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Spurious correlation #5,181 · View random

A linear line chart with years as the X-axis and two variables on the Y-axis. The first variable is Libertarian votes for Senators in Michigan and the second variable is Jet fuel used in Cambodia.  The chart goes from 1995 to 2014, and the two variables track closely in value over that time. Small Image

AI explanation

As Libertarian votes soared in Michigan, their platform of limited government intervention took off like a jet, inspiring Cambodian fuel suppliers to also go full throttle. It seems the fervor for freedom in one place can really fuel change in another!

Model: dalle-3
Prompt: Prompt: Generate an image of a comical scene where a cartoonish jet emblazoned with the libertarian party's logo is soaring over the state of Michigan, with voters below enthusiastically casting their votes. Meanwhile, in a separate scene, depict a group of cartoonish fuel suppliers in Cambodia revving up their engines with a mischievous expression, symbolizing the global momentum of the Libertarian movement. The overall tone should be lighthearted and humorous. 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: Libertarian votes for Senators in Michigan and Jet fuel used in Cambodia. 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: 3D Pixar Style 3D Pixar Style An image that looks like it is a scene from 'Star Wars' a funny image macro Brutalism
ChatGPT: a funny image macro

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 Libertarian votes for Senators in Michigan and Jet fuel used in Cambodia, in the following situation: As Libertarian votes soared in Michigan, their platform of limited government intervention took off like a jet, inspiring Cambodian fuel suppliers to also go full throttle. It seems the fervor for freedom in one place can really fuel change in another!. Keep the description simple.
ChatGPT: In Michigan, a wave of Libertarian supporters cast their votes for Senators, their message of limited government intervention taking flight like a jet across the state. Meanwhile, in Cambodia, fuel suppliers were seen revving up their engines, mirroring the momentum of the Libertarian movement across the globe.

Model: gpt-3.5-turbo-1106
System prompt: You write and improve image generation prompts for DALLE-3. You maintain the same subjects, but enhance the visuals.
User prompt: Please respond with an image generation prompt that would be likely to create an interesting visual using DALLE-3, using the following style: [ a funny image macro ] and depicting this scene: In Michigan, a wave of Libertarian supporters cast their votes for Senators, their message of limited government intervention taking flight like a jet across the state. Meanwhile, in Cambodia, fuel suppliers were seen revving up their engines, mirroring the momentum of the Libertarian movement across the globe. Keep the visual depiction simple. Do not include any words or speech bubbles.
ChatGPT: Prompt: Generate an image of a comical scene where a cartoonish jet emblazoned with the libertarian party's logo is soaring over the state of Michigan, with voters below enthusiastically casting their votes. Meanwhile, in a separate scene, depict a group of cartoonish fuel suppliers in Cambodia revving up their engines with a mischievous expression, symbolizing the global momentum of the Libertarian movement. The overall tone should be lighthearted and humorous.

*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 an increase in Libertarian votes for Senators in Michigan caused Jet fuel used in Cambodia to increase. Include one good pun.

AI academic paper

(Because p < 0.01)
The Jet Set: Exploring the Connection Between Libertarian Votes in Michigan and Jet Fuel Consumption in Cambodia

The Journal of Interconnected Absurdities

Jan 2024
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 witty academic researcher. Your writing sounds like it belongs in a statistics journal.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 Libertarian votes for Senators in Michigan and Jet fuel used in Cambodia. Make it seem dry like academic research paper, but with lots of subtle hidden offhand remarks, jokes, goofy observations, and puns.

Make the title punny if you can come up with clever pun. If not, just make it sound clever.

Your research team used data from MIT Election Data and Science Lab, Harvard Dataverse and Energy Information Administration to assess this nagging question. You found a correlation coefficient of 0.9359837 and p < 0.01 for 1995 to 2014.

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]]
The Jet Set: Exploring the Connection Between Libertarian Votes in Michigan and Jet Fuel Consumption in Cambodia

[[ABSTRACT]]
This paper investigates the seemingly unrelated yet curiously intertwined relationship between the level of Libertarian votes for Senators in Michigan and the amount of jet fuel used in Cambodia. By utilizing data from MIT Election Data and Science Lab, Harvard Dataverse, and the Energy Information Administration, we applied statistical analysis to scrutinize this curious connection. Our findings revealed a striking correlation coefficient of 0.9359837 with a significance level of p < 0.01 for the period spanning 1995 to 2014. The unexpected entanglement of these variables prompts a closer examination, shedding light on the vibrant and unpredictable nature of political and environmental data. This study underscores the need for interdisciplinary exploration, recognizing that statistical relationships can bring unexpected surprises akin to uncovering a hidden treasure trove.


Model: gpt-3.5-turbo-1106
System prompt: You are a witty academic researcher. Your writing sounds like it belongs in a statistics journal.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 Libertarian votes for Senators in Michigan and Jet fuel used in Cambodia. Make it seem dry like academic research paper, but with lots of subtle hidden offhand remarks, 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]]
The Jet Set: Exploring the Connection Between Libertarian Votes in Michigan and Jet Fuel Consumption in Cambodia

[[ABSTRACT]]
This paper investigates the seemingly unrelated yet curiously intertwined relationship between the level of Libertarian votes for Senators in Michigan and the amount of jet fuel used in Cambodia. By utilizing data from MIT Election Data and Science Lab, Harvard Dataverse, and the Energy Information Administration, we applied statistical analysis to scrutinize this curious connection. Our findings revealed a striking correlation coefficient of 0.9359837 with a significance level of p < 0.01 for the period spanning 1995 to 2014. The unexpected entanglement of these variables prompts a closer examination, shedding light on the vibrant and unpredictable nature of political and environmental data. This study underscores the need for interdisciplinary exploration, recognizing that statistical relationships can bring unexpected surprises akin to uncovering a hidden treasure trove.

-------

Your response should start like this:

[[INTRODUCTION]]



ChatGPT:
[[INTRODUCTION]]

Anecdotal connections often bewilder researchers, akin to finding a match in a haystack, or perhaps, a jet in a haystack. Against this backdrop, we aim to delve into the curious correlation between Libertarian votes for Senators in Michigan and the consumption of jet fuel in Cambodia. While on the surface, these variables may appear as disparate as a Republican in a sea of Democrats, our preliminary analysis has unveiled an unexpected link that is as surprising as discovering a statistical unicorn.

As researchers, we are constantly urged to unearth meaningful relationships amidst the labyrinth of data, akin to deciphering a P-value puzzle or untangling a covariate conundrum. With the aid of data from MIT Election Data and Science Lab, Harvard Dataverse, and the Energy Information Administration, we have embarked on a statistical voyage to discern the entwined nature of these unforeseen bedfellows. Our endeavor is akin to being detectives of data, seeking to untangle the web of statistical intrigue that has cast its spell on these seemingly incongruous variables.

The symmetry between electoral choices in the Great Lakes State and the consumption of aviation fuel in Southeast Asia prompts a medley of curious questions and eyebrow-raising interpretations, akin to a rollercoaster ride through a statistical carnival. This investigation, therefore, promises to be as enlightening as uncovering a hidden dataset gem, and as intriguing as stumbling upon a statistical eureka moment.

Together, we embark on this academic journey to highlight the capricious and capacious nature of data relationships, recognizing that within the statistical sea of variables, unexpected connections can emerge like undiscovered scientific species. This study serves as a testament to the serendipitous wonders of statistical exploration, where the threads of correlation weave a compelling narrative, akin to uncovering a random forest amidst the empirical undergrowth.


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

Please make up a literature review section of an academic research paper presenting the findings of the connection between Libertarian votes for Senators in Michigan and Jet fuel used in Cambodia. Make it seem dry like academic research paper, but with lots of subtle hidden offhand remarks, jokes, goofy observations, and puns.

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

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

Start by naming serious-sounding studies by authors like Smith, Doe, and Jones - but then quickly devolve. Name some real non-fiction books that would be related to the topic. Then name some real fiction books that sound like they could be related. Then name some movies that you watched that are tangentially related to the topic.

Here is the title and abstract of the paper:
[[TITLE]]
The Jet Set: Exploring the Connection Between Libertarian Votes in Michigan and Jet Fuel Consumption in Cambodia

[[ABSTRACT]]
This paper investigates the seemingly unrelated yet curiously intertwined relationship between the level of Libertarian votes for Senators in Michigan and the amount of jet fuel used in Cambodia. By utilizing data from MIT Election Data and Science Lab, Harvard Dataverse, and the Energy Information Administration, we applied statistical analysis to scrutinize this curious connection. Our findings revealed a striking correlation coefficient of 0.9359837 with a significance level of p < 0.01 for the period spanning 1995 to 2014. The unexpected entanglement of these variables prompts a closer examination, shedding light on the vibrant and unpredictable nature of political and environmental data. This study underscores the need for interdisciplinary exploration, recognizing that statistical relationships can bring unexpected surprises akin to uncovering a hidden treasure trove.

-------

And here is the introduction section that led to this literature review:
[[INTRODUCTION]]
Anecdotal connections often bewilder researchers, akin to finding a match in a haystack, or perhaps, a jet in a haystack. Against this backdrop, we aim to delve into the curious correlation between Libertarian votes for Senators in Michigan and the consumption of jet fuel in Cambodia. While on the surface, these variables may appear as disparate as a Republican in a sea of Democrats, our preliminary analysis has unveiled an unexpected link that is as surprising as discovering a statistical unicorn.
As researchers, we are constantly urged to unearth meaningful relationships amidst the labyrinth of data, akin to deciphering a P-value puzzle or untangling a covariate conundrum. With the aid of data from MIT Election Data and Science Lab, Harvard Dataverse, and the Energy Information Administration, we have embarked on a statistical voyage to discern the entwined nature of these unforeseen bedfellows. Our endeavor is akin to being detectives of data, seeking to untangle the web of statistical intrigue that has cast its spell on these seemingly incongruous variables.
The symmetry between electoral choices in the Great Lakes State and the consumption of aviation fuel in Southeast Asia prompts a medley of curious questions and eyebrow-raising interpretations, akin to a rollercoaster ride through a statistical carnival. This investigation, therefore, promises to be as enlightening as uncovering a hidden dataset gem, and as intriguing as stumbling upon a statistical eureka moment.
Together, we embark on this academic journey to highlight the capricious and capacious nature of data relationships, recognizing that within the statistical sea of variables, unexpected connections can emerge like undiscovered scientific species. This study serves as a testament to the serendipitous wonders of statistical exploration, where the threads of correlation weave a compelling narrative, akin to uncovering a random forest amidst the empirical undergrowth.

-------

Your response should start like this:

[[LITERATURE REVIEW]]



ChatGPT:
[[LITERATURE REVIEW]]

A multiplicity of studies have delved into the realm of political behavior and environmental impact, though few have ventured into the intriguing territory that lies at the intersection of Libertarian votes in Michigan and jet fuel consumption in Cambodia. Smith et al. (2012) explored the sociopolitical dynamics of voting patterns in the Great Lakes region, while Doe (2014) investigated the nuances of energy consumption in Southeast Asia. Jones and colleagues (2017) delved into the economic implications of third-party votes in U.S. Senate elections, providing a foundation for understanding the political landscape in which the Libertarian Party operates.

As we venture deeper into the literature on unrelated and obscure correlations, it is prudent to consider the wider expanse of knowledge that may bear upon our seemingly peculiar inquiry. In "Liberty and Energy: The Unlikely Affair" (2015), the authors draw parallels between political ideologies and environmental policy, offering a poignant analysis of the interplay between libertarian values and energy usage. "The Air and the Unfettered Mind" (2016) provides a philosophical reflection on the impact of air travel on human consciousness, presenting a series of metaphors that may offer insights into the enigmatic relationship between senatorial votes and jet fuel.

Addendum to the discourse encompasses fictitious narratives that, nonetheless, convey a semblance of relevance to our esoteric pursuit. In "Wings of Political Liberty" (2000), the protagonist navigates a world where political affiliations determine access to aviation fuel, capturing the essence of our investigation in an allegorical tapestry. Similarly, "The Cambodian Candidate" (2012) weaves a tale of electoral intrigue amid a backdrop of international fossil fuel trade, offering a fictive representation of the enigmatic relationship manifest in our statistical foray.

Moreover, the broader cultural landscape has not been void of cinematic expressions that, while not directly addressing our research question, bear semblance to the tangential themes therein. "Flying High: Detroit to Phnom Penh" (1999) offers a cinematic interpretation of the unexplored web of transcontinental travel, as seen through the lens of interpersonal connections rooted in the political ethos of the times. Similarly, "The Libertarian Jet Set" (2013) provides a satirical perspective on the intersecting worlds of political agency and global aviation, underscoring the humorous undertones that often accompany the seemingly juxtaposed subjects of our inquiry.

In the reflective pursuit of understanding the perplexing association between seemingly unrelated variables, it is imperative to recognize the broader scholarly and creative milieu, which, by virtue of its diversity, brings to light unexpected resonances and idiosyncrasies. Thus, as we lay the groundwork for further explorations, we recognize the potential for interdisciplinary engagement in untangling the obscure, the unexpected, and the statistically peculiar.


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

Please make up the methodology section of an academic research paper presenting the findings of the connection between Libertarian votes for Senators in Michigan and Jet fuel used in Cambodia. Make it seem dry like academic research paper, but with lots of subtle hidden offhand remarks, 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 MIT Election Data and Science Lab, Harvard Dataverse and Energy Information Administration . You used data from 1995 to 2014

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 Jet Set: Exploring the Connection Between Libertarian Votes in Michigan and Jet Fuel Consumption in Cambodia

[[ABSTRACT]]
This paper investigates the seemingly unrelated yet curiously intertwined relationship between the level of Libertarian votes for Senators in Michigan and the amount of jet fuel used in Cambodia. By utilizing data from MIT Election Data and Science Lab, Harvard Dataverse, and the Energy Information Administration, we applied statistical analysis to scrutinize this curious connection. Our findings revealed a striking correlation coefficient of 0.9359837 with a significance level of p < 0.01 for the period spanning 1995 to 2014. The unexpected entanglement of these variables prompts a closer examination, shedding light on the vibrant and unpredictable nature of political and environmental data. This study underscores the need for interdisciplinary exploration, recognizing that statistical relationships can bring unexpected surprises akin to uncovering a hidden treasure trove.

[[INTRODUCTION]]
Anecdotal connections often bewilder researchers, akin to finding a match in a haystack, or perhaps, a jet in a haystack. Against this backdrop, we aim to delve into the curious correlation between Libertarian votes for Senators in Michigan and the consumption of jet fuel in Cambodia. While on the surface, these variables may appear as disparate as a Republican in a sea of Democrats, our preliminary analysis has unveiled an unexpected link that is as surprising as discovering a statistical unicorn.
As researchers, we are constantly urged to unearth meaningful relationships amidst the labyrinth of data, akin to deciphering a P-value puzzle or untangling a covariate conundrum. With the aid of data from MIT Election Data and Science Lab, Harvard Dataverse, and the Energy Information Administration, we have embarked on a statistical voyage to discern the entwined nature of these unforeseen bedfellows. Our endeavor is akin to being detectives of data, seeking to untangle the web of statistical intrigue that has cast its spell on these seemingly incongruous variables.
The symmetry between electoral choices in the Great Lakes State and the consumption of aviation fuel in Southeast Asia prompts a medley of curious questions and eyebrow-raising interpretations, akin to a rollercoaster ride through a statistical carnival. This investigation, therefore, promises to be as enlightening as uncovering a hidden dataset gem, and as intriguing as stumbling upon a statistical eureka moment.
Together, we embark on this academic journey to highlight the capricious and capacious nature of data relationships, recognizing that within the statistical sea of variables, unexpected connections can emerge like undiscovered scientific species. This study serves as a testament to the serendipitous wonders of statistical exploration, where the threads of correlation weave a compelling narrative, akin to uncovering a random forest amidst the empirical undergrowth.

-------

Your response should start like this:

[[METHODOLOGY]]



ChatGPT:

[[METHODOLOGY]]

The methodology for this investigation involved a kaleidoscope of statistical techniques and data analysis methods, akin to peering through the lens of a research microscope, with curiosity as our guide and statistical significance as our compass. To begin this scientific odyssey, we embarked on a quest for data from the MIT Election Data and Science Lab, Harvard Dataverse, and the Energy Information Administration, akin to navigating a labyrinth in search of the lost city of R-squared.

Our first step, akin to the stepping stones of a statistical river, involved the collection of electoral data regarding Libertarian votes for Senators in Michigan from the chasms of the internet. Simultaneously, we extracted the voluminous information on jet fuel consumption in Cambodia from the Energy Information Administration, a task resembling deciphering hieroglyphics from the statistical pyramids of data repositories.

Once these datasets were compiled, we embarked on a statistical voyage, akin to navigating treacherous statistical waters with the statistical stars as our guide, towards the harbor of correlation. Utilizing the time series analysis approach, we sought to encapsulate the temporal dynamics of both the electoral choices in Michigan and the consumption of jet fuel in Cambodia, peppering our statistical arsenal with autoregressive integrated moving average (ARIMA) models, a statistical savoir-faire that can untangle the enigmatic dance of time series data.

To further enrich our statistical landscape, we employed Granger causality tests, a potent tool in unlocking the causal relationship between the two variables, akin to uncovering the elusive key to a statistical treasure chest. We meticulously scrutinized the statistical significance of the findings, mindful of the potential pitfalls lurking within the statistical matrix, akin to tiptoeing through a statistical minefield.

Moreover, we augmented our analysis with a cross-spectral coherence examination, a method resembling a symphonic performance where the harmonious statistical melodies of Libertarian votes and jet fuel consumption intertwined, culminating in a statistically-charged symphony of unanticipated correlation.

In parallel, we conducted a state-space modeling analysis, akin to navigating through the statistical cosmos, capturing the latent states of these variables and the complex interplay between Michigan's political milieu and Cambodia's jet fuel demands. This approach allowed us to unravel the hidden narrative woven within the statistical tapestry, akin to decrypting statistical hieroglyphs etched on the walls of empirical temples.

Finally, we validated the robustness of our findings through Monte Carlo simulations, a statistical ensemble of fictional journeys through a simulated landscape, guiding us through the labyrinth of statistical truth. This comprehensive methodology ensured that our exploration of the connection between Libertarian votes in Michigan and jet fuel consumption in Cambodia was anchored in robust statistical rigour, akin to constructing a statistical lighthouse to illuminate the murky waters of variable entwinement.


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

Please make up the results section of an academic research paper presenting the findings of the connection between Libertarian votes for Senators in Michigan and Jet fuel used in Cambodia. Make it seem dry like academic research paper, but with lots of subtle hidden offhand remarks, 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 MIT Election Data and Science Lab, Harvard Dataverse and Energy Information Administration .

For the time period 1995 to 2014, you found a correlation 0.9359837, r-squared of 0.8760655, 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 Jet Set: Exploring the Connection Between Libertarian Votes in Michigan and Jet Fuel Consumption in Cambodia

[[ABSTRACT]]
This paper investigates the seemingly unrelated yet curiously intertwined relationship between the level of Libertarian votes for Senators in Michigan and the amount of jet fuel used in Cambodia. By utilizing data from MIT Election Data and Science Lab, Harvard Dataverse, and the Energy Information Administration, we applied statistical analysis to scrutinize this curious connection. Our findings revealed a striking correlation coefficient of 0.9359837 with a significance level of p < 0.01 for the period spanning 1995 to 2014. The unexpected entanglement of these variables prompts a closer examination, shedding light on the vibrant and unpredictable nature of political and environmental data. This study underscores the need for interdisciplinary exploration, recognizing that statistical relationships can bring unexpected surprises akin to uncovering a hidden treasure trove.

-------

And here is the methodology section that led to this result:
[[METHODOLOGY]]
Anecdotal connections often bewilder researchers, akin to finding a match in a haystack, or perhaps, a jet in a haystack. Against this backdrop, we aim to delve into the curious correlation between Libertarian votes for Senators in Michigan and the consumption of jet fuel in Cambodia. While on the surface, these variables may appear as disparate as a Republican in a sea of Democrats, our preliminary analysis has unveiled an unexpected link that is as surprising as discovering a statistical unicorn.
As researchers, we are constantly urged to unearth meaningful relationships amidst the labyrinth of data, akin to deciphering a P-value puzzle or untangling a covariate conundrum. With the aid of data from MIT Election Data and Science Lab, Harvard Dataverse, and the Energy Information Administration, we have embarked on a statistical voyage to discern the entwined nature of these unforeseen bedfellows. Our endeavor is akin to being detectives of data, seeking to untangle the web of statistical intrigue that has cast its spell on these seemingly incongruous variables.
The symmetry between electoral choices in the Great Lakes State and the consumption of aviation fuel in Southeast Asia prompts a medley of curious questions and eyebrow-raising interpretations, akin to a rollercoaster ride through a statistical carnival. This investigation, therefore, promises to be as enlightening as uncovering a hidden dataset gem, and as intriguing as stumbling upon a statistical eureka moment.
Together, we embark on this academic journey to highlight the capricious and capacious nature of data relationships, recognizing that within the statistical sea of variables, unexpected connections can emerge like undiscovered scientific species. This study serves as a testament to the serendipitous wonders of statistical exploration, where the threads of correlation weave a compelling narrative, akin to uncovering a random forest amidst the empirical undergrowth.

-------

Your response should start like this:

[[RESULTS]]



ChatGPT:

[[RESULTS]]
In our quest to unravel the mystical entanglement between Libertarian votes for Senators in Michigan and jet fuel consumption in Cambodia, we discovered a remarkable correlation coefficient of 0.9359837, with an r-squared of 0.8760655, and a p-value of less than 0.01. This robust correlation emerged as quite the statistical jackpot, akin to stumbling upon a treasure trove of data amidst the statistical wilderness.
The sheer strength of the relationship between these seemingly disparate variables is as surprising as finding a needle in a haystack made entirely of statistical significance. It's as if the Statistical Fairy waved her magic wand over these data points, producing a remarkable dance of correlation that leaves even the most seasoned statisticians bewildered.
To visually encapsulate the extraordinary connection we unearthed, we provide Figure 1, a scatterplot that graphically portrays the strong and undeniable relationship between the level of Libertarian votes in Michigan and jet fuel consumption in Cambodia. This visual representation serves as a compelling testament to the unanticipated alignment of these variables, much like uncovering a rare and remarkable statistical gem within the vast expanse of data landscapes.
The serendipitous findings of this investigation underscore the unpredictability and revelry hidden within the realm of statistical exploration. Just as a cryptic crossword puzzle can lead to unexpected revelations, so too does this exploration of the improbable correlation between political choices and environmental fuel consumption shed light on the delightful mysteries that lurk within the numerical undergrowth of statistical analysis.


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

Please make up the discussion section of an academic research paper presenting the findings of the connection between Libertarian votes for Senators in Michigan and Jet fuel used in Cambodia. Make it seem dry like academic research paper, but with lots of subtle hidden offhand remarks, 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 Jet Set: Exploring the Connection Between Libertarian Votes in Michigan and Jet Fuel Consumption in Cambodia

[[ABSTRACT]]
This paper investigates the seemingly unrelated yet curiously intertwined relationship between the level of Libertarian votes for Senators in Michigan and the amount of jet fuel used in Cambodia. By utilizing data from MIT Election Data and Science Lab, Harvard Dataverse, and the Energy Information Administration, we applied statistical analysis to scrutinize this curious connection. Our findings revealed a striking correlation coefficient of 0.9359837 with a significance level of p < 0.01 for the period spanning 1995 to 2014. The unexpected entanglement of these variables prompts a closer examination, shedding light on the vibrant and unpredictable nature of political and environmental data. This study underscores the need for interdisciplinary exploration, recognizing that statistical relationships can bring unexpected surprises akin to uncovering a hidden treasure trove.

[[LITERATURE REVIEW]]
A multiplicity of studies have delved into the realm of political behavior and environmental impact, though few have ventured into the intriguing territory that lies at the intersection of Libertarian votes in Michigan and jet fuel consumption in Cambodia. Smith et al. (2012) explored the sociopolitical dynamics of voting patterns in the Great Lakes region, while Doe (2014) investigated the nuances of energy consumption in Southeast Asia. Jones and colleagues (2017) delved into the economic implications of third-party votes in U.S. Senate elections, providing a foundation for understanding the political landscape in which the Libertarian Party operates.
As we venture deeper into the literature on unrelated and obscure correlations, it is prudent to consider the wider expanse of knowledge that may bear upon our seemingly peculiar inquiry. In "Liberty and Energy: The Unlikely Affair" (2015), the authors draw parallels between political ideologies and environmental policy, offering a poignant analysis of the interplay between libertarian values and energy usage. "The Air and the Unfettered Mind" (2016) provides a philosophical reflection on the impact of air travel on human consciousness, presenting a series of metaphors that may offer insights into the enigmatic relationship between senatorial votes and jet fuel.
Addendum to the discourse encompasses fictitious narratives that, nonetheless, convey a semblance of relevance to our esoteric pursuit. In "Wings of Political Liberty" (2000), the protagonist navigates a world where political affiliations determine access to aviation fuel, capturing the essence of our investigation in an allegorical tapestry. Similarly, "The Cambodian Candidate" (2012) weaves a tale of electoral intrigue amid a backdrop of international fossil fuel trade, offering a fictive representation of the enigmatic relationship manifest in our statistical foray.
Moreover, the broader cultural landscape has not been void of cinematic expressions that, while not directly addressing our research question, bear semblance to the tangential themes therein. "Flying High: Detroit to Phnom Penh" (1999) offers a cinematic interpretation of the unexplored web of transcontinental travel, as seen through the lens of interpersonal connections rooted in the political ethos of the times. Similarly, "The Libertarian Jet Set" (2013) provides a satirical perspective on the intersecting worlds of political agency and global aviation, underscoring the humorous undertones that often accompany the seemingly juxtaposed subjects of our inquiry.
In the reflective pursuit of understanding the perplexing association between seemingly unrelated variables, it is imperative to recognize the broader scholarly and creative milieu, which, by virtue of its diversity, brings to light unexpected resonances and idiosyncrasies. Thus, as we lay the groundwork for further explorations, we recognize the potential for interdisciplinary engagement in untangling the obscure, the unexpected, and the statistically peculiar.

[[RESULTS]]
In our quest to unravel the mystical entanglement between Libertarian votes for Senators in Michigan and jet fuel consumption in Cambodia, we discovered a remarkable correlation coefficient of 0.9359837, with an r-squared of 0.8760655, and a p-value of less than 0.01. This robust correlation emerged as quite the statistical jackpot, akin to stumbling upon a treasure trove of data amidst the statistical wilderness.
The sheer strength of the relationship between these seemingly disparate variables is as surprising as finding a needle in a haystack made entirely of statistical significance. It's as if the Statistical Fairy waved her magic wand over these data points, producing a remarkable dance of correlation that leaves even the most seasoned statisticians bewildered.
To visually encapsulate the extraordinary connection we unearthed, we provide Figure 1, a scatterplot that graphically portrays the strong and undeniable relationship between the level of Libertarian votes in Michigan and jet fuel consumption in Cambodia. This visual representation serves as a compelling testament to the unanticipated alignment of these variables, much like uncovering a rare and remarkable statistical gem within the vast expanse of data landscapes.
The serendipitous findings of this investigation underscore the unpredictability and revelry hidden within the realm of statistical exploration. Just as a cryptic crossword puzzle can lead to unexpected revelations, so too does this exploration of the improbable correlation between political choices and environmental fuel consumption shed light on the delightful mysteries that lurk within the numerical undergrowth of statistical analysis.

-------

Your response should start like this:

[[DISCUSSION]]



ChatGPT:

[[DISCUSSION]]

The revelatory expedition into the interconnected realms of political choices and environmental fuel consumption has yielded intriguing findings that beckon us to reassess our preconceptions and embark on a whimsical journey through the labyrinth of statistical inquiry. Our study, akin to stepping into a veritable forest of data where the trees of statistical significance hide in plain sight, not only verified but also augmented the existing discourse on the junction between Libertarian votes in Michigan and jet fuel usage in Cambodia.

Our results stand as a testament to the remarkable resilience and vibrant unpredictability of statistical relationships, much like a treasure map leading us through the uncharted territories of improbable correlation. The robust correlation coefficient we unearthed mirrors the awe-inducing marvel of stumbling upon a rare and exquisite gemstone in the midst of statistical rough terrain. Though initially perplexing, our findings resonate with the parallel discourse presented in "Wings of Political Liberty" (2000), where the protagonist ventures through a world where political inclinations hold sway over access to aviation fuel. This parallel narrative, though fictional, bears an uncanny resemblance to the reality unearthed by our statistical delving.

The affable dance of correlation between Libertarian votes in Michigan and jet fuel consumption in Cambodia, portrayed vividly in our scatterplot akin to a dazzling performance by statistical virtuosos, extends an invitation to set forth on further explorations into unanticipated resonances and peculiar anomalies within the tapestry of obscure statistical associations. It is as if the statistics deities themselves orchestrated this captivating liaison between variables, inviting us to marvel at the dazzling spectacle of statistical serendipity.

In conclusion, this investigation serves as a testament to the captivating whimsy that accompanies delving into the arcane recesses of statistical exploration. Much like embarking on an unexpected voyage to uncover hidden treasures, our foray into the world of seemingly unrelated variables has unraveled a tale of spellbinding interconnection. As we navigate through the uncharted waters of statistical wonder, we are compelled to embrace the delightful mysteries that lurk within the numerical undergrowth, reminding us that statistical exploration is not merely a pursuit of knowledge, but a grand, unpredictable adventure.


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

Please make up a short conclusion of an academic research paper presenting the findings of the connection between Libertarian votes for Senators in Michigan and Jet fuel used in Cambodia. Make it seem dry like academic research paper, but with lots of subtle hidden offhand remarks, 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 Jet Set: Exploring the Connection Between Libertarian Votes in Michigan and Jet Fuel Consumption in Cambodia

[[ABSTRACT]]
This paper investigates the seemingly unrelated yet curiously intertwined relationship between the level of Libertarian votes for Senators in Michigan and the amount of jet fuel used in Cambodia. By utilizing data from MIT Election Data and Science Lab, Harvard Dataverse, and the Energy Information Administration, we applied statistical analysis to scrutinize this curious connection. Our findings revealed a striking correlation coefficient of 0.9359837 with a significance level of p < 0.01 for the period spanning 1995 to 2014. The unexpected entanglement of these variables prompts a closer examination, shedding light on the vibrant and unpredictable nature of political and environmental data. This study underscores the need for interdisciplinary exploration, recognizing that statistical relationships can bring unexpected surprises akin to uncovering a hidden treasure trove.

[[INTRDUCTION]]
Anecdotal connections often bewilder researchers, akin to finding a match in a haystack, or perhaps, a jet in a haystack. Against this backdrop, we aim to delve into the curious correlation between Libertarian votes for Senators in Michigan and the consumption of jet fuel in Cambodia. While on the surface, these variables may appear as disparate as a Republican in a sea of Democrats, our preliminary analysis has unveiled an unexpected link that is as surprising as discovering a statistical unicorn.
As researchers, we are constantly urged to unearth meaningful relationships amidst the labyrinth of data, akin to deciphering a P-value puzzle or untangling a covariate conundrum. With the aid of data from MIT Election Data and Science Lab, Harvard Dataverse, and the Energy Information Administration, we have embarked on a statistical voyage to discern the entwined nature of these unforeseen bedfellows. Our endeavor is akin to being detectives of data, seeking to untangle the web of statistical intrigue that has cast its spell on these seemingly incongruous variables.
The symmetry between electoral choices in the Great Lakes State and the consumption of aviation fuel in Southeast Asia prompts a medley of curious questions and eyebrow-raising interpretations, akin to a rollercoaster ride through a statistical carnival. This investigation, therefore, promises to be as enlightening as uncovering a hidden dataset gem, and as intriguing as stumbling upon a statistical eureka moment.
Together, we embark on this academic journey to highlight the capricious and capacious nature of data relationships, recognizing that within the statistical sea of variables, unexpected connections can emerge like undiscovered scientific species. This study serves as a testament to the serendipitous wonders of statistical exploration, where the threads of correlation weave a compelling narrative, akin to uncovering a random forest amidst the empirical undergrowth.

[[RESULTS]]
In our quest to unravel the mystical entanglement between Libertarian votes for Senators in Michigan and jet fuel consumption in Cambodia, we discovered a remarkable correlation coefficient of 0.9359837, with an r-squared of 0.8760655, and a p-value of less than 0.01. This robust correlation emerged as quite the statistical jackpot, akin to stumbling upon a treasure trove of data amidst the statistical wilderness.
The sheer strength of the relationship between these seemingly disparate variables is as surprising as finding a needle in a haystack made entirely of statistical significance. It's as if the Statistical Fairy waved her magic wand over these data points, producing a remarkable dance of correlation that leaves even the most seasoned statisticians bewildered.
To visually encapsulate the extraordinary connection we unearthed, we provide Figure 1, a scatterplot that graphically portrays the strong and undeniable relationship between the level of Libertarian votes in Michigan and jet fuel consumption in Cambodia. This visual representation serves as a compelling testament to the unanticipated alignment of these variables, much like uncovering a rare and remarkable statistical gem within the vast expanse of data landscapes.
The serendipitous findings of this investigation underscore the unpredictability and revelry hidden within the realm of statistical exploration. Just as a cryptic crossword puzzle can lead to unexpected revelations, so too does this exploration of the improbable correlation between political choices and environmental fuel consumption shed light on the delightful mysteries that lurk within the numerical undergrowth of statistical analysis.

-------

Your response should start like this:

[[CONCLUSION]]



ChatGPT:

[[CONCLUSION]]

In conclusion, our investigation into the seemingly fanciful yet surprisingly robust correlation between the level of Libertarian votes for Senators in Michigan and the consumption of jet fuel in Cambodia has unveiled an unexpected intertwining of these variables. The remarkable correlation coefficient of 0.9359837, coupled with a minuscule p-value, showcases a statistical marvel akin to witnessing a unicorn trotting across a scatterplot.

Much like stumbling upon an improbable equation or discovering an anomalous outlier, this study has demonstrated the enigmatic and capricious nature of statistical relationships. The unexpected coherence between political preferences in the American Midwest and jet fuel consumption in the heart of Southeast Asia serves as a compelling reminder that within the intricate tapestry of statistical data, surprises and mysteries abound.

As researchers, we are no strangers to unearthing statistical treasures amidst the empirical undergrowth, and the correlation uncovered in this study stands as a testament to the serendipitous wonders of interdisciplinary exploration. It is akin to encountering a statistical quirk that elicits both bewilderment and scholarly delight, reminiscent of uncovering a hidden dataset gem within the expansive terrain of empirical inquiry.

With these findings, we assert that further exploration into this beguiling connection between political choices and environmental factors may yield diminishing returns, much like a diminishing marginal utility curve in economic theory. Therefore, we cautiously conclude that the unexpected coherence observed in this study may stand as a statistical curiosity without necessitating further research.


Model: gpt-3.5-turbo-1106
System prompt: You provide fictional names of academic journals. You say nothing else, and you do not chat with the user.
User prompt: Please provide the name of a funny but plausible sounding research, scientific, or academic journal that would publish a paper entited The Jet Set: Exploring the Connection Between Libertarian Votes in Michigan and Jet Fuel Consumption in Cambodia. Respond only with the name of a fictional academic journal.

ChatGPT:

The Journal of Interconnected Absurdities


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 Jet Set: Exploring the Connection Between Libertarian Votes in Michigan and Jet Fuel Consumption in Cambodia. Respond only with the name of a fictional organization.

ChatGPT:

The Society for Global Energy Economics and Political Analysis


Model: gpt-3.5-turbo-1106
System prompt: You provide potential search keywords separated by commas. You say nothing else, and you do not chat with the user.
User prompt: Please provide potential search keywords for a paper titled The Jet Set: Exploring the Connection Between Libertarian Votes in Michigan and Jet Fuel Consumption in Cambodia with an abstract of This paper investigates the seemingly unrelated yet curiously intertwined relationship between the level of Libertarian votes for Senators in Michigan and the amount of jet fuel used in Cambodia. By utilizing data from MIT Election Data and Science Lab, Harvard Dataverse, and the Energy Information Administration, we applied statistical analysis to scrutinize this curious connection. Our findings revealed a striking correlation coefficient of 0.9359837 with a significance level of p < 0.01 for the period spanning 1995 to 2014. The unexpected entanglement of these variables prompts a closer examination, shedding light on the vibrant and unpredictable nature of political and environmental data. This study underscores the need for interdisciplinary exploration, recognizing that statistical relationships can bring unexpected surprises akin to uncovering a hidden treasure trove.

ChatGPT:

Libertarian votes, Michigan Senators, jet fuel consumption, Cambodia, MIT Election Data and Science Lab, Harvard Dataverse, Energy Information Administration, statistical analysis, correlation coefficient, interdisciplinary exploration

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



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Data details

Libertarian votes for Senators in Michigan
Detailed data title: Percentage of votes cast for Federal Libertarian Senate candidates in Michigan
Source: MIT Election Data and Science Lab, Harvard Dataverse
See what else correlates with Libertarian votes for Senators in Michigan

Jet fuel used in Cambodia
Detailed data title: Volume of jet fuel used consumed in Cambodia in millions of barrels per day
Source: Energy Information Administration
See what else correlates with Jet fuel used in Cambodia

Correlation r = 0.9359837 (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 = 0.8760655 (Coefficient of determination)
This means 87.6% of the change in the one variable (i.e., Jet fuel used in Cambodia) is predictable based on the change in the other (i.e., Libertarian votes for Senators in Michigan) over the 6 years from 1995 through 2014.

p < 0.01, which is statistically significant(Null hypothesis significance test)
The p-value is 0.00602. 0.0060159521917848380000000000
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 0.94 in 0.602% of random cases. Said differently, if you correlated 166 random variables Which I absolutely did.
with the same 5 degrees of freedom, Degrees of freedom is a measure of how many free components we are testing. In this case it is 5 because we have two variables measured over a period of 6 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.

[ 0.52, 0.99 ] 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.
199620002006200820122014
Libertarian votes for Senators in Michigan (Percentage of votes)0.9810040.7190080.7145761.574611.815632.01479
Jet fuel used in Cambodia (Million Barrels/Day)0.30.390.4996990.9533331.49911.99879




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.
  4. Very low n: There are not many data points included in this analysis. Even if the p-value is high, we should be suspicious of using so few datapoints in a correlation.




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([0.981004,0.719008,0.714576,1.57461,1.81563,2.01479,])
array_2 = np.array([0.3,0.39,0.499699,0.953333,1.4991,1.99879,])
array_1_name = "Libertarian votes for Senators in Michigan"
array_2_name = "Jet fuel used in Cambodia"

# 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 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. 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.

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Correlation ID: 5181 · Black Variable ID: 26405 · Red Variable ID: 24265
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