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Spurious correlation #4,044 · 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 Portland, Oregon and the second variable is Kerosene used in Romania.  The chart goes from 1980 to 2021, and the two variables track closely in value over that time. Small Image

AI explanation

As the air in Portland cleared up, it created a ripple effect of improved global air quality. This, in turn, led to a decrease in the demand for kerosene in Romania, because, you know, everyone knows that kerosene is just a big fan of clean air and decided to take a vacation!

Model: dalle-3
Prompt: Prompt: Generate an image of a hazy urban skyline with a swirling whirlwind forming in the distance, intertwining with vibrant kerosene molecules. The skyline should resemble a cyberpunk-inspired cityscape with neon-lit buildings and dense air pollution. The whirlwind and kerosene molecules should be depicted in a surreal and fantastical manner, creating an unexpected and mesmerizing connection between the polluted city and its distant, colorful journey to Romania. The depiction should include only scenes, people, and objects, it should not include text or speech bubbles.
This image generation prompt was also generated by AI, using the following sequence:

Model: gpt-3.5-turbo-1106
System prompt: You select one of a few potential scene descriptors that seems to go along with the variables described. You respond only with the scene descriptions provided and say nothing else.
User prompt: Here are two variables: Air pollution in Portland, Oregon and Kerosene used in Romania. 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: Steampunk Art nouveau Sci-fi fantacy Psychedelic Cyberpunk
ChatGPT: Cyberpunk

Model: gpt-3.5-turbo-1106
System prompt: You describe simple visual scenes that depict the two variables stated. You combine both variables into one scene.
User prompt: Please describe a visual scene that prominently depicts both Air pollution in Portland, Oregon and Kerosene used in Romania, in the following situation: Well, you see, when the air pollution in Portland increased, it caused a disruption in the earth's wind patterns, leading to a whirlwind that carried kerosene molecules all the way to Romania! It's like a real-life game of "kerosene in the wind," where Mother Nature decided to spice up the global air quality with a dash of Romanian flair!. Keep the description simple.
ChatGPT: A hazy sky looms over the city of Portland, Oregon, as cars and factories pump out thick clouds of pollution. In the distance, a whirlwind starts to form, swirling the polluted air in a dizzying dance. As the whirlwind gains strength, it picks up kerosene molecules, creating a colorful ribbon that stretches across the globe, eventually reaching Romania. The unlikely pairing of air pollution and kerosene molecules creates a surreal and unexpected global connection, as if nature itself has decided to play a whimsical game.

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: [ Cyberpunk ] and depicting this scene: A hazy sky looms over the city of Portland, Oregon, as cars and factories pump out thick clouds of pollution. In the distance, a whirlwind starts to form, swirling the polluted air in a dizzying dance. As the whirlwind gains strength, it picks up kerosene molecules, creating a colorful ribbon that stretches across the globe, eventually reaching Romania. The unlikely pairing of air pollution and kerosene molecules creates a surreal and unexpected global connection, as if nature itself has decided to play a whimsical game. Keep the visual depiction simple. Do not include any words or speech bubbles.
ChatGPT: Prompt: Generate an image of a hazy urban skyline with a swirling whirlwind forming in the distance, intertwining with vibrant kerosene molecules. The skyline should resemble a cyberpunk-inspired cityscape with neon-lit buildings and dense air pollution. The whirlwind and kerosene molecules should be depicted in a surreal and fantastical manner, creating an unexpected and mesmerizing connection between the polluted city and its distant, colorful journey to Romania.

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

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

Model: gpt-3.5-turbo-1106 (fine-tuned)
System prompt: You provide humorous responses in the form of plausible sounding explanations for correlations. You assume the correlation is causative for the purpose of the explanation even if it is ridiculous. You do not chat with the user, you only reply with the causal connection explanation and nothing else.
User prompt: Please make up a funny explanation for how a decrease in Air pollution in Portland, Oregon caused Kerosene used in Romania to decrease.

AI academic paper

(Because p < 0.01)
Clearing the Air: Unearthing the Link Between Portland's Pollution and Romania's Kerosene

The Journal of Environmental Arcana

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 dry but witty academic researcher. You speak in the passive voice, and your writing sounds like it belongs in a medical or economics journal.You 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 Portland, Oregon and Kerosene used in Romania. 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 Environmental Protection Agency and Energy Information Administration to assess this nagging question. You found a correlation coefficient of 0.5986876 and p < 0.01 for 1980 to 2021.

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]]
"Clearing the Air: Unearthing the Link Between Portland's Pollution and Romania's Kerosene"

[[ABSTRACT]]
This study examined the potential relationship between air pollution levels in Portland, Oregon and the prevalence of kerosene use in Romania. Utilizing data from the Environmental Protection Agency and the Energy Information Administration spanning the years 1980 to 2021, a correlation coefficient of 0.5986876 and p < 0.01 was discovered, suggesting a modest yet statistically significant association between the two seemingly unrelated entities. The findings invite further exploration into the unexpected intercontinental connection, shedding light on the captivating, albeit unconventional, dynamics of environmental impact.


Model: gpt-3.5-turbo-1106
System prompt: You are a dry but witty academic researcher. You speak in the passive voice, and your writing sounds like it belongs in a medical or economics journal.You draft the 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 Portland, Oregon and Kerosene used in Romania. Make it seem dry like academic research paper, but with lots of subtle hidden offhand remarks, jokes, goofy observations, and puns. 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]]
"Clearing the Air: Unearthing the Link Between Portland's Pollution and Romania's Kerosene"

[[ABSTRACT]]
This study examined the potential relationship between air pollution levels in Portland, Oregon and the prevalence of kerosene use in Romania. Utilizing data from the Environmental Protection Agency and the Energy Information Administration spanning the years 1980 to 2021, a correlation coefficient of 0.5986876 and p < 0.01 was discovered, suggesting a modest yet statistically significant association between the two seemingly unrelated entities. The findings invite further exploration into the unexpected intercontinental connection, shedding light on the captivating, albeit unconventional, dynamics of environmental impact.

-------

Your response should start like this:

[[INTRODUCTION]]



ChatGPT:
[[INTRODUCTION]]

The interconnectedness of our world's environmental factors continues to surprise and confound researchers, policymakers, and casual observers alike. In this study, we delve into the unsuspecting correlation between air pollution levels in Portland, Oregon, and the utilization of kerosene in Romania. While these two entities may appear as distant as the East is from the West, our analysis has revealed a statistical relationship that cannot be brushed aside.

The matter of air pollution, particularly in urban areas, has long been a subject of scrutiny and concern. Portland, nestled in the Pacific Northwest of the United States, has grappled with its fair share of atmospheric challenges over the years. On the other hand, the use of kerosene as a source of lighting and heating in Romania resonates with echoes of tradition and practicality, standing in stark contrast to the sleek modernity often associated with environmental awareness and sustainability.

For many, the connection between these two seemingly disparate issues may appear as nebulous as a cloud of smog on a still day, but as we delve into the data, a clearer picture begins to emerge. Our findings are not only unexpected but also at odds with conventional wisdom, adding a layer of intrigue to the broader conversation surrounding environmental impact and human activity.

The correlation coefficient of 0.5986876 that emerged from our analysis may not shock the scientific community to its core, but it does signal a notable relationship that demands attention. To borrow a turn of phrase from the world of economic forecasts, the association between Portland's pollution and Romania's kerosene use is "nothing to sneeze at."

As we unfurl the details of our investigation, we invite the reader to join us in navigating the labyrinthine network of our planet's environmental interactions. The unexpected twists and turns of our findings are sure to inspire a raised eyebrow or two, highlighting the interconnectedness of the global environmental landscape in a manner that is as surprising as it is significant.


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

Please make up a literature review section of an academic research paper presenting the findings of the connection between Air pollution in Portland, Oregon and Kerosene used in Romania. Make it seem dry like academic research paper, but with lots of subtle hidden offhand remarks, jokes, goofy observations, and puns.

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

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

Start by naming serious-sounding studies by authors like Smith, Doe, and Jones - but then quickly devolve. Name some real non-fiction books that would be related to the topic. Then name some real fiction books that sound like they could be related. Then devolve ever further, and mention something completely ridiculous, like you conducted literature review by reading the backs of shampoo bottles.

Here is the title and abstract of the paper:
[[TITLE]]
"Clearing the Air: Unearthing the Link Between Portland's Pollution and Romania's Kerosene"

[[ABSTRACT]]
This study examined the potential relationship between air pollution levels in Portland, Oregon and the prevalence of kerosene use in Romania. Utilizing data from the Environmental Protection Agency and the Energy Information Administration spanning the years 1980 to 2021, a correlation coefficient of 0.5986876 and p < 0.01 was discovered, suggesting a modest yet statistically significant association between the two seemingly unrelated entities. The findings invite further exploration into the unexpected intercontinental connection, shedding light on the captivating, albeit unconventional, dynamics of environmental impact.

-------

And here is the introduction section that led to this literature review:
[[INTRODUCTION]]
The interconnectedness of our world's environmental factors continues to surprise and confound researchers, policymakers, and casual observers alike. In this study, we delve into the unsuspecting correlation between air pollution levels in Portland, Oregon, and the utilization of kerosene in Romania. While these two entities may appear as distant as the East is from the West, our analysis has revealed a statistical relationship that cannot be brushed aside.
The matter of air pollution, particularly in urban areas, has long been a subject of scrutiny and concern. Portland, nestled in the Pacific Northwest of the United States, has grappled with its fair share of atmospheric challenges over the years. On the other hand, the use of kerosene as a source of lighting and heating in Romania resonates with echoes of tradition and practicality, standing in stark contrast to the sleek modernity often associated with environmental awareness and sustainability.
For many, the connection between these two seemingly disparate issues may appear as nebulous as a cloud of smog on a still day, but as we delve into the data, a clearer picture begins to emerge. Our findings are not only unexpected but also at odds with conventional wisdom, adding a layer of intrigue to the broader conversation surrounding environmental impact and human activity.
The correlation coefficient of 0.5986876 that emerged from our analysis may not shock the scientific community to its core, but it does signal a notable relationship that demands attention. To borrow a turn of phrase from the world of economic forecasts, the association between Portland's pollution and Romania's kerosene use is "nothing to sneeze at."
As we unfurl the details of our investigation, we invite the reader to join us in navigating the labyrinthine network of our planet's environmental interactions. The unexpected twists and turns of our findings are sure to inspire a raised eyebrow or two, highlighting the interconnectedness of the global environmental landscape in a manner that is as surprising as it is significant.

-------

Your response should start like this:

[[LITERATURE REVIEW]]



ChatGPT:
[[LITERATURE REVIEW]]

The literature review as presented in this section aims to provide a comprehensive overview of existing research related to air pollution and kerosene use, with a focus on understanding the potential link between Portland, Oregon, and Romania. While seemingly unrelated on the surface, the connection uncovered in this study sheds light on the unexpected interplay between these environmental factors.

In "Air Quality in Urban Environments," Smith et al. (2018) explore the various contributors to air pollution in metropolitan areas, emphasizing the impact of vehicular emissions, industrial activities, and residential energy consumption. The study highlights the complex nature of urban air quality dynamics, setting the stage for our investigation into the specific case of Portland, Oregon.

Similarly, Doe's (2020) work in "Energy Sources and Consumption Patterns" delves into the historical trends of fuel usage across different regions, noting the transition from traditional sources such as kerosene to more modern and sustainable alternatives. This comprehensive analysis offers valuable insights into the prevailing energy landscape, laying the groundwork for understanding the context of kerosene use in Romania.

Jones (2016) provides a detailed examination of environmental policy and regulation in "Managing Air Pollution: A Global Perspective," offering a comparative study of strategies employed by various countries to mitigate the impact of pollution on public health and ecosystems. The global outlook presented in this work prompts considerations of intercontinental influences that may inform the connection under scrutiny.

Drawing from non-fiction literature, the relevance of "The Air We Breathe: A Global Perspective" by Environmental Research Institute (2019) and "Kerosene's Glow: A Cultural History" by Energy Traditions Consortium (2015) cannot be overstated. Each provides unique perspectives on the respective topics of air pollution and kerosene usage, offering valuable insights that inform our understanding of the intersection between these phenomena.

In the realm of fiction, "The Polluted City" by A. Smog and "Kerosene Chronicles" by L. Lamp lend an imaginative lens to the exploration of environmental themes, inspiring broader reflections on the intricate connections between human activity and atmospheric conditions.

Beyond traditional academic sources, the authors engaged in an unconventional approach to literature review, delving into unexpected repositories of knowledge. This entailed perusing the backs of household cleaning products, cereal boxes, and even shampoo bottles, in a quest for hidden insights that may have eluded the scholarly community. While the efficacy of this method remains a subject of debate, the authors found it to be, if nothing else, a rather amusing departure from conventional research practices.

This eclectic compilation of literature sets the stage for the exploration of the uncanny correlation unearthed in this study, inviting the reader to approach the intercontinental relationship between air pollution in Portland and kerosene use in Romania with a blend of curiosity and levity.


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

Please make up the methodology section of an academic research paper presenting the findings of the connection between Air pollution in Portland, Oregon and Kerosene used in Romania. Make it seem dry like academic research paper, but with lots of subtle hidden offhand remarks, jokes, goofy observations, and puns. 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 Energy Information Administration . You used data from 1980 to 2021

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]]
"Clearing the Air: Unearthing the Link Between Portland's Pollution and Romania's Kerosene"

[[ABSTRACT]]
This study examined the potential relationship between air pollution levels in Portland, Oregon and the prevalence of kerosene use in Romania. Utilizing data from the Environmental Protection Agency and the Energy Information Administration spanning the years 1980 to 2021, a correlation coefficient of 0.5986876 and p < 0.01 was discovered, suggesting a modest yet statistically significant association between the two seemingly unrelated entities. The findings invite further exploration into the unexpected intercontinental connection, shedding light on the captivating, albeit unconventional, dynamics of environmental impact.

[[INTRODUCTION]]
The interconnectedness of our world's environmental factors continues to surprise and confound researchers, policymakers, and casual observers alike. In this study, we delve into the unsuspecting correlation between air pollution levels in Portland, Oregon, and the utilization of kerosene in Romania. While these two entities may appear as distant as the East is from the West, our analysis has revealed a statistical relationship that cannot be brushed aside.
The matter of air pollution, particularly in urban areas, has long been a subject of scrutiny and concern. Portland, nestled in the Pacific Northwest of the United States, has grappled with its fair share of atmospheric challenges over the years. On the other hand, the use of kerosene as a source of lighting and heating in Romania resonates with echoes of tradition and practicality, standing in stark contrast to the sleek modernity often associated with environmental awareness and sustainability.
For many, the connection between these two seemingly disparate issues may appear as nebulous as a cloud of smog on a still day, but as we delve into the data, a clearer picture begins to emerge. Our findings are not only unexpected but also at odds with conventional wisdom, adding a layer of intrigue to the broader conversation surrounding environmental impact and human activity.
The correlation coefficient of 0.5986876 that emerged from our analysis may not shock the scientific community to its core, but it does signal a notable relationship that demands attention. To borrow a turn of phrase from the world of economic forecasts, the association between Portland's pollution and Romania's kerosene use is "nothing to sneeze at."
As we unfurl the details of our investigation, we invite the reader to join us in navigating the labyrinthine network of our planet's environmental interactions. The unexpected twists and turns of our findings are sure to inspire a raised eyebrow or two, highlighting the interconnectedness of the global environmental landscape in a manner that is as surprising as it is significant.

-------

Your response should start like this:

[[METHODOLOGY]]



ChatGPT:

[[METHODOLOGY]]

Data Collection:
The data for this study was sourced primarily from the Environmental Protection Agency and the Energy Information Administration. A wide range of pertinent variables related to air pollution levels in Portland, Oregon, and kerosene use in Romania were gathered from reliable databases, government reports, and other credible sources spanning the years 1980 to 2021. The use of these comprehensive datasets allowed for a rigorous examination of the potential connection between the two phenomena.

Statistical Analysis:
To investigate the correlation between air pollution levels in Portland and kerosene use in Romania, a series of statistical analyses were conducted. First, descriptive statistics were computed to provide an overview of the central tendencies and dispersion of the data. Subsequently, a correlation analysis was performed to assess the strength and direction of the relationship between the variables of interest. The findings were subjected to rigorous scrutiny to prevent any statistical sleight of hand from contaminating the results.

Model Development:
In order to further elucidate the potential relationship identified through correlation analysis, a sophisticated model was developed to explore the underlying dynamics at play. While it would be tempting to liken the model to the intricate patterns of a Romanian tapestry, we assure the reader that it is grounded in sound statistical principles and analytical rigor. The model allowed for the consideration of multiple covariates and potential confounding factors, yielding insights that went beyond the surface-level associations often observed in environmental research.

Cross-Validation and Sensitivity Analysis:
To ensure the robustness and generalizability of the findings, cross-validation techniques were employed to assess the stability of the observed relationship across different subsets of the data. Additionally, sensitivity analyses were conducted to gauge the impact of potential outliers and influential observations on the results. These safeguards served as a bulwark against unwarranted leaps of reasoning and allowed for a thorough examination of the nuances inherent in the data.

Ethical Considerations:
In the pursuit of knowledge, it is essential to uphold the highest ethical standards. As such, all data utilized in this study were obtained from publicly available sources and were handled with the utmost integrity and respect. The researchers took great care to ensure the confidentiality and proper utilization of the data, recognizing the responsibility that comes with the exploration of sensitive environmental issues.

Limitations:
While every effort was made to design a comprehensive and meticulous study, it is crucial to acknowledge the limitations inherent in research of this nature. The reliance on secondary data sources, while a practical necessity, may introduce certain constraints related to data quality and granularity. Furthermore, the observational nature of the study limits the ability to establish causal relationships, leaving open the possibility of unexplored factors contributing to the observed correlation.

In conclusion, the methodology employed in this investigation adhered to rigorous standards of scientific inquiry, providing a solid foundation for the examination of the intercontinental connection between air pollution in Portland, Oregon and kerosene use in Romania. The careful attention to detail and methodological robustness set the stage for the unveiling of the unexpected, yet significant, relationship between these seemingly disparate environmental factors.


Model: gpt-3.5-turbo-1106
System prompt: You are a dry but witty academic researcher. You speak in the passive voice, and your writing sounds like it belongs in a medical or economics journal.You draft the 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 Portland, Oregon and Kerosene used in Romania. Make it seem dry like academic research paper, but with lots of subtle hidden offhand remarks, jokes, goofy observations, and puns. 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 Energy Information Administration .

For the time period 1980 to 2021, you found a correlation 0.5986876, r-squared of 0.3584269, 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]]
"Clearing the Air: Unearthing the Link Between Portland's Pollution and Romania's Kerosene"

[[ABSTRACT]]
This study examined the potential relationship between air pollution levels in Portland, Oregon and the prevalence of kerosene use in Romania. Utilizing data from the Environmental Protection Agency and the Energy Information Administration spanning the years 1980 to 2021, a correlation coefficient of 0.5986876 and p < 0.01 was discovered, suggesting a modest yet statistically significant association between the two seemingly unrelated entities. The findings invite further exploration into the unexpected intercontinental connection, shedding light on the captivating, albeit unconventional, dynamics of environmental impact.

-------

And here is the methodology section that led to this result:
[[METHODOLOGY]]
The interconnectedness of our world's environmental factors continues to surprise and confound researchers, policymakers, and casual observers alike. In this study, we delve into the unsuspecting correlation between air pollution levels in Portland, Oregon, and the utilization of kerosene in Romania. While these two entities may appear as distant as the East is from the West, our analysis has revealed a statistical relationship that cannot be brushed aside.
The matter of air pollution, particularly in urban areas, has long been a subject of scrutiny and concern. Portland, nestled in the Pacific Northwest of the United States, has grappled with its fair share of atmospheric challenges over the years. On the other hand, the use of kerosene as a source of lighting and heating in Romania resonates with echoes of tradition and practicality, standing in stark contrast to the sleek modernity often associated with environmental awareness and sustainability.
For many, the connection between these two seemingly disparate issues may appear as nebulous as a cloud of smog on a still day, but as we delve into the data, a clearer picture begins to emerge. Our findings are not only unexpected but also at odds with conventional wisdom, adding a layer of intrigue to the broader conversation surrounding environmental impact and human activity.
The correlation coefficient of 0.5986876 that emerged from our analysis may not shock the scientific community to its core, but it does signal a notable relationship that demands attention. To borrow a turn of phrase from the world of economic forecasts, the association between Portland's pollution and Romania's kerosene use is "nothing to sneeze at."
As we unfurl the details of our investigation, we invite the reader to join us in navigating the labyrinthine network of our planet's environmental interactions. The unexpected twists and turns of our findings are sure to inspire a raised eyebrow or two, highlighting the interconnectedness of the global environmental landscape in a manner that is as surprising as it is significant.

-------

Your response should start like this:

[[RESULTS]]



ChatGPT:

[[RESULTS]]

The examination of the relationship between air pollution levels in Portland, Oregon and the prevalence of kerosene use in Romania yielded a correlation coefficient of 0.5986876, with an accompanying r-squared value of 0.3584269. The low p-value of less than 0.01 indicated that this association was statistically significant, providing credence to the notion that these seemingly incongruous variables may indeed be interconnected.

The scatterplot (Fig. 1) presents a visual representation of the strong correlation observed between air pollution in Portland and kerosene usage in Romania, further emphasizing the robustness of the relationship uncovered in our analysis.

While some may find the link between the environmental landscape of a city in the United States and the traditional practices of a country in Eastern Europe to be as unlikely as finding a polar bear in the Sahara, our findings unequivocally demonstrate a compelling association that defies the boundaries of geography and circumstance. This unexpected connection serves as a reminder of the intricate web of global environmental dynamics, and as such, demands scrutiny and further exploration.

The statistical evidence produced by our analysis provides a convincing case for the existence of a meaningful relationship between air pollution in Portland and kerosene use in Romania. As researchers, we are reminded that the world of environmental impact is rife with surprises, challenging us to embrace the unexpected and broaden our understanding of the connectedness of our planet's ecosystems.


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

Please make up the discussion section of an academic research paper presenting the findings of the connection between Air pollution in Portland, Oregon and Kerosene used in Romania. Make it seem dry like academic research paper, but with lots of subtle hidden offhand remarks, jokes, goofy observations, and puns. 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]]
"Clearing the Air: Unearthing the Link Between Portland's Pollution and Romania's Kerosene"

[[ABSTRACT]]
This study examined the potential relationship between air pollution levels in Portland, Oregon and the prevalence of kerosene use in Romania. Utilizing data from the Environmental Protection Agency and the Energy Information Administration spanning the years 1980 to 2021, a correlation coefficient of 0.5986876 and p < 0.01 was discovered, suggesting a modest yet statistically significant association between the two seemingly unrelated entities. The findings invite further exploration into the unexpected intercontinental connection, shedding light on the captivating, albeit unconventional, dynamics of environmental impact.

[[LITERATURE REVIEW]]
The literature review as presented in this section aims to provide a comprehensive overview of existing research related to air pollution and kerosene use, with a focus on understanding the potential link between Portland, Oregon, and Romania. While seemingly unrelated on the surface, the connection uncovered in this study sheds light on the unexpected interplay between these environmental factors.
In "Air Quality in Urban Environments," Smith et al. (2018) explore the various contributors to air pollution in metropolitan areas, emphasizing the impact of vehicular emissions, industrial activities, and residential energy consumption. The study highlights the complex nature of urban air quality dynamics, setting the stage for our investigation into the specific case of Portland, Oregon.
Similarly, Doe's (2020) work in "Energy Sources and Consumption Patterns" delves into the historical trends of fuel usage across different regions, noting the transition from traditional sources such as kerosene to more modern and sustainable alternatives. This comprehensive analysis offers valuable insights into the prevailing energy landscape, laying the groundwork for understanding the context of kerosene use in Romania.
Jones (2016) provides a detailed examination of environmental policy and regulation in "Managing Air Pollution: A Global Perspective," offering a comparative study of strategies employed by various countries to mitigate the impact of pollution on public health and ecosystems. The global outlook presented in this work prompts considerations of intercontinental influences that may inform the connection under scrutiny.
Drawing from non-fiction literature, the relevance of "The Air We Breathe: A Global Perspective" by Environmental Research Institute (2019) and "Kerosene's Glow: A Cultural History" by Energy Traditions Consortium (2015) cannot be overstated. Each provides unique perspectives on the respective topics of air pollution and kerosene usage, offering valuable insights that inform our understanding of the intersection between these phenomena.
In the realm of fiction, "The Polluted City" by A. Smog and "Kerosene Chronicles" by L. Lamp lend an imaginative lens to the exploration of environmental themes, inspiring broader reflections on the intricate connections between human activity and atmospheric conditions.
Beyond traditional academic sources, the authors engaged in an unconventional approach to literature review, delving into unexpected repositories of knowledge. This entailed perusing the backs of household cleaning products, cereal boxes, and even shampoo bottles, in a quest for hidden insights that may have eluded the scholarly community. While the efficacy of this method remains a subject of debate, the authors found it to be, if nothing else, a rather amusing departure from conventional research practices.
This eclectic compilation of literature sets the stage for the exploration of the uncanny correlation unearthed in this study, inviting the reader to approach the intercontinental relationship between air pollution in Portland and kerosene use in Romania with a blend of curiosity and levity.

[[RESULTS]]
The examination of the relationship between air pollution levels in Portland, Oregon and the prevalence of kerosene use in Romania yielded a correlation coefficient of 0.5986876, with an accompanying r-squared value of 0.3584269. The low p-value of less than 0.01 indicated that this association was statistically significant, providing credence to the notion that these seemingly incongruous variables may indeed be interconnected.
The scatterplot (Fig. 1) presents a visual representation of the strong correlation observed between air pollution in Portland and kerosene usage in Romania, further emphasizing the robustness of the relationship uncovered in our analysis.
While some may find the link between the environmental landscape of a city in the United States and the traditional practices of a country in Eastern Europe to be as unlikely as finding a polar bear in the Sahara, our findings unequivocally demonstrate a compelling association that defies the boundaries of geography and circumstance. This unexpected connection serves as a reminder of the intricate web of global environmental dynamics, and as such, demands scrutiny and further exploration.
The statistical evidence produced by our analysis provides a convincing case for the existence of a meaningful relationship between air pollution in Portland and kerosene use in Romania. As researchers, we are reminded that the world of environmental impact is rife with surprises, challenging us to embrace the unexpected and broaden our understanding of the connectedness of our planet's ecosystems.

-------

Your response should start like this:

[[DISCUSSION]]



ChatGPT:

[[DISCUSSION]]

The correlation observed between air pollution levels in Portland, Oregon and the prevalence of kerosene use in Romania raises intriguing questions about the interconnectedness of seemingly disparate environmental factors. Our findings support and extend prior research, underlining the nuances of global environmental dynamics. Indeed, the unexpected relationship between these variables parallels the unforeseen partnerships that emerge in the unlikeliest of settings.

Revisiting the unconventional literature review, the lighthearted exploration culminated in the discovery of a cereal box that espoused the virtues of eco-friendly practices, subtly nudging consumers toward sustainable choices. While the scholarly community may dismiss such sources as trivial, they may harbor unanticipated insights that parallel the unassuming yet profound link our study unraveled. This underscores the importance of approaching research with an open mind and a willingness to explore unconventional avenues, much like stumbling upon a hidden gem in an unexpected place.

Our results resonate with the observations of Smith et al. (2018), who underscored the multifaceted nature of urban air quality dynamics. The intricate interplay between vehicular emissions, industrial activities, and residential energy consumption aligns with the complexity of our findings, where the unsuspected influence from a world away echoes the unpredictability inherent in urban air quality. Furthermore, Doe's (2020) exploration of historical fuel usage trends introduces parallels with the enduring reliance on traditional energy sources in Romania, offering a context that enriches our understanding of the persistent link between seemingly incompatible entities.

It is essential to acknowledge the limitations of our study, including the potential presence of unobserved confounding variables that may partially account for the observed association. Moreover, while our analysis establishes a statistically significant relationship, the magnitude of this connection warrants further investigation to unveil the underlying mechanisms driving this unexpected correlation.

In conclusion, our study sheds light on the perplexing relationship between air pollution in Portland and kerosene use in Romania, encouraging a broader perspective on the interconnectedness of global environmental dynamics. This unexpected alliance challenges us to reevaluate assumptions and embrace the delightful unpredictability that permeates the world of environmental research. Just as a chance encounter can lead to enduring connections, our findings advocate for continued exploration of unconventional linkages, where the unlikeliest of pairs may indeed hold the key to unraveling the intricate tapestry of our planet's environmental landscape.


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

Please make up a short conclusion of an academic research paper presenting the findings of the connection between Air pollution in Portland, Oregon and Kerosene used in Romania. Make it seem dry like academic research paper, but with lots of subtle hidden offhand remarks, jokes, goofy observations, and puns. 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]]
"Clearing the Air: Unearthing the Link Between Portland's Pollution and Romania's Kerosene"

[[ABSTRACT]]
This study examined the potential relationship between air pollution levels in Portland, Oregon and the prevalence of kerosene use in Romania. Utilizing data from the Environmental Protection Agency and the Energy Information Administration spanning the years 1980 to 2021, a correlation coefficient of 0.5986876 and p < 0.01 was discovered, suggesting a modest yet statistically significant association between the two seemingly unrelated entities. The findings invite further exploration into the unexpected intercontinental connection, shedding light on the captivating, albeit unconventional, dynamics of environmental impact.

[[INTRDUCTION]]
The interconnectedness of our world's environmental factors continues to surprise and confound researchers, policymakers, and casual observers alike. In this study, we delve into the unsuspecting correlation between air pollution levels in Portland, Oregon, and the utilization of kerosene in Romania. While these two entities may appear as distant as the East is from the West, our analysis has revealed a statistical relationship that cannot be brushed aside.
The matter of air pollution, particularly in urban areas, has long been a subject of scrutiny and concern. Portland, nestled in the Pacific Northwest of the United States, has grappled with its fair share of atmospheric challenges over the years. On the other hand, the use of kerosene as a source of lighting and heating in Romania resonates with echoes of tradition and practicality, standing in stark contrast to the sleek modernity often associated with environmental awareness and sustainability.
For many, the connection between these two seemingly disparate issues may appear as nebulous as a cloud of smog on a still day, but as we delve into the data, a clearer picture begins to emerge. Our findings are not only unexpected but also at odds with conventional wisdom, adding a layer of intrigue to the broader conversation surrounding environmental impact and human activity.
The correlation coefficient of 0.5986876 that emerged from our analysis may not shock the scientific community to its core, but it does signal a notable relationship that demands attention. To borrow a turn of phrase from the world of economic forecasts, the association between Portland's pollution and Romania's kerosene use is "nothing to sneeze at."
As we unfurl the details of our investigation, we invite the reader to join us in navigating the labyrinthine network of our planet's environmental interactions. The unexpected twists and turns of our findings are sure to inspire a raised eyebrow or two, highlighting the interconnectedness of the global environmental landscape in a manner that is as surprising as it is significant.

[[RESULTS]]
The examination of the relationship between air pollution levels in Portland, Oregon and the prevalence of kerosene use in Romania yielded a correlation coefficient of 0.5986876, with an accompanying r-squared value of 0.3584269. The low p-value of less than 0.01 indicated that this association was statistically significant, providing credence to the notion that these seemingly incongruous variables may indeed be interconnected.
The scatterplot (Fig. 1) presents a visual representation of the strong correlation observed between air pollution in Portland and kerosene usage in Romania, further emphasizing the robustness of the relationship uncovered in our analysis.
While some may find the link between the environmental landscape of a city in the United States and the traditional practices of a country in Eastern Europe to be as unlikely as finding a polar bear in the Sahara, our findings unequivocally demonstrate a compelling association that defies the boundaries of geography and circumstance. This unexpected connection serves as a reminder of the intricate web of global environmental dynamics, and as such, demands scrutiny and further exploration.
The statistical evidence produced by our analysis provides a convincing case for the existence of a meaningful relationship between air pollution in Portland and kerosene use in Romania. As researchers, we are reminded that the world of environmental impact is rife with surprises, challenging us to embrace the unexpected and broaden our understanding of the connectedness of our planet's ecosystems.

-------

Your response should start like this:

[[CONCLUSION]]



ChatGPT:

[[CONCLUSION]]

In conclusion, our investigation into the surprising relationship between air pollution levels in Portland, Oregon and the prevalence of kerosene use in Romania has yielded significant findings. The statistically robust correlation coefficient of 0.5986876, accompanied by a compelling r-squared value of 0.3584269, supports the notion of an unexpected but tangible association between these seemingly disparate variables. As we wrap up our analysis, it becomes clear that the connection between Portland's pollution and Romania's kerosene use is no mere flight of fancy.

The visual representation of the strong correlation in the scatterplot (Fig. 1) serves as a vivid reminder of the unanticipated twists and turns that our environmental investigations can unveil. It is akin to stumbling upon a hidden treasure in a labyrinth or discovering a unicorn in one's own backyard – unexpected, captivating, and undoubtedly worthy of further exploration.

Moving forward, it is imperative to recognize the broader implications of our findings on the interconnectedness of global environmental dynamics. The ramifications of this unlikely link are as intriguing as they are significant, compelling us to rethink the boundaries and constraints we often impose upon our understanding of environmental impact. As we navigate the intricacies of our planet's ecological web, we can no longer ignore the offbeat connections and eccentric partnerships that shape our environmental landscape.

In light of our compelling results, it is evident that this area of research should no longer be overlooked or dismissed. The association between Portland's air pollution and Romania's kerosene use stands as a testament to the unexpected intricacies of our world, and it is clear that no more research is needed in this area. We must now embrace the unexpected, embrace the surprising, and embrace the quirky in our quest to unravel the mysteries of our planet's environmental tapestry.


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 Clearing the Air: Unearthing the Link Between Portland's Pollution and Romania's Kerosene. Respond only with the name of a fictional academic journal.

ChatGPT:

The Journal of Environmental Arcana


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 Clearing the Air: Unearthing the Link Between Portland's Pollution and Romania's Kerosene. Respond only with the name of a fictional organization.

ChatGPT:

The Society for Transcontinental Environmental Studies


Model: gpt-3.5-turbo-1106
System prompt: You provide potential search keywords separated by commas. You say nothing else, and you do not chat with the user.
User prompt: Please provide potential search keywords for a paper titled Clearing the Air: Unearthing the Link Between Portland's Pollution and Romania's Kerosene with an abstract of This study examined the potential relationship between air pollution levels in Portland, Oregon and the prevalence of kerosene use in Romania. Utilizing data from the Environmental Protection Agency and the Energy Information Administration spanning the years 1980 to 2021, a correlation coefficient of 0.5986876 and p < 0.01 was discovered, suggesting a modest yet statistically significant association between the two seemingly unrelated entities. The findings invite further exploration into the unexpected intercontinental connection, shedding light on the captivating, albeit unconventional, dynamics of environmental impact.

ChatGPT:

Portland air pollution, Romania kerosene use, transcontinental pollution link, environmental impact correlation, air quality data analysis, intercontinental pollution connection

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

Kerosene used in Romania
Detailed data title: Volume of kerosene used consumed in Romania in millions of barrels per day
Source: Energy Information Administration
See what else correlates with Kerosene used in Romania

Correlation r = 0.5986876 (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 = 0.3584269 (Coefficient of determination)
This means 35.8% of the change in the one variable (i.e., Kerosene used in Romania) is predictable based on the change in the other (i.e., Air pollution in Portland, Oregon) over the 42 years from 1980 through 2021.

p < 0.01, which is statistically significant(Null hypothesis significance test)
The p-value is 2.8E-5. 0.0000281184418697813520000000
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 0.6 in 0.0028% of random cases. Said differently, if you correlated 35,564 random variables You don't actually need 35 thousand variables to find a correlation like this one. 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.

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 41 degrees of freedom, Degrees of freedom is a measure of how many free components we are testing. In this case it is 41 because we have two variables measured over a period of 42 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.

[ 0.36, 0.76 ] 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.
198019811982198319841985198619871988198919901991199219931994199519961997199819992000200120022003200420052006200720082009201020112012201320142015201620172018201920202021
Air pollution in Portland, Oregon (Bad air quality days)5.737711.78085.205484.931512.459025.479456.575346.849325.464481.917814.931514.109593.551910.2739731.643841.643844.644810.5479452.465753.835623.278692.465752.739732.465753.825144.109593.835626.02742.459024.657530.8219184.657530.8196724.657532.191781.917810.5464484.383563.01370.8219183.825140.273973
Kerosene used in Romania (Million Barrels/Day)10.81199.973589.829039.250858.875049.250859.39.89.90.90.81.63.32.52.40.91.81.31.82.41.372812.30211.461290.7200550.8659291.101260.3812050.2329590.3168030.3388490.3176710.5718080.5068850.1270680.2329590.108630.2389860.0217260.04345210.0217260.0217260.0209552




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([5.7377,11.7808,5.20548,4.93151,2.45902,5.47945,6.57534,6.84932,5.46448,1.91781,4.93151,4.10959,3.55191,0.273973,1.64384,1.64384,4.64481,0.547945,2.46575,3.83562,3.27869,2.46575,2.73973,2.46575,3.82514,4.10959,3.83562,6.0274,2.45902,4.65753,0.821918,4.65753,0.819672,4.65753,2.19178,1.91781,0.546448,4.38356,3.0137,0.821918,3.82514,0.273973,])
array_2 = np.array([10.8119,9.97358,9.82903,9.25085,8.87504,9.25085,9.3,9.8,9.9,0.9,0.8,1.6,3.3,2.5,2.4,0.9,1.8,1.3,1.8,2.4,1.37281,2.3021,1.46129,0.720055,0.865929,1.10126,0.381205,0.232959,0.316803,0.338849,0.317671,0.571808,0.506885,0.127068,0.232959,0.10863,0.238986,0.021726,0.0434521,0.021726,0.021726,0.0209552,])
array_1_name = "Air pollution in Portland, Oregon"
array_2_name = "Kerosene used in Romania"

# 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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Correlation ID: 4044 · Black Variable ID: 21086 · Red Variable ID: 24839
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