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Spurious correlation #1,914 · View random

A linear line chart with years as the X-axis and two variables on the Y-axis. The first variable is The number of mechanical drafters in Colorado and the second variable is Season wins for the Denver Broncos.  The chart goes from 2003 to 2022, and the two variables track closely in value over that time. Small Image
Download png
, svg

AI explanation

As the number of mechanical drafters in Colorado decreased, there was a subtle but significant shift in the airflow dynamics across the state. This unexpected change in air currents led to a slight disruption in the trajectory of footballs during crucial game moments. Essentially, the absence of these drafters inadvertently drafted a new playbook for Mother Nature, giving a whole new meaning to the phrase "air support" for the Denver Broncos.

Model: dalle-3
Prompt: Generate an image that merges the aesthetic of steampunk with a bustling Denver city scene. The image should depict a towering office building with steam-powered machinery and gears visible through the windows. A sign outside should display the building's number, with a vintage steampunk design. In the foreground, mechanical drafters can be seen working on detailed blueprints, surrounded by an atmosphere of industrial innovation. Meanwhile, in the distance, a massive sports stadium should be visible, where fans cheer on the Denver Broncos during a sunny fall day. The scene should capture the juxtaposition of old-world steampunk technology and bustling modern city life. 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: The number of mechanical drafters in Colorado and Season wins for the Denver Broncos. 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: Low poly Voxel art Steampunk Photorealism Low poly
ChatGPT: Steampunk

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 The number of mechanical drafters in Colorado and Season wins for the Denver Broncos together. Keep the description simple.
ChatGPT: In a bustling Denver office building, rows of mechanical drafters diligently work on blueprints and designs, their number marked on a sign outside. Meanwhile, on a sunny fall day, fans cheer as the Denver Broncos secure another season win at their home stadium, the roar of the crowd echoing in the distance.

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: [ Steampunk ] and depicting this scene: In a bustling Denver office building, rows of mechanical drafters diligently work on blueprints and designs, their number marked on a sign outside. Meanwhile, on a sunny fall day, fans cheer as the Denver Broncos secure another season win at their home stadium, the roar of the crowd echoing in the distance. Keep the visual depiction simple. Do not include any words or speech bubbles.
ChatGPT: Generate an image that merges the aesthetic of steampunk with a bustling Denver city scene. The image should depict a towering office building with steam-powered machinery and gears visible through the windows. A sign outside should display the building's number, with a vintage steampunk design. In the foreground, mechanical drafters can be seen working on detailed blueprints, surrounded by an atmosphere of industrial innovation. Meanwhile, in the distance, a massive sports stadium should be visible, where fans cheer on the Denver Broncos during a sunny fall day. The scene should capture the juxtaposition of old-world steampunk technology and bustling modern city life.

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

I sequence the requests into multiple prompts because I find GPT 3.5 to perform much better with short, well-managed contexts. Thus, I track the context directly in Python and only ask ChatGPT targeted questions.

Model: gpt-3.5-turbo-1106 (fine-tuned)
System prompt: You provide humorous responses in the form of plausible sounding explanations for correlations. You assume the correlation is causative for the purpose of the explanation even if it is ridiculous. You do not chat with the user, you only reply with the causal connection explanation and nothing else.
User prompt: Please make up a funny explanation for how a decrease in The number of mechanical drafters in Colorado caused Season wins for the Denver Broncos to decrease. Make it feel plausible.

AI academic paper

(Because p < 0.01)
Drawing Conclusions: The Drafting of Mechanical Drafters in Colorado and the Quarterback Drafting for the Denver Broncos

Journal of Drafting and Quarterback Studies

Jan 2024

Reminder: This paper is AI-generated. Not real!
Quick note: This sequence is long and repetitive. That's how the prompt engineering works for this one. I manage the output in Python to format it into this PDF.




Model: gpt-3.5-turbo-1106
System prompt: You are a researcher writing an academic paper.You write titles and abstracts of goofy academic research papers.
User prompt:
Pretend you are an academic researcher. Your writing sounds like it belongs in a medical or economics journal. However, you frequently crack jokes, make puns, and add unexpected twists in your writing.

Please draft the title and abstract of an academic research paper presenting the findings of the connection between The number of mechanical drafters in Colorado and Season wins for the Denver Broncos. Make lots of jokes, goofy observations, and puns.

Make the title seem clever.

Your research team used data from Bureau of Larbor Statistics and Pro-Football-Reference.com to assess this nagging question. You found a correlation coefficient of 0.8140859 and p < 0.01 for 2003 to 2022.

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

[[TITLE]]
Lorem ipsum dolor sit

[[ABSTRACT]]
Lorem ipsum dolor sit



ChatGPT:
[[TITLE]]
"Drawing Conclusions: The Drafting of Mechanical Drafters in Colorado and the Quarterback Drafting for the Denver Broncos"

[[ABSTRACT]]
In this study, we delve into the curious interplay between the number of mechanical drafters in Colorado and the seasonal performance of the Denver Broncos. Using a combination of data from the Bureau of Labor Statistics and Pro-Football-Reference.com, we set out to unpack this perplexing puzzle. Our rigorous analysis revealed a statistically significant correlation coefficient of 0.8140859 and p < 0.01 for the period spanning 2003 to 2022. Our findings, while unexpected, point to a potential causal relationship between the drafting of mechanical drafters and the drafting of quarterbacks for the Denver Broncos. We unpack the implications of our findings and discuss the possible mechanisms underlying this surprising connection. Despite the seeming absurdity of the topic, our research sheds light on a quirky aspect of occupational dynamics and sports team performance.


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

Please make up the introduction section of an academic research paper presenting the findings of the connection between The number of mechanical drafters in Colorado and Season wins for the Denver Broncos. Make lots of jokes, goofy observations, and puns. Sneak in some jokes and clever puns about science, research, statistics, and the variables.

Here is the title and abstract of the paper:
[[TITLE]]
"Drawing Conclusions: The Drafting of Mechanical Drafters in Colorado and the Quarterback Drafting for the Denver Broncos"

[[ABSTRACT]]
In this study, we delve into the curious interplay between the number of mechanical drafters in Colorado and the seasonal performance of the Denver Broncos. Using a combination of data from the Bureau of Labor Statistics and Pro-Football-Reference.com, we set out to unpack this perplexing puzzle. Our rigorous analysis revealed a statistically significant correlation coefficient of 0.8140859 and p < 0.01 for the period spanning 2003 to 2022. Our findings, while unexpected, point to a potential causal relationship between the drafting of mechanical drafters and the drafting of quarterbacks for the Denver Broncos. We unpack the implications of our findings and discuss the possible mechanisms underlying this surprising connection. Despite the seeming absurdity of the topic, our research sheds light on a quirky aspect of occupational dynamics and sports team performance.

-------

Your response should start like this:

[[INTRODUCTION]]



ChatGPT:
Alright, buckle up, folks, because we're about to embark on a wild and wacky ride through the world of mechanical drafters and football fortunes. Our quest? To unravel the enigmatic entanglement between the number of mechanical drafters in Colorado and the seasonal wins racked up by the mighty Denver Broncos. Yes, you heard that right—drafting meets drafting in a bizarre symphony of statistics and sports.

Now, before you raise an eyebrow and question the sanity of this research endeavor, we assure you that the correlation at play here is as real as a touchdown in the last few seconds of the fourth quarter. Armed with data from the Bureau of Labor Statistics and Pro-Football-Reference.com, we dared to tread where few have dared before—into the realms of occupational demographics and gridiron glory.

Picture this: the clinking of drafting tools in Colorado's design studios and the thunderous roar of the Broncos faithful at Mile High Stadium. Seemingly disparate worlds, right? That's what we thought—until we dove into the numbers and discovered a correlation coefficient that would make even the nerdiest statistician do a touchdown dance.

We're talking about a correlation coefficient of 0.8140859, accompanied by a p-value of less than 0.01. In the world of statistics, that's as close to a smoking gun as you can get without setting off the fire alarm. But what does this all mean? Is there a causal relationship between the drafting of mechanical drafters and the drafting of quarterbacks for the Denver Broncos? Or are we just witnessing the whimsy of the statistical gods at play?

Our journey through this peculiar nexus of drafting and draft picks has led us to some unexpected and downright quirky conclusions. Buckle in as we unpack the implications of our findings and explore the potential mechanisms underlying this unlikely connection. Science, it seems, has a sense of humor—and it's throwing us a curveball that not even the trickiest quarterback could dodge.

So, grab your lab coat and your lucky Broncos jersey, because we're about to take a deep dive into the intersection of occupational dynamics and sports superstitions. Whether you're a die-hard Broncos fan, a mechanical drafter with a love for the pigskin, or just a curious soul with a penchant for the unconventional, our findings are bound to leave you scratching your head and chuckling at the delightful absurdity of it all. Welcome to the world of "Drawing Conclusions" where statistical oddities and sporting pursuits collide in the most unexpected of fashions.


Model: gpt-3.5-turbo-1106
System prompt: You are a researcher writing an academic paper.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 The number of mechanical drafters in Colorado and Season wins for the Denver Broncos. 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 movies that you watched that are tangentially related to the topic.

Here is the title and abstract of the paper:
[[TITLE]]
"Drawing Conclusions: The Drafting of Mechanical Drafters in Colorado and the Quarterback Drafting for the Denver Broncos"

[[ABSTRACT]]
In this study, we delve into the curious interplay between the number of mechanical drafters in Colorado and the seasonal performance of the Denver Broncos. Using a combination of data from the Bureau of Labor Statistics and Pro-Football-Reference.com, we set out to unpack this perplexing puzzle. Our rigorous analysis revealed a statistically significant correlation coefficient of 0.8140859 and p < 0.01 for the period spanning 2003 to 2022. Our findings, while unexpected, point to a potential causal relationship between the drafting of mechanical drafters and the drafting of quarterbacks for the Denver Broncos. We unpack the implications of our findings and discuss the possible mechanisms underlying this surprising connection. Despite the seeming absurdity of the topic, our research sheds light on a quirky aspect of occupational dynamics and sports team performance.

-------

And here is the introduction section that led to this literature review:
[[INTRODUCTION]]
Alright, buckle up, folks, because we're about to embark on a wild and wacky ride through the world of mechanical drafters and football fortunes. Our quest? To unravel the enigmatic entanglement between the number of mechanical drafters in Colorado and the seasonal wins racked up by the mighty Denver Broncos. Yes, you heard that right—drafting meets drafting in a bizarre symphony of statistics and sports.
Now, before you raise an eyebrow and question the sanity of this research endeavor, we assure you that the correlation at play here is as real as a touchdown in the last few seconds of the fourth quarter. Armed with data from the Bureau of Labor Statistics and Pro-Football-Reference.com, we dared to tread where few have dared before—into the realms of occupational demographics and gridiron glory.
Picture this: the clinking of drafting tools in Colorado's design studios and the thunderous roar of the Broncos faithful at Mile High Stadium. Seemingly disparate worlds, right? That's what we thought—until we dove into the numbers and discovered a correlation coefficient that would make even the nerdiest statistician do a touchdown dance.
We're talking about a correlation coefficient of 0.8140859, accompanied by a p-value of less than 0.01. In the world of statistics, that's as close to a smoking gun as you can get without setting off the fire alarm. But what does this all mean? Is there a causal relationship between the drafting of mechanical drafters and the drafting of quarterbacks for the Denver Broncos? Or are we just witnessing the whimsy of the statistical gods at play?
Our journey through this peculiar nexus of drafting and draft picks has led us to some unexpected and downright quirky conclusions. Buckle in as we unpack the implications of our findings and explore the potential mechanisms underlying this unlikely connection. Science, it seems, has a sense of humor—and it's throwing us a curveball that not even the trickiest quarterback could dodge.
So, grab your lab coat and your lucky Broncos jersey, because we're about to take a deep dive into the intersection of occupational dynamics and sports superstitions. Whether you're a die-hard Broncos fan, a mechanical drafter with a love for the pigskin, or just a curious soul with a penchant for the unconventional, our findings are bound to leave you scratching your head and chuckling at the delightful absurdity of it all. Welcome to the world of "Drawing Conclusions" where statistical oddities and sporting pursuits collide in the most unexpected of fashions.

-------

Your response should start like this:

[[LITERATURE REVIEW]]



ChatGPT:
[[LITERATURE REVIEW]]

To comprehend the inexplicably entertaining correlation between the number of mechanical drafters in Colorado and the seasonal performance of the Denver Broncos, we first turn to the seminal work of Smith et al. In their landmark study, "Occupational Dynamics in the Rocky Mountain Region," the authors meticulously dissect the geographical distribution and employment trends of various occupations in Colorado, shedding light on the workforce composition across diverse industries. While not explicitly delving into the realm of American football, the insights gleaned from this study laid the foundation for our quirky quest to uncover the interplay between drafting professionals and pigskin pursuits.

But let's not stop at dry data for too long. Let's make a turn towards the more comical side of literature and examine the less serious works that could shed a light on our peculiar topic. In "A Game of Drafts" by George R. R. Martin, the characters dabble not in mechanical drawings but in power struggles and strategic maneuvers—a narrative that, to our surprise, may provide unexpected parallels to the nuanced dance of drafting mechanical professionals and football stars. Additionally, in "The Drafting Dead" by Robert Kirkman, the fictional characters navigate a post-apocalyptic world overrun by zombies, a far cry from the boardrooms and playing fields we're used to, but perhaps a metaphor for the unexpected plot twists we encountered in our own research.

Just when you thought we had exhausted all possible connections, we dare to venture into the silver screen territory. Picture this: "Drafts in Our Stars," a heartwarming, albeit fictional, tale of love and hope amidst the backdrop of mechanical design and football fandom, or "The Draftscape Now," a mind-bending sci-fi thriller that may not directly touch upon our dual topic, but certainly encapsulates the bewildering nature of our findings. And let's not forget the timeless classic "The Draftfather," a cinematic masterpiece that transcends generations—much like the enduring impact of our rather peculiar research.

As we developed our literature review, it became evident that the unexpected quirks and curiosities that emerged mirrored the light-hearted absurdity of our improbable correlation. Our findings may have raised eyebrows, elicited chuckles, and perhaps even prompted a few head-scratches, but beneath the goofiness lies a genuine attempt to unravel a statistical riddle that, against all odds, may hold a kernel of truth. So, join us as we march onward, armed with curious conclusions and a wink to the whimsy of statistical serendipity. After all, in the delightful realm of academia, it never hurts to infuse a touch of whimsy and wonder into our scholarly pursuits.


Model: gpt-3.5-turbo-1106
System prompt: You are a researcher writing an academic paper.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 The number of mechanical drafters in Colorado and Season wins for the Denver Broncos. 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 Bureau of Larbor Statistics and Pro-Football-Reference.com . You used data from 2003 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]]
"Drawing Conclusions: The Drafting of Mechanical Drafters in Colorado and the Quarterback Drafting for the Denver Broncos"

[[ABSTRACT]]
In this study, we delve into the curious interplay between the number of mechanical drafters in Colorado and the seasonal performance of the Denver Broncos. Using a combination of data from the Bureau of Labor Statistics and Pro-Football-Reference.com, we set out to unpack this perplexing puzzle. Our rigorous analysis revealed a statistically significant correlation coefficient of 0.8140859 and p < 0.01 for the period spanning 2003 to 2022. Our findings, while unexpected, point to a potential causal relationship between the drafting of mechanical drafters and the drafting of quarterbacks for the Denver Broncos. We unpack the implications of our findings and discuss the possible mechanisms underlying this surprising connection. Despite the seeming absurdity of the topic, our research sheds light on a quirky aspect of occupational dynamics and sports team performance.

[[INTRODUCTION]]
Alright, buckle up, folks, because we're about to embark on a wild and wacky ride through the world of mechanical drafters and football fortunes. Our quest? To unravel the enigmatic entanglement between the number of mechanical drafters in Colorado and the seasonal wins racked up by the mighty Denver Broncos. Yes, you heard that right—drafting meets drafting in a bizarre symphony of statistics and sports.
Now, before you raise an eyebrow and question the sanity of this research endeavor, we assure you that the correlation at play here is as real as a touchdown in the last few seconds of the fourth quarter. Armed with data from the Bureau of Labor Statistics and Pro-Football-Reference.com, we dared to tread where few have dared before—into the realms of occupational demographics and gridiron glory.
Picture this: the clinking of drafting tools in Colorado's design studios and the thunderous roar of the Broncos faithful at Mile High Stadium. Seemingly disparate worlds, right? That's what we thought—until we dove into the numbers and discovered a correlation coefficient that would make even the nerdiest statistician do a touchdown dance.
We're talking about a correlation coefficient of 0.8140859, accompanied by a p-value of less than 0.01. In the world of statistics, that's as close to a smoking gun as you can get without setting off the fire alarm. But what does this all mean? Is there a causal relationship between the drafting of mechanical drafters and the drafting of quarterbacks for the Denver Broncos? Or are we just witnessing the whimsy of the statistical gods at play?
Our journey through this peculiar nexus of drafting and draft picks has led us to some unexpected and downright quirky conclusions. Buckle in as we unpack the implications of our findings and explore the potential mechanisms underlying this unlikely connection. Science, it seems, has a sense of humor—and it's throwing us a curveball that not even the trickiest quarterback could dodge.
So, grab your lab coat and your lucky Broncos jersey, because we're about to take a deep dive into the intersection of occupational dynamics and sports superstitions. Whether you're a die-hard Broncos fan, a mechanical drafter with a love for the pigskin, or just a curious soul with a penchant for the unconventional, our findings are bound to leave you scratching your head and chuckling at the delightful absurdity of it all. Welcome to the world of "Drawing Conclusions" where statistical oddities and sporting pursuits collide in the most unexpected of fashions.

-------

Your response should start like this:

[[METHODOLOGY]]



ChatGPT:

[[METHODOLOGY]]

To tackle the perplexing puzzle of the correlation between the number of mechanical drafters in Colorado and the success of the Denver Broncos, we embarked on a journey through a whimsical maze of data mining and statistical acrobatics. Our approach was as robust as a defensive line and as agile as a nimble quarterback evading a blitz. Here’s how we navigated this quirky quagmire:

Data Collection:
We scoured the vast expanse of the internet, from the hallowed halls of the Bureau of Labor Statistics to the sacred archives of Pro-Football-Reference.com, in search of the holy grail of statistics. Our data extended from 2003 to 2022, capturing the ebbs and flows of mechanical drafting and gridiron glory over nearly two decades. We obtained employment counts for mechanical drafters in the state of Colorado and meticulously documented the seasonal wins, losses, and ties of the Denver Broncos.

Statistical Analysis:
With our treasure trove of data in hand, we employed a nifty array of statistical tools to disentangle the enigmatic relationship at play. We calculated correlation coefficients with the precision of a seasoned referee making a crucial call and wielded p-values like a discerning coach choosing plays that could tip the scales of a game. Our analysis unleashed the full might of regression models, drawing patterns and connections with the finesse of a meticulous playmaker mapping out strategic maneuvers on the field.

Controlling for Confounders:
In our pursuit of robust and reliable findings, we were acutely aware of the lurking specter of confounding variables, poised to throw a wrench in our statistical machinery. We diligently controlled for factors such as quarterback performance, team dynamics, and economic fluctuations, ensuring that our results remained as crisp and clear as a quarterback’s vision in the pocket.

Caveats and Limitations:
As with any scientific endeavor, we treaded cautiously amidst the pitfalls of limitations and caveats. We recognized the inherent whimsy of our research topic and the potential for unforeseen variables to pop up like unexpected fumbles on the field. Nevertheless, armed with statistical rigor and a healthy dose of skepticism, we navigated these treacherous territories with the grace of a seasoned tight end making a critical catch.

In sum, our methodology danced to the rhythm of science and statistics, while embracing the unpredictable nature of our research question. With a blend of rigor and whimsy, we ventured forth to uncover the curious connection between the drafting of mechanical drafters and the drafting of quarterbacks for the Denver Broncos. And in the end, we emerged with findings that paint a vivid picture of the strange and delightful interplay between occupational demographics and the gridiron’s grand tapestry.


Model: gpt-3.5-turbo-1106
System prompt: You are a researcher writing an academic paper.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 The number of mechanical drafters in Colorado and Season wins for the Denver Broncos. 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 Bureau of Larbor Statistics and Pro-Football-Reference.com .

For the time period 2003 to 2022, you found a correlation 0.8140859, r-squared of 0.6627358, 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]]
"Drawing Conclusions: The Drafting of Mechanical Drafters in Colorado and the Quarterback Drafting for the Denver Broncos"

[[ABSTRACT]]
In this study, we delve into the curious interplay between the number of mechanical drafters in Colorado and the seasonal performance of the Denver Broncos. Using a combination of data from the Bureau of Labor Statistics and Pro-Football-Reference.com, we set out to unpack this perplexing puzzle. Our rigorous analysis revealed a statistically significant correlation coefficient of 0.8140859 and p < 0.01 for the period spanning 2003 to 2022. Our findings, while unexpected, point to a potential causal relationship between the drafting of mechanical drafters and the drafting of quarterbacks for the Denver Broncos. We unpack the implications of our findings and discuss the possible mechanisms underlying this surprising connection. Despite the seeming absurdity of the topic, our research sheds light on a quirky aspect of occupational dynamics and sports team performance.

-------

And here is the methodology section that led to this result:
[[METHODOLOGY]]
Alright, buckle up, folks, because we're about to embark on a wild and wacky ride through the world of mechanical drafters and football fortunes. Our quest? To unravel the enigmatic entanglement between the number of mechanical drafters in Colorado and the seasonal wins racked up by the mighty Denver Broncos. Yes, you heard that right—drafting meets drafting in a bizarre symphony of statistics and sports.
Now, before you raise an eyebrow and question the sanity of this research endeavor, we assure you that the correlation at play here is as real as a touchdown in the last few seconds of the fourth quarter. Armed with data from the Bureau of Labor Statistics and Pro-Football-Reference.com, we dared to tread where few have dared before—into the realms of occupational demographics and gridiron glory.
Picture this: the clinking of drafting tools in Colorado's design studios and the thunderous roar of the Broncos faithful at Mile High Stadium. Seemingly disparate worlds, right? That's what we thought—until we dove into the numbers and discovered a correlation coefficient that would make even the nerdiest statistician do a touchdown dance.
We're talking about a correlation coefficient of 0.8140859, accompanied by a p-value of less than 0.01. In the world of statistics, that's as close to a smoking gun as you can get without setting off the fire alarm. But what does this all mean? Is there a causal relationship between the drafting of mechanical drafters and the drafting of quarterbacks for the Denver Broncos? Or are we just witnessing the whimsy of the statistical gods at play?
Our journey through this peculiar nexus of drafting and draft picks has led us to some unexpected and downright quirky conclusions. Buckle in as we unpack the implications of our findings and explore the potential mechanisms underlying this unlikely connection. Science, it seems, has a sense of humor—and it's throwing us a curveball that not even the trickiest quarterback could dodge.
So, grab your lab coat and your lucky Broncos jersey, because we're about to take a deep dive into the intersection of occupational dynamics and sports superstitions. Whether you're a die-hard Broncos fan, a mechanical drafter with a love for the pigskin, or just a curious soul with a penchant for the unconventional, our findings are bound to leave you scratching your head and chuckling at the delightful absurdity of it all. Welcome to the world of "Drawing Conclusions" where statistical oddities and sporting pursuits collide in the most unexpected of fashions.

-------

Your response should start like this:

[[RESULTS]]



ChatGPT:

[[RESULTS]]

After an intrepid journey into the world of mechanical drafters and football fandom, our research team discovered a surprising and robust correlation between the number of mechanical drafters in Colorado and the seasonal wins for the Denver Broncos. Drumroll, please! Our analysis revealed a correlation coefficient of 0.8140859, indicating a strong positive relationship between these seemingly disparate variables. In addition, the r-squared value of 0.6627358 suggests that approximately 66.27% of the variance in the Broncos' seasonal wins can be explained by the number of mechanical drafters in the state. Now, that's a statistical touchdown if I've ever seen one!

But hold on to your lab goggles, because the most mind-blowing part is yet to come. The p-value of less than 0.01 indicates that this correlation is not just a fluke. In the world of statistical significance, this finding is as rock-solid as a meticulously designed architectural blueprint.

To visually capture the strength of this relationship, we present Figure 1, a scatterplot displaying the unmistakable correlation between the number of mechanical drafters in Colorado and the Denver Broncos' seasonal wins. It's a sight to behold, folks, and a testament to the unexpected wonders that statistical research can unearth.


Model: gpt-3.5-turbo-1106
System prompt: You are a researcher writing an academic paper.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 The number of mechanical drafters in Colorado and Season wins for the Denver Broncos. 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]]
"Drawing Conclusions: The Drafting of Mechanical Drafters in Colorado and the Quarterback Drafting for the Denver Broncos"

[[ABSTRACT]]
In this study, we delve into the curious interplay between the number of mechanical drafters in Colorado and the seasonal performance of the Denver Broncos. Using a combination of data from the Bureau of Labor Statistics and Pro-Football-Reference.com, we set out to unpack this perplexing puzzle. Our rigorous analysis revealed a statistically significant correlation coefficient of 0.8140859 and p < 0.01 for the period spanning 2003 to 2022. Our findings, while unexpected, point to a potential causal relationship between the drafting of mechanical drafters and the drafting of quarterbacks for the Denver Broncos. We unpack the implications of our findings and discuss the possible mechanisms underlying this surprising connection. Despite the seeming absurdity of the topic, our research sheds light on a quirky aspect of occupational dynamics and sports team performance.

[[LITERATURE REVIEW]]
To comprehend the inexplicably entertaining correlation between the number of mechanical drafters in Colorado and the seasonal performance of the Denver Broncos, we first turn to the seminal work of Smith et al. In their landmark study, "Occupational Dynamics in the Rocky Mountain Region," the authors meticulously dissect the geographical distribution and employment trends of various occupations in Colorado, shedding light on the workforce composition across diverse industries. While not explicitly delving into the realm of American football, the insights gleaned from this study laid the foundation for our quirky quest to uncover the interplay between drafting professionals and pigskin pursuits.
But let's not stop at dry data for too long. Let's make a turn towards the more comical side of literature and examine the less serious works that could shed a light on our peculiar topic. In "A Game of Drafts" by George R. R. Martin, the characters dabble not in mechanical drawings but in power struggles and strategic maneuvers—a narrative that, to our surprise, may provide unexpected parallels to the nuanced dance of drafting mechanical professionals and football stars. Additionally, in "The Drafting Dead" by Robert Kirkman, the fictional characters navigate a post-apocalyptic world overrun by zombies, a far cry from the boardrooms and playing fields we're used to, but perhaps a metaphor for the unexpected plot twists we encountered in our own research.
Just when you thought we had exhausted all possible connections, we dare to venture into the silver screen territory. Picture this: "Drafts in Our Stars," a heartwarming, albeit fictional, tale of love and hope amidst the backdrop of mechanical design and football fandom, or "The Draftscape Now," a mind-bending sci-fi thriller that may not directly touch upon our dual topic, but certainly encapsulates the bewildering nature of our findings. And let's not forget the timeless classic "The Draftfather," a cinematic masterpiece that transcends generations—much like the enduring impact of our rather peculiar research.
As we developed our literature review, it became evident that the unexpected quirks and curiosities that emerged mirrored the light-hearted absurdity of our improbable correlation. Our findings may have raised eyebrows, elicited chuckles, and perhaps even prompted a few head-scratches, but beneath the goofiness lies a genuine attempt to unravel a statistical riddle that, against all odds, may hold a kernel of truth. So, join us as we march onward, armed with curious conclusions and a wink to the whimsy of statistical serendipity. After all, in the delightful realm of academia, it never hurts to infuse a touch of whimsy and wonder into our scholarly pursuits.

[[RESULTS]]
After an intrepid journey into the world of mechanical drafters and football fandom, our research team discovered a surprising and robust correlation between the number of mechanical drafters in Colorado and the seasonal wins for the Denver Broncos. Drumroll, please! Our analysis revealed a correlation coefficient of 0.8140859, indicating a strong positive relationship between these seemingly disparate variables. In addition, the r-squared value of 0.6627358 suggests that approximately 66.27% of the variance in the Broncos' seasonal wins can be explained by the number of mechanical drafters in the state. Now, that's a statistical touchdown if I've ever seen one!
But hold on to your lab goggles, because the most mind-blowing part is yet to come. The p-value of less than 0.01 indicates that this correlation is not just a fluke. In the world of statistical significance, this finding is as rock-solid as a meticulously designed architectural blueprint.
To visually capture the strength of this relationship, we present Figure 1, a scatterplot displaying the unmistakable correlation between the number of mechanical drafters in Colorado and the Denver Broncos' seasonal wins. It's a sight to behold, folks, and a testament to the unexpected wonders that statistical research can unearth.

-------

Your response should start like this:

[[DISCUSSION]]



ChatGPT:

[[DISCUSSION]]

Well, folks, hold onto your helmets as we dive into the delightful dance of data and the gridiron glory. Our results have indeed painted a picture as vivid and bold as a cheerleader's pom-poms. The link between the number of mechanical drafters in Colorado and the Denver Broncos' seasonal wins seems to be as clear as a 4th-quarter Hail Mary!

Our study's findings have aligned with the scholarly musings of Smith et al., who laid the groundwork for our research. By golly, those sage insights into occupational dynamics in the Rocky Mountain region set the stage for our unexpected touchdown of a discovery. And let's not forget our comically curious traversing through literature, from the strategic maneuvers of "A Game of Drafts" to the unlikely pairing of mechanical designs and pigskin pursuits in "Drafts in Our Stars." Who would've thunk that our goofy literary romp would find such resonance with our scientific exploits?

Now, to tackle the meat and potatoes of our results. We have unearthed a robust correlation and a p-value as solid as a perfectly constructed paper airplane. With an r-squared value of approximately 66.27%, it seems that our study has Mitchell-and-Ness'ed a significant portion of the variance in the Broncos' wins. It's as if our statistical findings have donned the orange and blue with pride!

The consensus of our results leaves us with one intriguing question: what in the world could be fueling this unexpected linkage between the drafting of mechanical talent and the drafting of gridiron gladiators? Is it the mountain air infusing drafts with a touch of magic, or perhaps statistical serendipity playing its mischievous hand? Regardless, our study stands as a delightful testament to the whimsy of the research world.

In the grand tapestry of academia, it's always delightful to stumble upon a statistical touchdown in the most unexpected of places. Let's revel in the statistical antics that brought us to this exhilarating revelation and hail the Broncos with a resounding "Draft On!"


Model: gpt-3.5-turbo-1106
System prompt: You are a researcher writing an academic paper.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 The number of mechanical drafters in Colorado and Season wins for the Denver Broncos. 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]]
"Drawing Conclusions: The Drafting of Mechanical Drafters in Colorado and the Quarterback Drafting for the Denver Broncos"

[[ABSTRACT]]
In this study, we delve into the curious interplay between the number of mechanical drafters in Colorado and the seasonal performance of the Denver Broncos. Using a combination of data from the Bureau of Labor Statistics and Pro-Football-Reference.com, we set out to unpack this perplexing puzzle. Our rigorous analysis revealed a statistically significant correlation coefficient of 0.8140859 and p < 0.01 for the period spanning 2003 to 2022. Our findings, while unexpected, point to a potential causal relationship between the drafting of mechanical drafters and the drafting of quarterbacks for the Denver Broncos. We unpack the implications of our findings and discuss the possible mechanisms underlying this surprising connection. Despite the seeming absurdity of the topic, our research sheds light on a quirky aspect of occupational dynamics and sports team performance.

[[INTRDUCTION]]
Alright, buckle up, folks, because we're about to embark on a wild and wacky ride through the world of mechanical drafters and football fortunes. Our quest? To unravel the enigmatic entanglement between the number of mechanical drafters in Colorado and the seasonal wins racked up by the mighty Denver Broncos. Yes, you heard that right—drafting meets drafting in a bizarre symphony of statistics and sports.
Now, before you raise an eyebrow and question the sanity of this research endeavor, we assure you that the correlation at play here is as real as a touchdown in the last few seconds of the fourth quarter. Armed with data from the Bureau of Labor Statistics and Pro-Football-Reference.com, we dared to tread where few have dared before—into the realms of occupational demographics and gridiron glory.
Picture this: the clinking of drafting tools in Colorado's design studios and the thunderous roar of the Broncos faithful at Mile High Stadium. Seemingly disparate worlds, right? That's what we thought—until we dove into the numbers and discovered a correlation coefficient that would make even the nerdiest statistician do a touchdown dance.
We're talking about a correlation coefficient of 0.8140859, accompanied by a p-value of less than 0.01. In the world of statistics, that's as close to a smoking gun as you can get without setting off the fire alarm. But what does this all mean? Is there a causal relationship between the drafting of mechanical drafters and the drafting of quarterbacks for the Denver Broncos? Or are we just witnessing the whimsy of the statistical gods at play?
Our journey through this peculiar nexus of drafting and draft picks has led us to some unexpected and downright quirky conclusions. Buckle in as we unpack the implications of our findings and explore the potential mechanisms underlying this unlikely connection. Science, it seems, has a sense of humor—and it's throwing us a curveball that not even the trickiest quarterback could dodge.
So, grab your lab coat and your lucky Broncos jersey, because we're about to take a deep dive into the intersection of occupational dynamics and sports superstitions. Whether you're a die-hard Broncos fan, a mechanical drafter with a love for the pigskin, or just a curious soul with a penchant for the unconventional, our findings are bound to leave you scratching your head and chuckling at the delightful absurdity of it all. Welcome to the world of "Drawing Conclusions" where statistical oddities and sporting pursuits collide in the most unexpected of fashions.

[[RESULTS]]
After an intrepid journey into the world of mechanical drafters and football fandom, our research team discovered a surprising and robust correlation between the number of mechanical drafters in Colorado and the seasonal wins for the Denver Broncos. Drumroll, please! Our analysis revealed a correlation coefficient of 0.8140859, indicating a strong positive relationship between these seemingly disparate variables. In addition, the r-squared value of 0.6627358 suggests that approximately 66.27% of the variance in the Broncos' seasonal wins can be explained by the number of mechanical drafters in the state. Now, that's a statistical touchdown if I've ever seen one!
But hold on to your lab goggles, because the most mind-blowing part is yet to come. The p-value of less than 0.01 indicates that this correlation is not just a fluke. In the world of statistical significance, this finding is as rock-solid as a meticulously designed architectural blueprint.
To visually capture the strength of this relationship, we present Figure 1, a scatterplot displaying the unmistakable correlation between the number of mechanical drafters in Colorado and the Denver Broncos' seasonal wins. It's a sight to behold, folks, and a testament to the unexpected wonders that statistical research can unearth.

-------

Your response should start like this:

[[CONCLUSION]]



ChatGPT:

[[CONCLUSION]]

In conclusion, our foray into the whimsical world of mechanical drafters and Denver Broncos' wins has revealed a correlation that is as surprising as finding a football in a drafting studio. With a correlation coefficient of 0.8140859 and a p-value of less than 0.01, the bond between these unlikely bedfellows is as strong as Von Miller sacking a rival quarterback. Our findings suggest that about 66.27% of the Broncos' seasonal wins can be explained by the number of mechanical drafters in Colorado—a statistical twist that even the most seasoned researcher could hardly foresee.

The implications of our research are as puzzling as an unexpected onside kick. Do the drafting of mechanical drafters influence the drafting decisions of the Broncos' quarterbacks, or is it merely the statistical cosmos playing a mischievous game? It's a head-scratcher that even the most astute scientist would find as confounding as a reverse psychology play call.

Our study not only sheds light on this quirky correlation but also serves as a reminder that in the vast universe of data, surprises lurk where we least expect them. It's a reminder that statistical analysis, much like a football game, can be full of unexpected turns, blindside hits, and game-changing interceptions.

So, as we hang up our lab coats and stash away our football jerseys, we declare that this quirky conundrum has been given the thorough investigation it deserves. There's no need for a rematch, no overtime required, and certainly no need for further research in this delightfully peculiar tale of drafting dynamics and gridiron glory. It's a touchdown for statistical oddities and occupational enigmas, and as the final whistle blows, we bid adieu to this improbable intersection of mechanical mastery and mile-high victories.

In the immortal words of the late, great John Madden, "Boom! Tough actin' Tinactin!"


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 Drawing Conclusions: The Drafting of Mechanical Drafters in Colorado and the Quarterback Drafting for the Denver Broncos. Respond only with the name of a fictional academic journal.

ChatGPT:

Journal of Drafting and Quarterback Studies


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 Drawing Conclusions: The Drafting of Mechanical Drafters in Colorado and the Quarterback Drafting for the Denver Broncos. Respond only with the name of a fictional organization.

ChatGPT:

The Society for Whimsical Research and Nonsensical Studies


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 Drawing Conclusions: The Drafting of Mechanical Drafters in Colorado and the Quarterback Drafting for the Denver Broncos with an abstract of In this study, we delve into the curious interplay between the number of mechanical drafters in Colorado and the seasonal performance of the Denver Broncos. Using a combination of data from the Bureau of Labor Statistics and Pro-Football-Reference.com, we set out to unpack this perplexing puzzle. Our rigorous analysis revealed a statistically significant correlation coefficient of 0.8140859 and p < 0.01 for the period spanning 2003 to 2022. Our findings, while unexpected, point to a potential causal relationship between the drafting of mechanical drafters and the drafting of quarterbacks for the Denver Broncos. We unpack the implications of our findings and discuss the possible mechanisms underlying this surprising connection. Despite the seeming absurdity of the topic, our research sheds light on a quirky aspect of occupational dynamics and sports team performance.

ChatGPT:

mechanical drafters, Colorado, Denver Broncos, drafting, correlation, occupational dynamics, sports team performance

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



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Data details

The number of mechanical drafters in Colorado
Detailed data title: BLS estimate of mechanical drafters in Colorado
Source: Bureau of Larbor Statistics
See what else correlates with The number of mechanical drafters in Colorado

Season wins for the Denver Broncos
Detailed data title: Number of season wins by the Denver Broncos
Source: Pro-Football-Reference.com
See what else correlates with Season wins for the Denver Broncos

Correlation r = 0.8140859 (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 = 0.6627358 (Coefficient of determination)
This means 66.3% of the change in the one variable (i.e., Season wins for the Denver Broncos) is predictable based on the change in the other (i.e., The number of mechanical drafters in Colorado) over the 20 years from 2003 through 2022.

p < 0.01, which is statistically significant(Null hypothesis significance test)
The p-value is 1.3E-5. 0.0000125561336704749800000000
The p-value is a measure of how probable it is that we would randomly find a result this extreme. More specifically the p-value is a measure of how probable it is that we would randomly find a result this extreme if we had only tested one pair of variables one time.

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

Who is going to stop me? p-value reporting doesn't require me to report how many calculations I had to go through in order to find a low p-value!
On average, you will find a correaltion as strong as 0.81 in 0.0013% of random cases. Said differently, if you correlated 79,642 random variables You don't actually need 79 thousand variables to find a correlation like this one. I don't have that many variables in my database. You can also correlate variables that are not independent. I do this a lot.

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

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

Just to be clear: I'm being completely transparent about the calculations. There is no math trickery. This is just how statistics shakes out when you calculate hundreds of millions of random correlations.
with the same 19 degrees of freedom, Degrees of freedom is a measure of how many free components we are testing. In this case it is 19 because we have two variables measured over a period of 20 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.

[ 0.58, 0.92 ] 95% correlation confidence interval (using the Fisher z-transformation)
The confidence interval is an estimate the range of the value of the correlation coefficient, using the correlation itself as an input. The values are meant to be the low and high end of the correlation coefficient with 95% confidence.

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


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

Still, sometimes one of the variables has more years of data available than the other. This page only shows the overlapping years. To see all the years, click on "See what else correlates with..." link above.
20032004200520062007200820092010201120122013201420152016201720182019202020212022
The number of mechanical drafters in Colorado (Mechanical Drafters)98010109607407707506706808409509601000960880600530440540620720
Season wins for the Denver Broncos (Broncos wins)101013978848131312129567575




Why this works

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




Try it yourself

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

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

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

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

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

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

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

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

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


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

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

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

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

    return correlation, r_squared, p_value

# These are the arrays for the variables shown on this page, but you can modify them to be any two sets of numbers
array_1 = np.array([980,1010,960,740,770,750,670,680,840,950,960,1000,960,880,600,530,440,540,620,720,])
array_2 = np.array([10,10,13,9,7,8,8,4,8,13,13,12,12,9,5,6,7,5,7,5,])
array_1_name = "The number of mechanical drafters in Colorado"
array_2_name = "Season wins for the Denver Broncos"

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

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



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

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

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

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Correlation ID: 1914 · Black Variable ID: 5681 · Red Variable ID: 19657
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