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Spurious correlation #1,638 · View random

A linear line chart with years as the X-axis and two variables on the Y-axis. The first variable is Air pollution in Amarillo, Texas and the second variable is Canadian Natural Resources' stock price (CNQ).  The chart goes from 2002 to 2023, and the two variables track closely in value over that time. Small Image
Download png
, svg

AI explanation

As the air pollution in Amarillo, Texas rose, more people started cranking up the AC to combat the smog. This led to an increase in demand for electricity, causing a surge in power consumption. Since Canadian Natural Resources is an energy company, their stock price (CNQ) got a breath of fresh air and rose as they profited from selling more power. It seems like CNQ is just riding the smoggy wave of success!

Model: dalle-3
Prompt: Create an image of a TIME magazine cover featuring a smoggy sky over Amarillo, Texas, with a subtle hint of pollution lingering in the air. Meanwhile, the stock ticker displays a downward trend in the stock price of Canadian Natural Resources, capturing the juxtaposition of environmental impact and financial decline. The image should evoke a sense of environmental concern and economic implication without the need for any text or speech bubbles. The depiction should include only scenes, people, and objects, it should not include text or speech bubbles.
This image generation prompt was also generated by AI, using the following sequence:

Model: gpt-3.5-turbo-1106
System prompt: You select one of a few potential scene descriptors that seems to go along with the variables described. You respond only with the scene descriptions provided and say nothing else.
User prompt: Here are two variables: Less than ideal air quality in Amarillo, Texas and Canadian Natural Resources' stock price. 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: Charcoal Woodblock painting A TIME magazine cover image Pop art Cute 2D animation
ChatGPT: A TIME magazine cover image

Model: gpt-3.5-turbo-1106
System prompt: You describe simple visual scenes that depict the two variables stated. You combine both variables into one scene.
User prompt: Please describe a visual scene that prominently depicts both Less than ideal air quality in Amarillo, Texas and Canadian Natural Resources' stock price together. Keep the description simple.
ChatGPT: In Amarillo, Texas, the sky appears hazy with a noticeable thin layer of smog, and a slight smell of pollution in the air. Meanwhile, on the stock ticker, Canadian Natural Resources' stock price is shown with a downward trend, indicating a slight decline.

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 TIME magazine cover image ] and depicting this scene: In Amarillo, Texas, the sky appears hazy with a noticeable thin layer of smog, and a slight smell of pollution in the air. Meanwhile, on the stock ticker, Canadian Natural Resources' stock price is shown with a downward trend, indicating a slight decline. Keep the visual depiction simple. Do not include any words or speech bubbles.
ChatGPT: Create an image of a TIME magazine cover featuring a smoggy sky over Amarillo, Texas, with a subtle hint of pollution lingering in the air. Meanwhile, the stock ticker displays a downward trend in the stock price of Canadian Natural Resources, capturing the juxtaposition of environmental impact and financial decline. The image should evoke a sense of environmental concern and economic implication without the need for any text or speech bubbles.

*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 Air pollution in Amarillo, Texas caused Canadian Natural Resources' stock price (CNQ) to increase. Include one good pun.

AI academic paper

(Because p < 0.01)
Smogged in Stocks: The Air Pollution-Amarillo Connection and CNQ Stock Price Effects

The Journal of Ecological Economics and Financial Impact 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 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 Air pollution in Amarillo, Texas and Canadian Natural Resources' stock price (CNQ). You can't resist a good dad joke. Add a relevant dad joke related to the content every couple of sentences.

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

Your research team used data from Environmental Protection Agency and LSEG Analytics (Refinitiv) to assess this nagging question. You found a correlation coefficient of 0.8191433 and p < 0.01 for 2002 to 2023.

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]]
"Smogged in Stocks: The Air Pollution-Amarillo Connection and CNQ Stock Price Effects"

[[ABSTRACT]]
This paper delves into the unexpected connection between air pollution in Amarillo, Texas and the stock price of Canadian Natural Resources (CNQ). We conducted a rigorous analysis using data from the Environmental Protection Agency and LSEG Analytics (Refinitiv) to answer the pressing question, "How does air pollution in Amarillo relate to CNQ stock price movements?" Our findings reveal a significant correlation coefficient of 0.8191433 with p < 0.01 over the period from 2002 to 2023.

Our results suggest that as air pollution levels in Amarillo rise, it is associated with fluctuations in CNQ stock price, bringing a breath of fresh air to the field of econometric analysis. It seems that the stock market may be quite "sensitive" to the environmental conditions in seemingly distant locations, much like a sensitive nose to pungent fumes.

Understanding this connection offers valuable insights into the interplay between environmental factors and financial markets, painting a picture of pollution's influence that is both smoggy and financially weighty. It appears that when it comes to assessing CNQ stock price, the air isn't the only thing that's "hazy" - the relationship with Amarillo's air pollution levels seems to be a bit foggy as well!


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 Air pollution in Amarillo, Texas and Canadian Natural Resources' stock price (CNQ). You can't resist a good dad joke. Add a relevant dad joke related to the content every couple of sentences. Stay serious and dry most of the time, but then occasionally let your wit shine through.

Here is the title and abstract of the paper:
[[TITLE]]
"Smogged in Stocks: The Air Pollution-Amarillo Connection and CNQ Stock Price Effects"

[[ABSTRACT]]
This paper delves into the unexpected connection between air pollution in Amarillo, Texas and the stock price of Canadian Natural Resources (CNQ). We conducted a rigorous analysis using data from the Environmental Protection Agency and LSEG Analytics (Refinitiv) to answer the pressing question, "How does air pollution in Amarillo relate to CNQ stock price movements?" Our findings reveal a significant correlation coefficient of 0.8191433 with p < 0.01 over the period from 2002 to 2023.

Our results suggest that as air pollution levels in Amarillo rise, it is associated with fluctuations in CNQ stock price, bringing a breath of fresh air to the field of econometric analysis. It seems that the stock market may be quite "sensitive" to the environmental conditions in seemingly distant locations, much like a sensitive nose to pungent fumes.

Understanding this connection offers valuable insights into the interplay between environmental factors and financial markets, painting a picture of pollution's influence that is both smoggy and financially weighty. It appears that when it comes to assessing CNQ stock price, the air isn't the only thing that's "hazy" - the relationship with Amarillo's air pollution levels seems to be a bit foggy as well!

-------

Your response should start like this:

[[INTRODUCTION]]



ChatGPT:
[[INTRODUCTION]]

The link between environmental conditions and financial markets has been a subject of growing interest and concern. As the world grapples with the consequences of climate change and the urgency to transition towards sustainable practices, understanding how environmental factors impact economic indicators has become increasingly crucial. In this vein, our study takes a closer look at the unexpected relationship between air pollution in Amarillo, Texas, and the stock price of Canadian Natural Resources (CNQ).

Now, you might be thinking, "What do air pollution in Texas and CNQ stock price have in common? Is there an invisible smokescreen affecting the financial health of the energy sector?" Well, our research sets out to answer these questions by peering through the haze of data to uncover the connections that may not be immediately apparent.

The idea that air pollution in Amarillo, Texas, could have any bearing on a Canadian energy company's stock price might seem far-fetched, like trying to find fresh air in a crowded city. However, our analysis challenges these preconceptions and unearths a relationship that is statistically robust, much like a sturdy umbrella in a storm of confounding variables.

Our investigation aims to shed light on this previously overlooked aspect of environmental and financial entanglement, illuminating the pathways through which air pollution in Amarillo may swirl into the intricate fabric of CNQ's stock price movements. It's time to clear the air, both literally and metaphorically, in the realm of economic analysis.

As we embark on this journey of exploration, we envision a landscape dotted with data points, where the numbers whisper hints of hidden correlations, much like a secret code waiting to be deciphered. So, let us venture forth into the smoggy terrain of Amarillo's air pollution and financial markets, armed with our analytical compass and a healthy dose of statistical rigor.


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 Air pollution in Amarillo, Texas and Canadian Natural Resources' stock price (CNQ). You can't resist a good dad joke. Add a relevant dad joke related to the content every couple of sentences.

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

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

Start by naming serious-sounding studies by authors like Smith, Doe, and Jones - but then quickly devolve. Name some real non-fiction books that would be related to the topic. Then name some real fiction books that sound like they could be related. Then name a couple popular internet memes that are related to one of the topics.

Here is the title and abstract of the paper:
[[TITLE]]
"Smogged in Stocks: The Air Pollution-Amarillo Connection and CNQ Stock Price Effects"

[[ABSTRACT]]
This paper delves into the unexpected connection between air pollution in Amarillo, Texas and the stock price of Canadian Natural Resources (CNQ). We conducted a rigorous analysis using data from the Environmental Protection Agency and LSEG Analytics (Refinitiv) to answer the pressing question, "How does air pollution in Amarillo relate to CNQ stock price movements?" Our findings reveal a significant correlation coefficient of 0.8191433 with p < 0.01 over the period from 2002 to 2023.

Our results suggest that as air pollution levels in Amarillo rise, it is associated with fluctuations in CNQ stock price, bringing a breath of fresh air to the field of econometric analysis. It seems that the stock market may be quite "sensitive" to the environmental conditions in seemingly distant locations, much like a sensitive nose to pungent fumes.

Understanding this connection offers valuable insights into the interplay between environmental factors and financial markets, painting a picture of pollution's influence that is both smoggy and financially weighty. It appears that when it comes to assessing CNQ stock price, the air isn't the only thing that's "hazy" - the relationship with Amarillo's air pollution levels seems to be a bit foggy as well!

-------

And here is the introduction section that led to this literature review:
[[INTRODUCTION]]
The link between environmental conditions and financial markets has been a subject of growing interest and concern. As the world grapples with the consequences of climate change and the urgency to transition towards sustainable practices, understanding how environmental factors impact economic indicators has become increasingly crucial. In this vein, our study takes a closer look at the unexpected relationship between air pollution in Amarillo, Texas, and the stock price of Canadian Natural Resources (CNQ).
Now, you might be thinking, "What do air pollution in Texas and CNQ stock price have in common? Is there an invisible smokescreen affecting the financial health of the energy sector?" Well, our research sets out to answer these questions by peering through the haze of data to uncover the connections that may not be immediately apparent.
The idea that air pollution in Amarillo, Texas, could have any bearing on a Canadian energy company's stock price might seem far-fetched, like trying to find fresh air in a crowded city. However, our analysis challenges these preconceptions and unearths a relationship that is statistically robust, much like a sturdy umbrella in a storm of confounding variables.
Our investigation aims to shed light on this previously overlooked aspect of environmental and financial entanglement, illuminating the pathways through which air pollution in Amarillo may swirl into the intricate fabric of CNQ's stock price movements. It's time to clear the air, both literally and metaphorically, in the realm of economic analysis.
As we embark on this journey of exploration, we envision a landscape dotted with data points, where the numbers whisper hints of hidden correlations, much like a secret code waiting to be deciphered. So, let us venture forth into the smoggy terrain of Amarillo's air pollution and financial markets, armed with our analytical compass and a healthy dose of statistical rigor.

-------

Your response should start like this:

[[LITERATURE REVIEW]]



ChatGPT:
[[LITERATURE REVIEW]]

Previous research has explored various links between environmental factors and financial markets, from the impact of climate change on stock prices to the influence of pollution on corporate valuation. In "Smith et al.," the authors find lorem and ipsum. Similarly, Doe's study uncovered lorem and ipsum. Jones' research contributes to this body of knowledge by investigating lorem and ipsum. Despite the serious nature of these investigations, it seems that the connection between air pollution in Amarillo, Texas and Canadian Natural Resources' stock price (CNQ) may have slipped through the cracks, much like the elusive scent of a burrito truck on a windy day.

Delving into more specific literature, real-world accounts such as "Polluted Promises: Environmental Factors in Financial Markets" and "Greenbacks and Smog: An Unexpected Romance" offer unique perspectives on the intersection of environmental conditions and corporate finances. These works shed light on the intricate dance between pollution and stock price movements, painting a picture that is both financially intriguing and environmentally concerning. It's as if the market and the environment are engaged in an intricate tango, leaving investors and environmentalists to ponder the steps of this unexpected partnership.

On a more fictional note, novels such as "The Polluted Profits Paradox" and "Smoggy Skies, Sunny Stocks" present imaginative narratives that blur the boundaries between environmental calamities and financial ventures. These literary works playfully dance across the line between reality and fiction, much like an investor juggling numbers in a whimsical dream. It's almost as if the stock market itself is a character in these tales, adapting to the whims of nature in both predictable and unexpected ways.

Turning to the realm of internet culture, the popular meme "Hide the Pain Harold" serves as a lighthearted yet relevant example. In this meme, the character Harold appears to smile through clenched teeth, much like an investor trying to stay upbeat amidst fluctuating stock prices influenced by distant environmental conditions. It's a humorous reminder that even in the face of unexpected correlations, a well-timed smile can go a long way - much like a well-timed pun in a research paper.

As we navigate through the multiplicity of perspectives, from rigorous academic studies to fictional escapades and internet memes, it becomes clear that the connection between air pollution in Amarillo, Texas and CNQ stock price movements is a topic ripe for exploration and discovery. The air of anticipation is palpable, much like the scent of freshly popped popcorn at a bustling stock exchange.


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 Air pollution in Amarillo, Texas and Canadian Natural Resources' stock price (CNQ). You can't resist a good dad joke. Add a relevant dad joke related to the content every couple of sentences. Stay serious and dry most of the time, but then occasionally let your wit shine through.

Your research team collected data from all across the internet, but mostly just used information from Environmental Protection Agency and LSEG Analytics (Refinitiv) . You used data from 2002 to 2023

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]]
"Smogged in Stocks: The Air Pollution-Amarillo Connection and CNQ Stock Price Effects"

[[ABSTRACT]]
This paper delves into the unexpected connection between air pollution in Amarillo, Texas and the stock price of Canadian Natural Resources (CNQ). We conducted a rigorous analysis using data from the Environmental Protection Agency and LSEG Analytics (Refinitiv) to answer the pressing question, "How does air pollution in Amarillo relate to CNQ stock price movements?" Our findings reveal a significant correlation coefficient of 0.8191433 with p < 0.01 over the period from 2002 to 2023.

Our results suggest that as air pollution levels in Amarillo rise, it is associated with fluctuations in CNQ stock price, bringing a breath of fresh air to the field of econometric analysis. It seems that the stock market may be quite "sensitive" to the environmental conditions in seemingly distant locations, much like a sensitive nose to pungent fumes.

Understanding this connection offers valuable insights into the interplay between environmental factors and financial markets, painting a picture of pollution's influence that is both smoggy and financially weighty. It appears that when it comes to assessing CNQ stock price, the air isn't the only thing that's "hazy" - the relationship with Amarillo's air pollution levels seems to be a bit foggy as well!

[[INTRODUCTION]]
The link between environmental conditions and financial markets has been a subject of growing interest and concern. As the world grapples with the consequences of climate change and the urgency to transition towards sustainable practices, understanding how environmental factors impact economic indicators has become increasingly crucial. In this vein, our study takes a closer look at the unexpected relationship between air pollution in Amarillo, Texas, and the stock price of Canadian Natural Resources (CNQ).
Now, you might be thinking, "What do air pollution in Texas and CNQ stock price have in common? Is there an invisible smokescreen affecting the financial health of the energy sector?" Well, our research sets out to answer these questions by peering through the haze of data to uncover the connections that may not be immediately apparent.
The idea that air pollution in Amarillo, Texas, could have any bearing on a Canadian energy company's stock price might seem far-fetched, like trying to find fresh air in a crowded city. However, our analysis challenges these preconceptions and unearths a relationship that is statistically robust, much like a sturdy umbrella in a storm of confounding variables.
Our investigation aims to shed light on this previously overlooked aspect of environmental and financial entanglement, illuminating the pathways through which air pollution in Amarillo may swirl into the intricate fabric of CNQ's stock price movements. It's time to clear the air, both literally and metaphorically, in the realm of economic analysis.
As we embark on this journey of exploration, we envision a landscape dotted with data points, where the numbers whisper hints of hidden correlations, much like a secret code waiting to be deciphered. So, let us venture forth into the smoggy terrain of Amarillo's air pollution and financial markets, armed with our analytical compass and a healthy dose of statistical rigor.

-------

Your response should start like this:

[[METHODOLOGY]]



ChatGPT:

[[METHODOLOGY]]

Data Collection:
To unravel the enigmatic connection between air pollution in Amarillo, Texas, and the stock price of Canadian Natural Resources (CNQ), our research team delved into a plethora of data sources, including the Environmental Protection Agency and LSEG Analytics (Refinitiv). We extracted air quality data from Amarillo, ranging from particulate matter to ozone levels, and obtained CNQ stock price data for the period from 2002 to 2023. Like a prospector panning for hidden treasure, we meticulously sifted through the digital expanse to procure our invaluable datasets.

Dad Joke Break: Why did the statistics professor bring a ladder to the lecture? Because he heard the discussion was going to be on a higher level!

Statistical Analysis:
Our methodology employed a series of sophisticated statistical techniques to unearth the underlying relationship between air pollution in Amarillo and CNQ stock price movements. We utilized time-series analysis to capture the dynamic interplay between air quality indicators and CNQ stock prices over the 21-year period. Additionally, we employed econometric modeling, teasing out the nuanced associations through multivariate modeling and regression analysis. Like expert puzzle solvers, we meticulously pieced together the statistical puzzle to reveal the intricate connections.

Dad Joke Break: Why do economists make for good company at social gatherings? Because they always bring a wealth of knowledge and a surplus of puns!

Control Variables:
In our endeavor to disentangle the web of confounding factors, we meticulously controlled for a myriad of variables that could potentially influence CNQ stock prices, including macroeconomic indicators, industry-specific news, and global energy market trends. Our meticulous attention to these control variables engendered a comprehensive and robust analysis, akin to safeguarding a precious artifact from the clutches of extraneous influences.

Dad Joke Break: How does an economist apologize? "I'm sorry for the supply and demand disruption - it was an unintended external shock!"

Robustness Checks:
To ensure the reliability and robustness of our findings, we subjected our statistical models to a battery of rigorous robustness checks. From sensitivity analyses to diagnostic tests, our investigation underwent meticulous scrutiny, much like a meticulous inspector meticulously combing through the evidence for any signs of statistical mischief.

Dad Joke Break: Why did the economist break up with his girlfriend? He felt there was too much inflation in the relationship and not enough real growth!

Ethical Considerations:
Our research adhered rigorously to ethical guidelines and data privacy regulations, ensuring the confidentiality and integrity of the information obtained from public databases. Like ethical sentinels, we safeguarded the sanctity of data and maintained the highest standards of professional conduct throughout our investigation.

Dad Joke Break: Why did the statistician take a boat to work? They wanted to use a "confidence interval" to cross the river!


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 Air pollution in Amarillo, Texas and Canadian Natural Resources' stock price (CNQ). You can't resist a good dad joke. Add a relevant dad joke related to the content every couple of sentences. Stay serious and dry most of the time, but then occasionally let your wit shine through.

Your research team collected data from all across the internet, but mostly just used information from Environmental Protection Agency and LSEG Analytics (Refinitiv) .

For the time period 2002 to 2023, you found a correlation 0.8191433, r-squared of 0.6709957, 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]]
"Smogged in Stocks: The Air Pollution-Amarillo Connection and CNQ Stock Price Effects"

[[ABSTRACT]]
This paper delves into the unexpected connection between air pollution in Amarillo, Texas and the stock price of Canadian Natural Resources (CNQ). We conducted a rigorous analysis using data from the Environmental Protection Agency and LSEG Analytics (Refinitiv) to answer the pressing question, "How does air pollution in Amarillo relate to CNQ stock price movements?" Our findings reveal a significant correlation coefficient of 0.8191433 with p < 0.01 over the period from 2002 to 2023.

Our results suggest that as air pollution levels in Amarillo rise, it is associated with fluctuations in CNQ stock price, bringing a breath of fresh air to the field of econometric analysis. It seems that the stock market may be quite "sensitive" to the environmental conditions in seemingly distant locations, much like a sensitive nose to pungent fumes.

Understanding this connection offers valuable insights into the interplay between environmental factors and financial markets, painting a picture of pollution's influence that is both smoggy and financially weighty. It appears that when it comes to assessing CNQ stock price, the air isn't the only thing that's "hazy" - the relationship with Amarillo's air pollution levels seems to be a bit foggy as well!

-------

And here is the methodology section that led to this result:
[[METHODOLOGY]]
The link between environmental conditions and financial markets has been a subject of growing interest and concern. As the world grapples with the consequences of climate change and the urgency to transition towards sustainable practices, understanding how environmental factors impact economic indicators has become increasingly crucial. In this vein, our study takes a closer look at the unexpected relationship between air pollution in Amarillo, Texas, and the stock price of Canadian Natural Resources (CNQ).
Now, you might be thinking, "What do air pollution in Texas and CNQ stock price have in common? Is there an invisible smokescreen affecting the financial health of the energy sector?" Well, our research sets out to answer these questions by peering through the haze of data to uncover the connections that may not be immediately apparent.
The idea that air pollution in Amarillo, Texas, could have any bearing on a Canadian energy company's stock price might seem far-fetched, like trying to find fresh air in a crowded city. However, our analysis challenges these preconceptions and unearths a relationship that is statistically robust, much like a sturdy umbrella in a storm of confounding variables.
Our investigation aims to shed light on this previously overlooked aspect of environmental and financial entanglement, illuminating the pathways through which air pollution in Amarillo may swirl into the intricate fabric of CNQ's stock price movements. It's time to clear the air, both literally and metaphorically, in the realm of economic analysis.
As we embark on this journey of exploration, we envision a landscape dotted with data points, where the numbers whisper hints of hidden correlations, much like a secret code waiting to be deciphered. So, let us venture forth into the smoggy terrain of Amarillo's air pollution and financial markets, armed with our analytical compass and a healthy dose of statistical rigor.

-------

Your response should start like this:

[[RESULTS]]



ChatGPT:

[[RESULTS]]

Our analysis revealed a strong positive correlation between air pollution levels in Amarillo, Texas, and the stock price of Canadian Natural Resources (CNQ). The correlation coefficient of 0.8191433 indicates a robust positive relationship between these seemingly disparate variables. It's as if the winds of the stock market are carrying the scent of Amarillo's pollution, influencing CNQ's stock price in unseen ways.

The r-squared value of 0.6709957 suggests that approximately 67.10% of the variability in CNQ stock price can be explained by changes in air pollution levels in Amarillo. This finding further underscores the substantial impact that environmental conditions in one location can have on the financial performance of a company operating thousands of miles away. It's like a little bit of Amarillo's pollution riding the coattails of CNQ's stock price.

Furthermore, the statistical significance with p < 0.01 strengthens our confidence in the observed relationship. The probability of observing such a strong association between air pollution in Amarillo and CNQ stock price movements by random chance is less than 1%. It's like finding a needle in a haystack, except in this case, the needle is a significant correlation buried in the data "haystack."

Fig. 1 illustrates the strong positive correlation between air pollution levels in Amarillo and CNQ stock prices. The scatterplot showcases how the fluctuations in air pollution align with changes in CNQ stock prices, as if the pollution particles are dancing along with the stock price movements. It's a visual representation of how a seemingly distant factor can weave into the financial fabric, much like a gust of wind carrying the scent of pollution across borders.

In conclusion, our findings provide compelling evidence that air pollution levels in Amarillo, Texas, are correlated with the stock price of Canadian Natural Resources. This unexpected connection sheds light on the intricate interplay between environmental conditions and financial markets, hinting at a relationship that is as elusive and complex as the path of stray pollutants through the atmosphere.


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 Air pollution in Amarillo, Texas and Canadian Natural Resources' stock price (CNQ). You can't resist a good dad joke. Add a relevant dad joke related to the content every couple of sentences. Stay serious and dry most of the time, but then occasionally let your wit shine through.

Limit your response to 500 tokens.

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

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

[[TITLE]]
"Smogged in Stocks: The Air Pollution-Amarillo Connection and CNQ Stock Price Effects"

[[ABSTRACT]]
This paper delves into the unexpected connection between air pollution in Amarillo, Texas and the stock price of Canadian Natural Resources (CNQ). We conducted a rigorous analysis using data from the Environmental Protection Agency and LSEG Analytics (Refinitiv) to answer the pressing question, "How does air pollution in Amarillo relate to CNQ stock price movements?" Our findings reveal a significant correlation coefficient of 0.8191433 with p < 0.01 over the period from 2002 to 2023.

Our results suggest that as air pollution levels in Amarillo rise, it is associated with fluctuations in CNQ stock price, bringing a breath of fresh air to the field of econometric analysis. It seems that the stock market may be quite "sensitive" to the environmental conditions in seemingly distant locations, much like a sensitive nose to pungent fumes.

Understanding this connection offers valuable insights into the interplay between environmental factors and financial markets, painting a picture of pollution's influence that is both smoggy and financially weighty. It appears that when it comes to assessing CNQ stock price, the air isn't the only thing that's "hazy" - the relationship with Amarillo's air pollution levels seems to be a bit foggy as well!

[[LITERATURE REVIEW]]
Previous research has explored various links between environmental factors and financial markets, from the impact of climate change on stock prices to the influence of pollution on corporate valuation. In "Smith et al.," the authors find lorem and ipsum. Similarly, Doe's study uncovered lorem and ipsum. Jones' research contributes to this body of knowledge by investigating lorem and ipsum. Despite the serious nature of these investigations, it seems that the connection between air pollution in Amarillo, Texas and Canadian Natural Resources' stock price (CNQ) may have slipped through the cracks, much like the elusive scent of a burrito truck on a windy day.
Delving into more specific literature, real-world accounts such as "Polluted Promises: Environmental Factors in Financial Markets" and "Greenbacks and Smog: An Unexpected Romance" offer unique perspectives on the intersection of environmental conditions and corporate finances. These works shed light on the intricate dance between pollution and stock price movements, painting a picture that is both financially intriguing and environmentally concerning. It's as if the market and the environment are engaged in an intricate tango, leaving investors and environmentalists to ponder the steps of this unexpected partnership.
On a more fictional note, novels such as "The Polluted Profits Paradox" and "Smoggy Skies, Sunny Stocks" present imaginative narratives that blur the boundaries between environmental calamities and financial ventures. These literary works playfully dance across the line between reality and fiction, much like an investor juggling numbers in a whimsical dream. It's almost as if the stock market itself is a character in these tales, adapting to the whims of nature in both predictable and unexpected ways.
Turning to the realm of internet culture, the popular meme "Hide the Pain Harold" serves as a lighthearted yet relevant example. In this meme, the character Harold appears to smile through clenched teeth, much like an investor trying to stay upbeat amidst fluctuating stock prices influenced by distant environmental conditions. It's a humorous reminder that even in the face of unexpected correlations, a well-timed smile can go a long way - much like a well-timed pun in a research paper.
As we navigate through the multiplicity of perspectives, from rigorous academic studies to fictional escapades and internet memes, it becomes clear that the connection between air pollution in Amarillo, Texas and CNQ stock price movements is a topic ripe for exploration and discovery. The air of anticipation is palpable, much like the scent of freshly popped popcorn at a bustling stock exchange.

[[RESULTS]]
Our analysis revealed a strong positive correlation between air pollution levels in Amarillo, Texas, and the stock price of Canadian Natural Resources (CNQ). The correlation coefficient of 0.8191433 indicates a robust positive relationship between these seemingly disparate variables. It's as if the winds of the stock market are carrying the scent of Amarillo's pollution, influencing CNQ's stock price in unseen ways.
The r-squared value of 0.6709957 suggests that approximately 67.10% of the variability in CNQ stock price can be explained by changes in air pollution levels in Amarillo. This finding further underscores the substantial impact that environmental conditions in one location can have on the financial performance of a company operating thousands of miles away. It's like a little bit of Amarillo's pollution riding the coattails of CNQ's stock price.
Furthermore, the statistical significance with p < 0.01 strengthens our confidence in the observed relationship. The probability of observing such a strong association between air pollution in Amarillo and CNQ stock price movements by random chance is less than 1%. It's like finding a needle in a haystack, except in this case, the needle is a significant correlation buried in the data "haystack."
Fig. 1 illustrates the strong positive correlation between air pollution levels in Amarillo and CNQ stock prices. The scatterplot showcases how the fluctuations in air pollution align with changes in CNQ stock prices, as if the pollution particles are dancing along with the stock price movements. It's a visual representation of how a seemingly distant factor can weave into the financial fabric, much like a gust of wind carrying the scent of pollution across borders.
In conclusion, our findings provide compelling evidence that air pollution levels in Amarillo, Texas, are correlated with the stock price of Canadian Natural Resources. This unexpected connection sheds light on the intricate interplay between environmental conditions and financial markets, hinting at a relationship that is as elusive and complex as the path of stray pollutants through the atmosphere.

-------

Your response should start like this:

[[DISCUSSION]]



ChatGPT:

[[DISCUSSION]]

Our study set out to investigate the relationship between air pollution in Amarillo, Texas, and the stock price of Canadian Natural Resources (CNQ). The robust positive correlation we uncovered between these seemingly unrelated variables has significant implications for both the financial and environmental spheres. It's as if a gust of air from Amarillo has blown through the financial markets, leaving a distinctive fragrance in the form of CNQ stock price movements.

Building upon prior research that has explored the influence of environmental factors on stock prices, our findings support the notion that environmental conditions can indeed have a tangible impact on the valuation of companies. This aligns with the work of Smith et al. and Doe, who delved into the intricacies of environmental variables and financial market performance. It's clear that the air in Amarillo isn't just carrying pollutants - it's also carrying a signal that resonates in the stock prices of distant corporations.

While our investigation into the connection between Amarillo's air pollution and CNQ stock price movements may initially seem unusual, it echoes the playful juxtapositions found in literature and internet memes. Just like the fictional narratives that blur the boundaries between environmental calamities and financial ventures, our findings highlight the unexpected ways in which seemingly distant events can intertwine in the world of finance.

The statistical significance of our results, with a p-value of less than 0.01, reinforces the solidity of the observed relationship. It's akin to finding a hidden treasure amidst an abundance of data "haystack," albeit in this case, the treasure is a significant correlation nestled within the numbers. And speaking of hidden treasures, our study offers an insight that is as valuable as it is unexpected - the understanding that the air in Amarillo may hold the scent of financial movements across borders.

Our research serves as a reminder that the financial world, much like an investor navigating market fluctuations, must remain attuned to the influences of distant environmental conditions. As such, our findings not only contribute to the literature on the connections between environmental factors and financial markets but also demonstrate the relevance of unexpected correlations in the world of econometric analysis.

In summary, the unexpected connection we've uncovered between air pollution in Amarillo, Texas, and CNQ stock price movements sheds light on the hidden interplay between seemingly unrelated variables. The significance of this finding underscores the necessity for investors and policymakers to consider the broader environmental context when assessing the financial implications for companies operating in distant locations. It's as if the invisible hand of Amarillo's air pollution has left an indelible mark on the stock prices of Canadian Natural Resources, reminding us that financial markets, much like life, often prove to be as hazy as they are fascinating.


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 Air pollution in Amarillo, Texas and Canadian Natural Resources' stock price (CNQ). You can't resist a good dad joke. Add a relevant dad joke related to the content every couple of sentences. Stay serious and dry most of the time, but then occasionally let your wit shine through.

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

Here are the title, abstract, introduction, and results sections.
[[TITLE]]
"Smogged in Stocks: The Air Pollution-Amarillo Connection and CNQ Stock Price Effects"

[[ABSTRACT]]
This paper delves into the unexpected connection between air pollution in Amarillo, Texas and the stock price of Canadian Natural Resources (CNQ). We conducted a rigorous analysis using data from the Environmental Protection Agency and LSEG Analytics (Refinitiv) to answer the pressing question, "How does air pollution in Amarillo relate to CNQ stock price movements?" Our findings reveal a significant correlation coefficient of 0.8191433 with p < 0.01 over the period from 2002 to 2023.

Our results suggest that as air pollution levels in Amarillo rise, it is associated with fluctuations in CNQ stock price, bringing a breath of fresh air to the field of econometric analysis. It seems that the stock market may be quite "sensitive" to the environmental conditions in seemingly distant locations, much like a sensitive nose to pungent fumes.

Understanding this connection offers valuable insights into the interplay between environmental factors and financial markets, painting a picture of pollution's influence that is both smoggy and financially weighty. It appears that when it comes to assessing CNQ stock price, the air isn't the only thing that's "hazy" - the relationship with Amarillo's air pollution levels seems to be a bit foggy as well!

[[INTRDUCTION]]
The link between environmental conditions and financial markets has been a subject of growing interest and concern. As the world grapples with the consequences of climate change and the urgency to transition towards sustainable practices, understanding how environmental factors impact economic indicators has become increasingly crucial. In this vein, our study takes a closer look at the unexpected relationship between air pollution in Amarillo, Texas, and the stock price of Canadian Natural Resources (CNQ).
Now, you might be thinking, "What do air pollution in Texas and CNQ stock price have in common? Is there an invisible smokescreen affecting the financial health of the energy sector?" Well, our research sets out to answer these questions by peering through the haze of data to uncover the connections that may not be immediately apparent.
The idea that air pollution in Amarillo, Texas, could have any bearing on a Canadian energy company's stock price might seem far-fetched, like trying to find fresh air in a crowded city. However, our analysis challenges these preconceptions and unearths a relationship that is statistically robust, much like a sturdy umbrella in a storm of confounding variables.
Our investigation aims to shed light on this previously overlooked aspect of environmental and financial entanglement, illuminating the pathways through which air pollution in Amarillo may swirl into the intricate fabric of CNQ's stock price movements. It's time to clear the air, both literally and metaphorically, in the realm of economic analysis.
As we embark on this journey of exploration, we envision a landscape dotted with data points, where the numbers whisper hints of hidden correlations, much like a secret code waiting to be deciphered. So, let us venture forth into the smoggy terrain of Amarillo's air pollution and financial markets, armed with our analytical compass and a healthy dose of statistical rigor.

[[RESULTS]]
Our analysis revealed a strong positive correlation between air pollution levels in Amarillo, Texas, and the stock price of Canadian Natural Resources (CNQ). The correlation coefficient of 0.8191433 indicates a robust positive relationship between these seemingly disparate variables. It's as if the winds of the stock market are carrying the scent of Amarillo's pollution, influencing CNQ's stock price in unseen ways.
The r-squared value of 0.6709957 suggests that approximately 67.10% of the variability in CNQ stock price can be explained by changes in air pollution levels in Amarillo. This finding further underscores the substantial impact that environmental conditions in one location can have on the financial performance of a company operating thousands of miles away. It's like a little bit of Amarillo's pollution riding the coattails of CNQ's stock price.
Furthermore, the statistical significance with p < 0.01 strengthens our confidence in the observed relationship. The probability of observing such a strong association between air pollution in Amarillo and CNQ stock price movements by random chance is less than 1%. It's like finding a needle in a haystack, except in this case, the needle is a significant correlation buried in the data "haystack."
Fig. 1 illustrates the strong positive correlation between air pollution levels in Amarillo and CNQ stock prices. The scatterplot showcases how the fluctuations in air pollution align with changes in CNQ stock prices, as if the pollution particles are dancing along with the stock price movements. It's a visual representation of how a seemingly distant factor can weave into the financial fabric, much like a gust of wind carrying the scent of pollution across borders.
In conclusion, our findings provide compelling evidence that air pollution levels in Amarillo, Texas, are correlated with the stock price of Canadian Natural Resources. This unexpected connection sheds light on the intricate interplay between environmental conditions and financial markets, hinting at a relationship that is as elusive and complex as the path of stray pollutants through the atmosphere.

-------

Your response should start like this:

[[CONCLUSION]]



ChatGPT:

[[CONCLUSION]]

In conclusion, our research has illuminated a significant and robust positive correlation between air pollution levels in Amarillo, Texas, and the stock price of Canadian Natural Resources (CNQ). These findings challenge conventional wisdom and suggest that environmental conditions in one location can indeed have a tangible impact on the financial performance of a company operating thousands of miles away.

It appears that the relationship between the air pollution in Amarillo and CNQ stock price movements is not just blowing in the wind; it is a palpable and statistically significant association. One might say that the scent of success for CNQ may be carried by the winds of Amarillo's pollution.

The results of our study have broader implications for the intersection of environmental and financial factors, providing a clear signal that the effects of air pollution are not confined by geographical borders but can permeate financial markets in unexpected ways. Our research has peeled back the layers of this connection, much like uncovering a hidden treasure chest buried beneath a pile of statistical rubble.

This study opens the door to a new avenue for understanding the interconnectedness of seemingly disparate variables, giving a breath of fresh air to the field of environmental economics as we navigate through the fog of environmental conditions and financial indicators. It is clear that our findings are nothing to sneeze at!

As for future research directions, it seems that the air pollution in Amarillo and its influence on CNQ stock prices has been thoroughly sniffed out, leaving no further avenues unexplored. Therefore, we assert that no more research is needed in this area. It looks like we can finally breathe easy knowing that the connection between air pollution and CNQ stock price has been thoroughly examined.


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 Smogged in Stocks: The Air Pollution-Amarillo Connection and CNQ Stock Price Effects. Respond only with the name of a fictional academic journal.

ChatGPT:

The Journal of Ecological Economics and Financial Impact 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 Smogged in Stocks: The Air Pollution-Amarillo Connection and CNQ Stock Price Effects. Respond only with the name of a fictional organization.

ChatGPT:

The Society for Environmental Economics and Investment Research


Model: gpt-3.5-turbo-1106
System prompt: You provide potential search keywords separated by commas. You say nothing else, and you do not chat with the user.
User prompt: Please provide potential search keywords for a paper titled Smogged in Stocks: The Air Pollution-Amarillo Connection and CNQ Stock Price Effects with an abstract of This paper delves into the unexpected connection between air pollution in Amarillo, Texas and the stock price of Canadian Natural Resources (CNQ). We conducted a rigorous analysis using data from the Environmental Protection Agency and LSEG Analytics (Refinitiv) to answer the pressing question, "How does air pollution in Amarillo relate to CNQ stock price movements?" Our findings reveal a significant correlation coefficient of 0.8191433 with p < 0.01 over the period from 2002 to 2023.
Our results suggest that as air pollution levels in Amarillo rise, it is associated with fluctuations in CNQ stock price, bringing a breath of fresh air to the field of econometric analysis. It seems that the stock market may be quite "sensitive" to the environmental conditions in seemingly distant locations, much like a sensitive nose to pungent fumes.
Understanding this connection offers valuable insights into the interplay between environmental factors and financial markets, painting a picture of pollution's influence that is both smoggy and financially weighty. It appears that when it comes to assessing CNQ stock price, the air isn't the only thing that's "hazy" - the relationship with Amarillo's air pollution levels seems to be a bit foggy as well!

ChatGPT:

Air pollution, Amarillo, Texas, Canadian Natural Resources, CNQ, stock price, correlation, environmental factors, financial markets, econometric analysis, pollution, stock market, environmental conditions, pollution's influence

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



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Data details

Air pollution in Amarillo, Texas
Detailed data title: Percentage of days with moderate or worse air quality in Amarillo, TX
Source: Environmental Protection Agency
See what else correlates with Air pollution in Amarillo, Texas

Canadian Natural Resources' stock price (CNQ)
Detailed data title: Opening price of Canadian Natural Resources (CNQ) on the first trading day of the year
Source: LSEG Analytics (Refinitiv)
Additional Info: Via Microsoft Excel Stockhistory function

See what else correlates with Canadian Natural Resources' stock price (CNQ)

Correlation r = 0.8191433 (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 = 0.6709957 (Coefficient of determination)
This means 67.1% of the change in the one variable (i.e., Canadian Natural Resources' stock price (CNQ)) is predictable based on the change in the other (i.e., Air pollution in Amarillo, Texas) over the 22 years from 2002 through 2023.

p < 0.01, which is statistically significant(Null hypothesis significance test)
The p-value is 3.1E-6. 0.0000031291126247560930000000
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 0.82 in 0.00031% of random cases. Said differently, if you correlated 319,579 random variables You don't actually need 319 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 21 degrees of freedom, Degrees of freedom is a measure of how many free components we are testing. In this case it is 21 because we have two variables measured over a period of 22 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.

[ 0.61, 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.
2002200320042005200620072008200920102011201220132014201520162017201820192020202120222023
Air pollution in Amarillo, Texas (Bad air quality days)2.290088.088233.27.71354.9315112.054821.038315.06859.3150733.51836.065625.479521.153816.986311.748622.191827.671221.917824.590221.153827.397333.4906
Canadian Natural Resources' stock price (CNQ) (Stock price)2.973.666.2610.5624.4925.7736.2620.0236.3144.8737.7129.1433.0129.8821.132.1535.2523.0932.0624.3242.3254.93




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([2.29008,8.08823,3.2,7.7135,4.93151,12.0548,21.0383,15.0685,9.31507,33.518,36.0656,25.4795,21.1538,16.9863,11.7486,22.1918,27.6712,21.9178,24.5902,21.1538,27.3973,33.4906,])
array_2 = np.array([2.97,3.66,6.26,10.56,24.49,25.77,36.26,20.02,36.31,44.87,37.71,29.14,33.01,29.88,21.1,32.15,35.25,23.09,32.06,24.32,42.32,54.93,])
array_1_name = "Air pollution in Amarillo, Texas"
array_2_name = "Canadian Natural Resources' stock price (CNQ)"

# 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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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."

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Correlation ID: 1638 · Black Variable ID: 20260 · Red Variable ID: 1679
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