive groups' or worse in Sacramento--Roseville--Arden-Arcade, CA
Source: Environmental Protection Agency
See what else correlates with Air pollution in Sacramento

Physical album shipment volume in the United States
Source: Statista
See what else correlates with Physical album shipment volume in the United States

Correlation r = 0.9039559 (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 = 0.8171363 (Coefficient of determination)
This means 81.7% of the change in the one variable (i.e., Physical album shipment volume in the United States) is predictable based on the change in the other (i.e., Air pollution in Sacramento) over the 24 years from 1999 through 2022.

p < 0.01, which is statistically significant(Null hypothesis significance test)
The p-value is 1.41E-9.^Show 0.0000000014095615937145944000
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 0.9 in 1.41E-7% of random cases. Said differently, if you correlated 709,440,442 random variables^Note You don't actually need 709 million 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 23 degrees of freedom, ^Note Degrees of freedom is a measure of how many free components we are testing. In this case it is 23 because we have two variables measured over a period of 24 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.

[ 0.79, 0.96 ] 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.

	1999	2000	2001	2002	2003	2004	2005	2006	2007	2008	2009	2010	2011	2012	2013	2014	2015	2016	2017	2018	2019	2020	2021	2022
Air pollution in Sacramento (Bad air quality days)	38.0822	28.6885	31.7808	39.726	31.2329	30.6011	25.2055	33.1507	26.5753	24.3169	18.9041	11.5068	21.3699	21.5847	13.6986	15.6164	10.9589	16.1202	15.3425	15.6164	5.47945	13.6612	15.8904	11.2329
Physical album shipment volume in the United States (Units)	938900000	942500000	881900000	803300000	746000000	767000000	705400000	619700000	511100000	368400000	292900000	253000000	240800000	198200000	172200000	142800000	122900000	97600000	87700000	52000000	47500000	31600000	46700000	33400000

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([38.0822,28.6885,31.7808,39.726,31.2329,30.6011,25.2055,33.1507,26.5753,24.3169,18.9041,11.5068,21.3699,21.5847,13.6986,15.6164,10.9589,16.1202,15.3425,15.6164,5.47945,13.6612,15.8904,11.2329,])
array_2 = np.array([938900000,942500000,881900000,803300000,746000000,767000000,705400000,619700000,511100000,368400000,292900000,253000000,240800000,198200000,172200000,142800000,122900000,97600000,87700000,52000000,47500000,31600000,46700000,33400000,])
array_1_name = "Air pollution in Sacramento"
array_2_name = "Physical album shipment volume in the United States"

# 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 Sacramento
Line chart for only Physical album shipment volume in the United States
AI-generated correlation image
The spurious research paper: A Breath of Fresh Vinyl: Exploring the Correlation Between Air Pollution in Sacramento and Physical Album Shipment Volume in the United States

View another random correlation

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Correlation ID: 2881 · Black Variable ID: 21171 · Red Variable ID: 155


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