Spurious correlation #1,616 · 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 Yakima, Washington and the second variable is Automotive recalls issued by Mercedes-Benz USA. The chart goes from 1980 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 Yakima, Washington and the second variable is Automotive recalls issued by Mercedes-Benz USA. The chart goes from 1980 to 2022, and the two variables track closely in value over that time.

Download png, svg

AI explanation

The smog in Yakima was so thick that it clogged up the sensors in Mercedes-Benz cars, triggering a wave of recalls as the cars couldn't differentiate between polluted air and actual malfunctions.

^{Show image generation prompt} Model: dalle-3
Prompt: Create a surreal vaporwave-inspired image of a line of sleek Mercedes-Benz cars parked against a backdrop of a hazy, pastel-colored sky in Yakima, Washington. The air quality gives off a dreamy, ethereal feel, and the cars symbolize the recall repair process. Infuse the scene with retro-futuristic elements, such as neon glows and geometric patterns, evoking a sense of nostalgia and digital aesthetics. 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: Unhealthy air quality in Yakima, Washington and Automotive recalls issued by Mercedes-Benz USA. 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: inspired by bauhaus Symbolism Cyber folk Sci-fi fantacy Vaporwave
ChatGPT: Vaporwave

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 Unhealthy air quality in Yakima, Washington and Automotive recalls issued by Mercedes-Benz USA together. Keep the description simple.
ChatGPT: In Yakima, Washington, where the air quality is unhealthy, a line of Mercedes-Benz cars is parked, awaiting a recall repair. The hazy sky shows the effects of the poor air quality, while the Mercedes-Benz cars symbolize the automotive recalls issued by the manufacturer.

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: [ Vaporwave ] and depicting this scene: In Yakima, Washington, where the air quality is unhealthy, a line of Mercedes-Benz cars is parked, awaiting a recall repair. The hazy sky shows the effects of the poor air quality, while the Mercedes-Benz cars symbolize the automotive recalls issued by the manufacturer. Keep the visual depiction simple. Do not include any words or speech bubbles.
ChatGPT: Create a surreal vaporwave-inspired image of a line of sleek Mercedes-Benz cars parked against a backdrop of a hazy, pastel-colored sky in Yakima, Washington. The air quality gives off a dreamy, ethereal feel, and the cars symbolize the recall repair process. Infuse the scene with retro-futuristic elements, such as neon glows and geometric patterns, evoking a sense of nostalgia and digital aesthetics.

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

I sequence the requests into multiple prompts because I find GPT 3.5 to perform much better with short, well-managed contexts. Thus, I track the context directly in Python and only ask ChatGPT targeted questions.
^{Show prompt for explanation} Model: gpt-3.5-turbo-1106 (fine-tuned)
System prompt: You provide humorous responses in the form of plausible sounding explanations for correlations. You assume the correlation is causative for the purpose of the explanation even if it is ridiculous. You do not chat with the user, you only reply with the causal connection explanation and nothing else.
User prompt: Please make up a funny explanation for how increases in Air pollution in Yakima, Washington positively influenced Automotive recalls issued by Mercedes-Benz USA.

AI academic paper

(Because p < 0.01)

The Dirty Truth: Uncovering the Smoggy Relationship Between Air Pollution in Yakima, Washington, and the Mercedes-Benz USA Recalls

The Journal of Environmental Epidemiology and Automotive Anomalies

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 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 Yakima, Washington and Automotive recalls issued by Mercedes-Benz USA. 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 some cartoons and childrens' shows that you watched that are related to the topic.

Here is the title and abstract of the paper:
[[TITLE]]
The Dirty Truth: Uncovering the Smoggy Relationship Between Air Pollution in Yakima, Washington, and the Mercedes-Benz USA Recalls

[[ABSTRACT]]
The correlation between air pollution in Yakima, Washington, and automotive recalls issued by Mercedes-Benz USA has long been a source of controversy and speculation. In this study, we delved into the swirling fog of data to unravel the mysterious connection between these two seemingly disparate factors. Leveraging data from the Environmental Protection Agency and the US Department of Transportation spanning the years 1980 to 2022, our research team uncovered a surprising correlation coefficient of 0.6924859 with the p-value less than 0.01, shedding light on a relationship that has long been clouded in uncertainty.

Our findings challenge the conventional wisdom and emphasize the need for further investigation into the murky intersection of air quality and luxury automotive engineering. This research is a breath of fresh air for a scientific community often bogged down in dry statistical analysis, offering a peek under the hood of a perplexing puzzle and revealing the unexpected ways in which air pollution and automotive recalls may be intertwined. So, buckle up and prepare for a ride through this curious connection with emissions of humor and puns that just might turbocharge your understanding of these complex dynamics.

-------

And here is the introduction section that led to this literature review:
[[INTRODUCTION]]
Ah, the sweet smell of exhaust fumes and the lulling hum of air conditioners working overtime. We find ourselves at the crossroads of two seemingly unrelated phenomena: air pollution in the picturesque Yakima, Washington, and the sleek, sophisticated world of Mercedes-Benz USA automotive recalls. It is in this unlikely collision of worlds that we embark on a quest to unravel the enigmatic relationship between these confounding variables.
Our research sets out to peel back the layers of complexity and delve into the smoggy depths of correlation, causation, and perhaps a dash of serendipity. As we navigate the treacherous terrain of statistical analysis and variable engagement, we are careful to keep our heads above the metaphorical clouds of uncertainty (and maybe a few literal ones too – thanks, Yakima).
The prevailing wisdom suggests that air pollution and luxury automobiles are about as compatible as oil and water, or in this case, oil and air. However, it is our contention that there may be more than meets the eye – or the tailpipe, as it were. Our study aims to debunk the myths and misconceptions surrounding these phenomena, steering clear of the fog of ambiguity and blazing a trail towards clarity.
Prepare yourself for an exhilarating journey through the winding roads of data analysis, where the rubber meets the road, and statistical significance meets fresh mountain air. Along the way, we’ll be wielding correlation coefficients like trusty compasses and brandishing p-values like noble swords, all in the name of shedding light on this tumultuous tango between emissions and automotive malfunctions.
So, fasten your seatbelts and grip the wheel tightly as we embark on this wild ride through the juncture of air quality and luxury automotive engineering, armed with science, statistics, and a healthy dose of wry humor. Let’s rev up our engines and embark on this intellectual joyride, traversing the terrain of Yakima’s air and Mercedes-Benz’s recalls with all the curiosity and whimsy that befits such an unexpected union.

-------

Your response should start like this:

[[LITERATURE REVIEW]]

ChatGPT:
[[LITERATURE REVIEW]]

In "Smith et al.," the authors find a significant correlation between air pollution levels in Yakima, Washington, and the number of automotive recalls issued by Mercedes-Benz USA. The study highlights the potential impact of environmental factors on the performance and safety of luxury vehicles, prompting further investigation into the intricate relationship between air quality and automotive engineering.

However, as we traverse this expanse of scholarly work, it becomes evident that the landscape of research on this topic is not without its twists and turns. In "Doe and Jones," the authors delve into the nuances of air pollution and its effects on vehicle emissions, offering a comprehensive analysis of the interplay between environmental factors and automotive performance. The findings beg the question: could the smoggy skies of Yakima be casting a shadow on the mechanical prowess of luxury automobiles?

As we venture beyond the realm of academic journals, "Air Pollution and its Impact on Vehicle Performance" by Lorem Ipsum provides a comprehensive overview of the environmental challenges faced by automotive manufacturers. The book offers a breath of fresh air in understanding the complexities of air pollution and its potential ramifications for vehicle safety and reliability. With each turn of the page, we find ourselves drawn deeper into the smokescreen of uncertainty surrounding the intersection of air quality and automotive excellence.

Turning to the realm of fiction, "The Cloudy Chronicles: Tales of Emissions and Recalls" offers a whimsical take on the interconnectedness of air pollution and automotive malfunctions. While the book may not offer empirical evidence, its imaginative exploration of these themes provides a refreshing departure from the often somber tone of academic literature. Who knew that the world of automotive engineering could be so shrouded in mist and mystery?

Let's not forget the invaluable insights we gleaned from childhood favorites such as "The Smoggy Adventures of Captain Carbon" and "Pollution Patrol: Saving the Day, One Emission at a Time." While these animated escapades may not align with the rigors of scholarly research, they do serve as a poignant reminder of the enduring fascination with environmental themes and their potential impact on the world of automotive engineering.

In summary, our journey through the literature has been nothing short of a rollercoaster ride, complete with unexpected detours into the realms of imagination and nostalgia. As we move forward with our investigation, it's clear that the connection between air pollution in Yakima, Washington, and automotive recalls issued by Mercedes-Benz USA is a puzzle worthy of our most creative and analytical endeavors. So, let's rev up our engines and dive headfirst into the murky depths of this captivating conundrum, armed with scholarly acumen and a splash of whimsy.

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 Yakima, Washington and Automotive recalls issued by Mercedes-Benz USA. Make lots of jokes, goofy observations, and puns. Sneak in some jokes and clever puns about science, research, statistics, and the variables.

Your research team collected data from all across the internet, but mostly just used information from Environmental Protection Agency and US DOT . You used data from 1980 to 2022

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

Here is the title, abstract, and introduction of the paper:
[[TITLE]]
The Dirty Truth: Uncovering the Smoggy Relationship Between Air Pollution in Yakima, Washington, and the Mercedes-Benz USA Recalls

[[ABSTRACT]]
The correlation between air pollution in Yakima, Washington, and automotive recalls issued by Mercedes-Benz USA has long been a source of controversy and speculation. In this study, we delved into the swirling fog of data to unravel the mysterious connection between these two seemingly disparate factors. Leveraging data from the Environmental Protection Agency and the US Department of Transportation spanning the years 1980 to 2022, our research team uncovered a surprising correlation coefficient of 0.6924859 with the p-value less than 0.01, shedding light on a relationship that has long been clouded in uncertainty.

Our findings challenge the conventional wisdom and emphasize the need for further investigation into the murky intersection of air quality and luxury automotive engineering. This research is a breath of fresh air for a scientific community often bogged down in dry statistical analysis, offering a peek under the hood of a perplexing puzzle and revealing the unexpected ways in which air pollution and automotive recalls may be intertwined. So, buckle up and prepare for a ride through this curious connection with emissions of humor and puns that just might turbocharge your understanding of these complex dynamics.

[[INTRODUCTION]]
Ah, the sweet smell of exhaust fumes and the lulling hum of air conditioners working overtime. We find ourselves at the crossroads of two seemingly unrelated phenomena: air pollution in the picturesque Yakima, Washington, and the sleek, sophisticated world of Mercedes-Benz USA automotive recalls. It is in this unlikely collision of worlds that we embark on a quest to unravel the enigmatic relationship between these confounding variables.
Our research sets out to peel back the layers of complexity and delve into the smoggy depths of correlation, causation, and perhaps a dash of serendipity. As we navigate the treacherous terrain of statistical analysis and variable engagement, we are careful to keep our heads above the metaphorical clouds of uncertainty (and maybe a few literal ones too – thanks, Yakima).
The prevailing wisdom suggests that air pollution and luxury automobiles are about as compatible as oil and water, or in this case, oil and air. However, it is our contention that there may be more than meets the eye – or the tailpipe, as it were. Our study aims to debunk the myths and misconceptions surrounding these phenomena, steering clear of the fog of ambiguity and blazing a trail towards clarity.
Prepare yourself for an exhilarating journey through the winding roads of data analysis, where the rubber meets the road, and statistical significance meets fresh mountain air. Along the way, we’ll be wielding correlation coefficients like trusty compasses and brandishing p-values like noble swords, all in the name of shedding light on this tumultuous tango between emissions and automotive malfunctions.
So, fasten your seatbelts and grip the wheel tightly as we embark on this wild ride through the juncture of air quality and luxury automotive engineering, armed with science, statistics, and a healthy dose of wry humor. Let’s rev up our engines and embark on this intellectual joyride, traversing the terrain of Yakima’s air and Mercedes-Benz’s recalls with all the curiosity and whimsy that befits such an unexpected union.

-------

Your response should start like this:

[[METHODOLOGY]]

ChatGPT:

[[METHODOLOGY]]

Before embarking on our expedition into the enigmatic realm of air pollution and automotive recalls, we endeavored to construct a methodological framework sturdy enough to weather the unpredictable terrain of statistical analysis and variables engagement. Our approach was as systematic as it was whimsical, blending the rigor of scientific inquiry with the playfulness of a high-stakes game of "connect the dots."

First, we scoured the digital expanse, navigating the virtual highways and byways of the internet, all in pursuit of precious data nuggets. Our primary sources of information were the venerable Environmental Protection Agency and the indispensable US Department of Transportation. Like intrepid treasure hunters, we combed through data spanning over four decades, from the neon-hued days of 1980 to the futuristic frontier of 2022. We documented air pollution levels in Yakima, Washington, with meticulous precision, tracking the ebb and flow of pollutants with the zeal of enthusiastic birdwatchers keeping tally of rare avian sightings.

As for our quest to unearth the intricacies of Mercedes-Benz USA recalls, we adopted an equally fervent approach. We delved into the labyrinthine archives of recall announcements, dissecting the intricacies of each automotive hiccup with the fervor of sleuths unraveling a grand mystery. Our research team left no stone unturned, no gearbox unturned, if you will, in our quest for the golden thread linking air pollution and luxury automotive malfunctions.

Armed with our trusty data, we then unleashed the formidable power of statistical analysis. We brought out the big guns – correlation coefficients, p-values, and regression analyses – to wrangle the unruly variables into submission. We measured the strength of the relationship between air pollution in Yakima and Mercedes-Benz USA recalls with a confidence that rivaled a lion tamer facing down a rowdy feline.

Our chosen statistical tools had a sense of humor, though - they regaled us with jokes about standard deviations and regaled in the pun-derful world of statistical significance. There's nothing quite like a laughter-filled regression analysis to brighten one’s day, especially when dealing with the exhaustingly complex dynamics of air pollution and automotive foibles.

In essence, our methodology was not merely a means to an end; it was an adventure in and of itself, a grand quest to wrestle with the data dragons and breathe life into the narratives woven by numbers and insights. So, with our satchels full of data, our spirits high, and our statistical compasses pointing true north, we set forth into the captivating unknown of correlation and causation, eager to expose the captivating dance between Yakima's air and Mercedes-Benz's mechanical tribulations.

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 Yakima, Washington and Automotive recalls issued by Mercedes-Benz USA. Make lots of jokes, goofy observations, and puns. Sneak in some jokes and clever puns about science, research, statistics, and the variables.

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

For the time period 1980 to 2022, you found a correlation 0.6924859, r-squared of 0.4795368, and p < 0.01.

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

Here is the title and abstract of the paper:
[[TITLE]]
The Dirty Truth: Uncovering the Smoggy Relationship Between Air Pollution in Yakima, Washington, and the Mercedes-Benz USA Recalls

[[ABSTRACT]]
The correlation between air pollution in Yakima, Washington, and automotive recalls issued by Mercedes-Benz USA has long been a source of controversy and speculation. In this study, we delved into the swirling fog of data to unravel the mysterious connection between these two seemingly disparate factors. Leveraging data from the Environmental Protection Agency and the US Department of Transportation spanning the years 1980 to 2022, our research team uncovered a surprising correlation coefficient of 0.6924859 with the p-value less than 0.01, shedding light on a relationship that has long been clouded in uncertainty.

Our findings challenge the conventional wisdom and emphasize the need for further investigation into the murky intersection of air quality and luxury automotive engineering. This research is a breath of fresh air for a scientific community often bogged down in dry statistical analysis, offering a peek under the hood of a perplexing puzzle and revealing the unexpected ways in which air pollution and automotive recalls may be intertwined. So, buckle up and prepare for a ride through this curious connection with emissions of humor and puns that just might turbocharge your understanding of these complex dynamics.

-------

And here is the methodology section that led to this result:
[[METHODOLOGY]]
Ah, the sweet smell of exhaust fumes and the lulling hum of air conditioners working overtime. We find ourselves at the crossroads of two seemingly unrelated phenomena: air pollution in the picturesque Yakima, Washington, and the sleek, sophisticated world of Mercedes-Benz USA automotive recalls. It is in this unlikely collision of worlds that we embark on a quest to unravel the enigmatic relationship between these confounding variables.
Our research sets out to peel back the layers of complexity and delve into the smoggy depths of correlation, causation, and perhaps a dash of serendipity. As we navigate the treacherous terrain of statistical analysis and variable engagement, we are careful to keep our heads above the metaphorical clouds of uncertainty (and maybe a few literal ones too – thanks, Yakima).
The prevailing wisdom suggests that air pollution and luxury automobiles are about as compatible as oil and water, or in this case, oil and air. However, it is our contention that there may be more than meets the eye – or the tailpipe, as it were. Our study aims to debunk the myths and misconceptions surrounding these phenomena, steering clear of the fog of ambiguity and blazing a trail towards clarity.
Prepare yourself for an exhilarating journey through the winding roads of data analysis, where the rubber meets the road, and statistical significance meets fresh mountain air. Along the way, we’ll be wielding correlation coefficients like trusty compasses and brandishing p-values like noble swords, all in the name of shedding light on this tumultuous tango between emissions and automotive malfunctions.
So, fasten your seatbelts and grip the wheel tightly as we embark on this wild ride through the juncture of air quality and luxury automotive engineering, armed with science, statistics, and a healthy dose of wry humor. Let’s rev up our engines and embark on this intellectual joyride, traversing the terrain of Yakima’s air and Mercedes-Benz’s recalls with all the curiosity and whimsy that befits such an unexpected union.

-------

Your response should start like this:

[[RESULTS]]

ChatGPT:

[[RESULTS]]

In our quest to demystify the relationship between air pollution in Yakima, Washington, and automotive recalls issued by Mercedes-Benz USA, our research team unearthed some eye-opening results. After painstakingly crunching numbers and analyzing data from the Environmental Protection Agency and the US Department of Transportation spanning over four decades, we uncovered a striking correlation coefficient of 0.6924859 between these seemingly unrelated variables. To put it simply, the connection between smoggy air in Yakima and luxury car malfunctions is as clear as, well, a foggy day in Yakima.

Furthermore, our analysis revealed an r-squared value of 0.4795368, underscoring the significant proportion of variance in Mercedes-Benz USA automotive recalls that can be attributed to air pollution in Yakima. In other words, nearly half of the variability in recalls can be explained by the level of air pollution in this scenic city. That's a statistical revelation worth celebrating – maybe with a breath of fresh, unpolluted air!

And as if that weren't enough to raise eyebrows, our findings also boast a p-value less than 0.01 – indicating an extremely low probability that the observed correlation occurred by chance. In scientific terms, this means we can confidently assert that the relationship between air pollution in Yakima and Mercedes-Benz USA recalls is not just a fluke or a statistical hiccup. It's the real deal, folks.

To visually capture the essence of this revelatory correlation, we present Fig. 1, a scatterplot that graphically encapsulates the strong association between air pollution in Yakima, Washington, and automotive recalls issued by Mercedes-Benz USA. Prepare to be mesmerized by the beauty of data points aligning like stars in the night sky, albeit with a slightly less romantic backdrop – we're talking about emissions and car troubles, after all.

Our discoveries challenge preconceived notions and beckon for further investigation into this intriguing nexus of air quality and luxury automotive design. It's a reminder that in the world of scientific inquiry, even the most peculiar correlations can emerge from the statistical woodwork. This research not only opens the hood on a perplexing puzzle but also emphasizes the interconnectedness of seemingly disparate phenomena, offering a breath of fresh air to the often stifling world of academic inquiry.

So, as we revel in these surprising connections and revelatory findings, let's not forget to appreciate the whimsical dance of data that led us to this crossroads of air pollution and automotive engineering. The scientific journey is often peppered with unexpected detours and surprising intersections, and our study is a testament to the exhilarating, and sometimes downright quirky, nature of scientific exploration.

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 Yakima, Washington and Automotive recalls issued by Mercedes-Benz USA. Make lots of jokes, goofy observations, and puns. Sneak in some jokes and clever puns about science, research, statistics, and the variables.

Limit your response to 500 tokens.

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

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

[[TITLE]]
The Dirty Truth: Uncovering the Smoggy Relationship Between Air Pollution in Yakima, Washington, and the Mercedes-Benz USA Recalls

[[ABSTRACT]]
The correlation between air pollution in Yakima, Washington, and automotive recalls issued by Mercedes-Benz USA has long been a source of controversy and speculation. In this study, we delved into the swirling fog of data to unravel the mysterious connection between these two seemingly disparate factors. Leveraging data from the Environmental Protection Agency and the US Department of Transportation spanning the years 1980 to 2022, our research team uncovered a surprising correlation coefficient of 0.6924859 with the p-value less than 0.01, shedding light on a relationship that has long been clouded in uncertainty.

Our findings challenge the conventional wisdom and emphasize the need for further investigation into the murky intersection of air quality and luxury automotive engineering. This research is a breath of fresh air for a scientific community often bogged down in dry statistical analysis, offering a peek under the hood of a perplexing puzzle and revealing the unexpected ways in which air pollution and automotive recalls may be intertwined. So, buckle up and prepare for a ride through this curious connection with emissions of humor and puns that just might turbocharge your understanding of these complex dynamics.

[[LITERATURE REVIEW]]
In "Smith et al.," the authors find a significant correlation between air pollution levels in Yakima, Washington, and the number of automotive recalls issued by Mercedes-Benz USA. The study highlights the potential impact of environmental factors on the performance and safety of luxury vehicles, prompting further investigation into the intricate relationship between air quality and automotive engineering.
However, as we traverse this expanse of scholarly work, it becomes evident that the landscape of research on this topic is not without its twists and turns. In "Doe and Jones," the authors delve into the nuances of air pollution and its effects on vehicle emissions, offering a comprehensive analysis of the interplay between environmental factors and automotive performance. The findings beg the question: could the smoggy skies of Yakima be casting a shadow on the mechanical prowess of luxury automobiles?
As we venture beyond the realm of academic journals, "Air Pollution and its Impact on Vehicle Performance" by Lorem Ipsum provides a comprehensive overview of the environmental challenges faced by automotive manufacturers. The book offers a breath of fresh air in understanding the complexities of air pollution and its potential ramifications for vehicle safety and reliability. With each turn of the page, we find ourselves drawn deeper into the smokescreen of uncertainty surrounding the intersection of air quality and automotive excellence.
Turning to the realm of fiction, "The Cloudy Chronicles: Tales of Emissions and Recalls" offers a whimsical take on the interconnectedness of air pollution and automotive malfunctions. While the book may not offer empirical evidence, its imaginative exploration of these themes provides a refreshing departure from the often somber tone of academic literature. Who knew that the world of automotive engineering could be so shrouded in mist and mystery?
Let's not forget the invaluable insights we gleaned from childhood favorites such as "The Smoggy Adventures of Captain Carbon" and "Pollution Patrol: Saving the Day, One Emission at a Time." While these animated escapades may not align with the rigors of scholarly research, they do serve as a poignant reminder of the enduring fascination with environmental themes and their potential impact on the world of automotive engineering.
In summary, our journey through the literature has been nothing short of a rollercoaster ride, complete with unexpected detours into the realms of imagination and nostalgia. As we move forward with our investigation, it's clear that the connection between air pollution in Yakima, Washington, and automotive recalls issued by Mercedes-Benz USA is a puzzle worthy of our most creative and analytical endeavors. So, let's rev up our engines and dive headfirst into the murky depths of this captivating conundrum, armed with scholarly acumen and a splash of whimsy.

[[RESULTS]]
In our quest to demystify the relationship between air pollution in Yakima, Washington, and automotive recalls issued by Mercedes-Benz USA, our research team unearthed some eye-opening results. After painstakingly crunching numbers and analyzing data from the Environmental Protection Agency and the US Department of Transportation spanning over four decades, we uncovered a striking correlation coefficient of 0.6924859 between these seemingly unrelated variables. To put it simply, the connection between smoggy air in Yakima and luxury car malfunctions is as clear as, well, a foggy day in Yakima.
Furthermore, our analysis revealed an r-squared value of 0.4795368, underscoring the significant proportion of variance in Mercedes-Benz USA automotive recalls that can be attributed to air pollution in Yakima. In other words, nearly half of the variability in recalls can be explained by the level of air pollution in this scenic city. That's a statistical revelation worth celebrating – maybe with a breath of fresh, unpolluted air!
And as if that weren't enough to raise eyebrows, our findings also boast a p-value less than 0.01 – indicating an extremely low probability that the observed correlation occurred by chance. In scientific terms, this means we can confidently assert that the relationship between air pollution in Yakima and Mercedes-Benz USA recalls is not just a fluke or a statistical hiccup. It's the real deal, folks.
To visually capture the essence of this revelatory correlation, we present Fig. 1, a scatterplot that graphically encapsulates the strong association between air pollution in Yakima, Washington, and automotive recalls issued by Mercedes-Benz USA. Prepare to be mesmerized by the beauty of data points aligning like stars in the night sky, albeit with a slightly less romantic backdrop – we're talking about emissions and car troubles, after all.
Our discoveries challenge preconceived notions and beckon for further investigation into this intriguing nexus of air quality and luxury automotive design. It's a reminder that in the world of scientific inquiry, even the most peculiar correlations can emerge from the statistical woodwork. This research not only opens the hood on a perplexing puzzle but also emphasizes the interconnectedness of seemingly disparate phenomena, offering a breath of fresh air to the often stifling world of academic inquiry.
So, as we revel in these surprising connections and revelatory findings, let's not forget to appreciate the whimsical dance of data that led us to this crossroads of air pollution and automotive engineering. The scientific journey is often peppered with unexpected detours and surprising intersections, and our study is a testament to the exhilarating, and sometimes downright quirky, nature of scientific exploration.

-------

Your response should start like this:

[[DISCUSSION]]

ChatGPT:

[[DISCUSSION]]

Our research has unveiled a remarkable link between air pollution in Yakima, Washington, and the automotive recalls issued by Mercedes-Benz USA, reinforcing the notion that even the most unexpected pairings can rev up the gears of statistical significance. With a correlation coefficient of 0.6924859 and a p-value less than 0.01, our findings provide compelling evidence of a relationship that's as intertwined as rush-hour traffic.

The literature review, despite its detours into whimsy, offered some serious considerations that our results have echoed. It became clear that the smoggy skies of Yakima might indeed cast a shadow on the mechanical prowess of luxury automobiles, as suggested by "Doe and Jones." Our study offers empirical support for these theoretical musings and lends credence to the notion that environmental factors play a significant role in the performance and safety of high-end vehicles.

These results also resonate with the imaginative tales found in "The Cloudy Chronicles" and childhood favorites like "The Smoggy Adventures of Captain Carbon." While these fictional narratives may seem like a drive into the realm of make-believe, our research demonstrates that the intricate dance of air pollution and automotive recalls is more than just a flight of fancy.

The correlation we've uncovered, with nearly half of the variability in recalls attributable to air pollution in Yakima, is a statistical marvel worthy of celebration. It's a reminder that in the world of research, even the most unexpected connections can emerge from the hazy mist of data analysis. And let's not overlook the visual allure of our scatterplot, where data points align like constellations in the night sky, revealing the hidden choreography of smog and automotive malfunctions.

In conclusion, our study propels us into a territory where the unexpected becomes the expected and the quirky becomes the norm. As we continue to peel back the layers of this captivating conundrum, armed with scholarly acumen and a splash of whimsy, the road ahead promises to be as unpredictable as a driver in a roundabout. So, fasten your seatbelts, folks – we're in for a wild ride through the curious confluence of emissions, recalls, and statistical revelations.

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 Yakima, Washington and Automotive recalls issued by Mercedes-Benz USA. Make lots of jokes, goofy observations, and puns. Sneak in some jokes and clever puns about science, research, statistics, and the variables.

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

Here are the title, abstract, introduction, and results sections.
[[TITLE]]
The Dirty Truth: Uncovering the Smoggy Relationship Between Air Pollution in Yakima, Washington, and the Mercedes-Benz USA Recalls

[[ABSTRACT]]
The correlation between air pollution in Yakima, Washington, and automotive recalls issued by Mercedes-Benz USA has long been a source of controversy and speculation. In this study, we delved into the swirling fog of data to unravel the mysterious connection between these two seemingly disparate factors. Leveraging data from the Environmental Protection Agency and the US Department of Transportation spanning the years 1980 to 2022, our research team uncovered a surprising correlation coefficient of 0.6924859 with the p-value less than 0.01, shedding light on a relationship that has long been clouded in uncertainty.

Our findings challenge the conventional wisdom and emphasize the need for further investigation into the murky intersection of air quality and luxury automotive engineering. This research is a breath of fresh air for a scientific community often bogged down in dry statistical analysis, offering a peek under the hood of a perplexing puzzle and revealing the unexpected ways in which air pollution and automotive recalls may be intertwined. So, buckle up and prepare for a ride through this curious connection with emissions of humor and puns that just might turbocharge your understanding of these complex dynamics.

[[INTRDUCTION]]
Ah, the sweet smell of exhaust fumes and the lulling hum of air conditioners working overtime. We find ourselves at the crossroads of two seemingly unrelated phenomena: air pollution in the picturesque Yakima, Washington, and the sleek, sophisticated world of Mercedes-Benz USA automotive recalls. It is in this unlikely collision of worlds that we embark on a quest to unravel the enigmatic relationship between these confounding variables.
Our research sets out to peel back the layers of complexity and delve into the smoggy depths of correlation, causation, and perhaps a dash of serendipity. As we navigate the treacherous terrain of statistical analysis and variable engagement, we are careful to keep our heads above the metaphorical clouds of uncertainty (and maybe a few literal ones too – thanks, Yakima).
The prevailing wisdom suggests that air pollution and luxury automobiles are about as compatible as oil and water, or in this case, oil and air. However, it is our contention that there may be more than meets the eye – or the tailpipe, as it were. Our study aims to debunk the myths and misconceptions surrounding these phenomena, steering clear of the fog of ambiguity and blazing a trail towards clarity.
Prepare yourself for an exhilarating journey through the winding roads of data analysis, where the rubber meets the road, and statistical significance meets fresh mountain air. Along the way, we’ll be wielding correlation coefficients like trusty compasses and brandishing p-values like noble swords, all in the name of shedding light on this tumultuous tango between emissions and automotive malfunctions.
So, fasten your seatbelts and grip the wheel tightly as we embark on this wild ride through the juncture of air quality and luxury automotive engineering, armed with science, statistics, and a healthy dose of wry humor. Let’s rev up our engines and embark on this intellectual joyride, traversing the terrain of Yakima’s air and Mercedes-Benz’s recalls with all the curiosity and whimsy that befits such an unexpected union.

[[RESULTS]]
In our quest to demystify the relationship between air pollution in Yakima, Washington, and automotive recalls issued by Mercedes-Benz USA, our research team unearthed some eye-opening results. After painstakingly crunching numbers and analyzing data from the Environmental Protection Agency and the US Department of Transportation spanning over four decades, we uncovered a striking correlation coefficient of 0.6924859 between these seemingly unrelated variables. To put it simply, the connection between smoggy air in Yakima and luxury car malfunctions is as clear as, well, a foggy day in Yakima.
Furthermore, our analysis revealed an r-squared value of 0.4795368, underscoring the significant proportion of variance in Mercedes-Benz USA automotive recalls that can be attributed to air pollution in Yakima. In other words, nearly half of the variability in recalls can be explained by the level of air pollution in this scenic city. That's a statistical revelation worth celebrating – maybe with a breath of fresh, unpolluted air!
And as if that weren't enough to raise eyebrows, our findings also boast a p-value less than 0.01 – indicating an extremely low probability that the observed correlation occurred by chance. In scientific terms, this means we can confidently assert that the relationship between air pollution in Yakima and Mercedes-Benz USA recalls is not just a fluke or a statistical hiccup. It's the real deal, folks.
To visually capture the essence of this revelatory correlation, we present Fig. 1, a scatterplot that graphically encapsulates the strong association between air pollution in Yakima, Washington, and automotive recalls issued by Mercedes-Benz USA. Prepare to be mesmerized by the beauty of data points aligning like stars in the night sky, albeit with a slightly less romantic backdrop – we're talking about emissions and car troubles, after all.
Our discoveries challenge preconceived notions and beckon for further investigation into this intriguing nexus of air quality and luxury automotive design. It's a reminder that in the world of scientific inquiry, even the most peculiar correlations can emerge from the statistical woodwork. This research not only opens the hood on a perplexing puzzle but also emphasizes the interconnectedness of seemingly disparate phenomena, offering a breath of fresh air to the often stifling world of academic inquiry.
So, as we revel in these surprising connections and revelatory findings, let's not forget to appreciate the whimsical dance of data that led us to this crossroads of air pollution and automotive engineering. The scientific journey is often peppered with unexpected detours and surprising intersections, and our study is a testament to the exhilarating, and sometimes downright quirky, nature of scientific exploration.

-------

Your response should start like this:

[[CONCLUSION]]

ChatGPT:

[[CONCLUSION]]

As we wrap up our exploration of the entangled web of air pollution in Yakima, Washington, and the automotive recalls issued by Mercedes-Benz USA, we find ourselves marveling at the unexpected connections that statistical analysis can unveil. It's as if we've stumbled upon a mysterious love affair between exhaust fumes and luxury automobiles, a steamy romance hidden amidst the foggy landscapes and turbocharged engines.

Our findings, with a correlation coefficient of 0.6924859, remind us that in the world of statistics, even the unlikeliest pairs can waltz to the beat of significance. It's like witnessing a statistical tango where the partners are emissions and automotive malfunctions, spinning around the dance floor of data with unconventional grace.

With an r-squared value of 0.4795368, we can confidently assert that nearly half of the variability in Mercedes-Benz USA recalls can be attributed to the level of air pollution in Yakima. That's a statistical revelation that might just make your head spin faster than a well-tuned engine.

And let's not forget the star of the show – the p-value less than 0.01, indicating that the observed correlation is so improbable it'll make your data-loving heart flutter. It's as if statistical significance and scientific whimsy have collided in a symphony of correlation that leaves us all in awe.

In the words of the great statistical bard, "All's well that ends with a p-value." Our study has shed light on this curious relationship, revealing a world where air quality and automotive design dance hand in hand, twirling through the jargon-laden halls of statistical inference.

So, as we bid adieu to the data points and scatterplots that have accompanied us on this scientific journey, we raise our beakers to the unexpected, the quirky, and the intellectually exhilarating. Truly, no more research is needed in this area, for our findings have turbocharged the understanding of this peculiar connection between Yakima's air and Mercedes-Benz's recalls. And with that, we rev our engines and drive off into the sunset of statistical discovery, leaving behind a trail of exhaust fumes and wry statistical humor.

No more research, no more riddles - it's time to cruise into the statistical sunset.

Model: gpt-3.5-turbo-1106
System prompt: You provide fictional names of academic journals. You say nothing else, and you do not chat with the user.
User prompt: Please provide the name of a funny but plausible sounding research, scientific, or academic journal that would publish a paper entited The Dirty Truth: Uncovering the Smoggy Relationship Between Air Pollution in Yakima, Washington, and the Mercedes-Benz USA Recalls. Respond only with the name of a fictional academic journal.

ChatGPT:

The Journal of Environmental Epidemiology and Automotive Anomalies

Model: gpt-3.5-turbo-1106
System prompt: You provide fictional names of nonprofit research organizations and associations. You say nothing else, and you do not chat with the user.
User prompt: Please provide the name of a funny but plausible sounding nonprofit, academic, or scientific association or organization that would sponsor research that resulted in a paper entited The Dirty Truth: Uncovering the Smoggy Relationship Between Air Pollution in Yakima, Washington, and the Mercedes-Benz USA Recalls. Respond only with the name of a fictional organization.

ChatGPT:

The Society for Ethical Inquiry and Civic Studies (SEICS)

Model: gpt-3.5-turbo-1106
System prompt: You provide potential search keywords separated by commas. You say nothing else, and you do not chat with the user.
User prompt: Please provide potential search keywords for a paper titled The Dirty Truth: Uncovering the Smoggy Relationship Between Air Pollution in Yakima, Washington, and the Mercedes-Benz USA Recalls with an abstract of The correlation between air pollution in Yakima, Washington, and automotive recalls issued by Mercedes-Benz USA has long been a source of controversy and speculation. In this study, we delved into the swirling fog of data to unravel the mysterious connection between these two seemingly disparate factors. Leveraging data from the Environmental Protection Agency and the US Department of Transportation spanning the years 1980 to 2022, our research team uncovered a surprising correlation coefficient of 0.6924859 with the p-value less than 0.01, shedding light on a relationship that has long been clouded in uncertainty.
Our findings challenge the conventional wisdom and emphasize the need for further investigation into the murky intersection of air quality and luxury automotive engineering. This research is a breath of fresh air for a scientific community often bogged down in dry statistical analysis, offering a peek under the hood of a perplexing puzzle and revealing the unexpected ways in which air pollution and automotive recalls may be intertwined. So, buckle up and prepare for a ride through this curious connection with emissions of humor and puns that just might turbocharge your understanding of these complex dynamics.

ChatGPT:

air pollution, Yakima Washington, Mercedes-Benz USA, automotive recalls, correlation coefficient, Environmental Protection Agency, US Department of Transportation, luxury automotive engineering, statistical analysis, air quality, emissions, pollution, automotive industry

*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 Yakima, Washington
Detailed data title: Percentage of days with air quality at 'unhealthy for sensitive groups' or worse in Yakima, WA
Source: Environmental Protection Agency
See what else correlates with Air pollution in Yakima, Washington

Automotive recalls issued by Mercedes-Benz USA
Detailed data title: Automotive recals issued by Mercedes-Benz USA
Source: US DOT
See what else correlates with Automotive recalls issued by Mercedes-Benz USA

Correlation r = 0.6924859 (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 = 0.4795368 (Coefficient of determination)
This means 48% of the change in the one variable (i.e., Automotive recalls issued by Mercedes-Benz USA) is predictable based on the change in the other (i.e., Air pollution in Yakima, Washington) over the 43 years from 1980 through 2022.

p < 0.01, which is statistically significant(Null hypothesis significance test)
The p-value is 2.7E-7.^Show 0.0000002679874512999277700000
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 0.69 in 2.7E-5% of random cases. Said differently, if you correlated 3,731,518 random variables^Note You don't actually need 3 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 42 degrees of freedom, ^Note Degrees of freedom is a measure of how many free components we are testing. In this case it is 42 because we have two variables measured over a period of 43 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.

[ 0.5, 0.82 ] 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.

	1980	1981	1982	1983	1984	1985	1986	1987	1988	1989	1990	1991	1992	1993	1994	1995	1996	1997	1998	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 Yakima, Washington (Bad air quality days)	0.687285	0.852273	0.561798	0.888889	1.5015	2.84091	1.64384	2.19178	0.273224	0	0	1.92837	0.278551	0	0	0	0.273224	0	0	0.277008	0.819672	1.10803	0.803213	0.813008	2.91262	3.83562	3.56164	1.91781	4.09836	2.73973	1.09589	2.74725	2.18579	4.93151	2.46575	5.50964	3.27869	7.94521	4.38356	2.73973	4.09836	7.39726	1.64384
Automotive recalls issued by Mercedes-Benz USA (Recalls)	2	0	0	2	3	2	1	2	2	0	3	1	1	3	2	2	3	1	2	4	4	6	5	3	4	5	5	3	8	3	3	4	8	4	6	18	23	38	39	33	38	49	35

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.
Outlandish outliers: There are "outliers" in this data.^Note In concept, "outlier" just means "way different than the rest of your dataset." When calculating a correlation like this, they are particularly impactful because a single outlier can substantially increase your correlation.

For the purposes of this project, I counted a point as an outlier if it the residual was two standard deviations from the mean.

(This bullet point only shows up in the details page on charts that do, in fact, have outliers.)
They stand out on the scatterplot above: notice the dots that are far away from any other dots. I intentionally mishandeled outliers, which makes the correlation look extra strong.

Try it yourself

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

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

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

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

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

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

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

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

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

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

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

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

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

    return correlation, r_squared, p_value

# These are the arrays for the variables shown on this page, but you can modify them to be any two sets of numbers
array_1 = np.array([0.687285,0.852273,0.561798,0.888889,1.5015,2.84091,1.64384,2.19178,0.273224,0,0,1.92837,0.278551,0,0,0,0.273224,0,0,0.277008,0.819672,1.10803,0.803213,0.813008,2.91262,3.83562,3.56164,1.91781,4.09836,2.73973,1.09589,2.74725,2.18579,4.93151,2.46575,5.50964,3.27869,7.94521,4.38356,2.73973,4.09836,7.39726,1.64384,])
array_2 = np.array([2,0,0,2,3,2,1,2,2,0,3,1,1,3,2,2,3,1,2,4,4,6,5,3,4,5,5,3,8,3,3,4,8,4,6,18,23,38,39,33,38,49,35,])
array_1_name = "Air pollution in Yakima, Washington"
array_2_name = "Automotive recalls issued by Mercedes-Benz USA"

# 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
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Line chart for only Air pollution in Yakima, Washington
Line chart for only Automotive recalls issued by Mercedes-Benz USA
AI-generated correlation image
The spurious research paper: The Dirty Truth: Uncovering the Smoggy Relationship Between Air Pollution in Yakima, Washington, and the Mercedes-Benz USA Recalls

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Correlation ID: 1616 · Black Variable ID: 21481 · Red Variable ID: 1122


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