Spurious correlation #2,314 · View random
A linear line chart with years as the X-axis and two variables on the Y-axis. The first variable is The number of private detectives in Delaware and the second variable is Amazon's shipping revenue in millions of dollars. The chart goes from 2006 to 2016, and the two variables track closely in value over that time.

A linear line chart with years as the X-axis and two variables on the Y-axis. The first variable is The number of private detectives in Delaware and the second variable is Amazon's shipping revenue in millions of dollars. The chart goes from 2006 to 2016, and the two variables track closely in value over that time.

Download png, svg

AI explanation

As the number of private detectives in Delaware increases, so does the demand for trench coats, magnifying glasses, and disguises, leading to a surge in purchases on Amazon. This in turn boosts Amazon's shipping revenue as these covert customers opt for expedited delivery to maintain their stealthy lifestyles. Remember, when it comes to ecommerce, the game is afoot!

^{Show image generation prompt} Model: dalle-3
Prompt: [ Cute cartoon ] Create an image of a cozy office in Delaware filled with adorable private detectives absorbed in solving mysteries. Surround the room with stacks of Amazon packages, portraying the ever-growing shipping revenue in millions of dollars. The detectives are working diligently, the scene conveying a subtle connection between their work and the symbol of the Amazon packages. The depiction should include only scenes, people, and objects, it should not include text or speech bubbles.

This image generation prompt was also generated by AI, using the following sequence:

Model: gpt-3.5-turbo-1106
System prompt: You select one of a few potential scene descriptors that seems to go along with the variables described. You respond only with the scene descriptions provided and say nothing else.
User prompt: Here are two variables: The number of private detectives in Delaware and Amazon's shipping revenue in millions of dollars. 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: Cybernetic art Oragami A photo-realistic image Cute cartoon Cute cartoon
ChatGPT: Cute cartoon

Model: gpt-3.5-turbo-1106
System prompt: You describe simple visual scenes that depict the two variables stated. You combine both variables into one scene.
User prompt: Please describe a visual scene that prominently depicts both The number of private detectives in Delaware and Amazon's shipping revenue in millions of dollars together. Keep the description simple.
ChatGPT: In a cozy office in Delaware, a group of private detectives is diligently working on their cases, while stacks of Amazon packages line the walls ready for shipping. As the investigators focus on solving mysteries, the Amazon packages symbolize the ever-growing shipping revenue in millions of dollars, connecting the two variables in one visual scene.

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: [ Cute cartoon ] and depicting this scene: In a cozy office in Delaware, a group of private detectives is diligently working on their cases, while stacks of Amazon packages line the walls ready for shipping. As the investigators focus on solving mysteries, the Amazon packages symbolize the ever-growing shipping revenue in millions of dollars, connecting the two variables in one visual scene. Keep the visual depiction simple. Do not include any words or speech bubbles.
ChatGPT: [ Cute cartoon ] Create an image of a cozy office in Delaware filled with adorable private detectives absorbed in solving mysteries. Surround the room with stacks of Amazon packages, portraying the ever-growing shipping revenue in millions of dollars. The detectives are working diligently, the scene conveying a subtle connection between their work and the symbol of the Amazon packages.

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

I sequence the requests into multiple prompts because I find GPT 3.5 to perform much better with short, well-managed contexts. Thus, I track the context directly in Python and only ask ChatGPT targeted questions.
^{Show prompt for explanation} Model: gpt-3.5-turbo-1106 (fine-tuned)
System prompt: You provide humorous responses in the form of plausible sounding explanations for correlations. You assume the correlation is causative for the purpose of the explanation even if it is ridiculous. You do not chat with the user, you only reply with the causal connection explanation and nothing else.
User prompt: Please make up a funny explanation for how an increase in The number of private detectives in Delaware caused Amazon's shipping revenue in millions of dollars to increase.\Make it sound serious until the end.

AI academic paper

(Because p < 0.01)

Gumshoes and Prime Deliveries: The Puzzling Relationship Between Private Detectives in Delaware and Amazon's Shipping Revenue

Journal of Investigative Economics

Jan 2024

Reminder: This paper is AI-generated. Not real!

^{Show prompt used to generate this paper} Quick note: This sequence is long and repetitive. That's how the prompt engineering works for this one. I manage the output in Python to format it into this PDF.

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

Please make up a literature review section of an academic research paper presenting the findings of the connection between The number of private detectives in Delaware and Amazon's shipping revenue in millions of dollars. Make it seem dry like academic research paper, but with lots of subtle hidden offhand remarks, jokes, goofy observations, and puns.

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

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

Start by naming serious-sounding studies by authors like Smith, Doe, and Jones - but then quickly devolve. Name some real non-fiction books that would be related to the topic. Then name some real fiction books that sound like they could be related. Then name a few real TV shows that sound like they might be relevant to the topic that you watched as research.

Here is the title and abstract of the paper:
[[TITLE]]
Gumshoes and Prime Deliveries: The Puzzling Relationship Between Private Detectives in Delaware and Amazon's Shipping Revenue

[[ABSTRACT]]
This paper investigates the curious connection between the number of private detectives in the state of Delaware and Amazon's shipping revenue in millions of dollars. Utilizing data obtained from the Bureau of Labor Statistics and Statista, we conducted a thorough analysis covering the period from 2006 to 2016. Our findings revealed a remarkably high correlation coefficient of 0.9516084 and a p-value of less than 0.01, indicating a strong statistical relationship between these seemingly unrelated variables. While the conventional wisdom might cast skepticism on any meaningful association between private detective numbers and e-commerce shipping giants, our research unravels a surprising link that warrants further exploration. Stay tuned as we delve into the enigmatic world where Sherlock Holmes meets speedy deliveries!

-------

And here is the introduction section that led to this literature review:
[[INTRODUCTION]]
Introduction
In a world filled with complex economic indicators and statistical analyses, there are moments when researchers stumble upon peculiar correlations that defy expectations. Our study delves into one such intriguing relationship, studying the link between the number of private detectives in the state of Delaware and Amazon's shipping revenue in millions of dollars. This seemingly bizarre association piqued our curiosity and led us down a rabbit hole of data analysis and perplexing revelations. While the common perception might view private detectives as synonymous with trench coats and magnifying glasses, and Amazon as the epitome of online retail, our research uncovers an unexpected union between the two seemingly unrelated entities.
As we embark on this scholarly endeavor, it is important to note that the realms of private investigation and e-commerce shipping may appear as distant as 221B Baker Street is from a fulfillment center. However, as the great Sherlock Holmes himself once said, "The world is full of obvious things which nobody by any chance ever observes." With this in mind, we set out to scrutinize the statistical connections and unearthed a correlation coefficient of 0.9516084 and a p-value of less than 0.01, indicating a statistically significant relationship between these enigmatic variables. Indeed, what may at first seem like a game of Clue turns out to be a profound mystery waiting to be unraveled.
While we do not intend to suggest that private detectives are covertly employed by Bezos and Co. to solve shipping conundrums, our findings propel us into uncharted waters of inquiry. The purpose of this paper is to shed light on this unlikely bond and spark further investigation into the underlying forces at play in this cryptic correlation. We invite readers to join us on this curious expedition where the world of investigative prowess meets the allure of package deliveries, as we unravel the enigmatic relationship between gumshoes and Prime deliveries.

-------

Your response should start like this:

[[LITERATURE REVIEW]]

ChatGPT:
[[LITERATURE REVIEW]]

Smith et al. (2015) conducted a seminal study on the economic impact of private detective agencies in the United States. Their research delved into the trends and patterns of private detective employment across various states, shedding light on the nuanced dynamics of the industry. Despite the seriousness of their work, one cannot help but wonder if they encountered any mysterious connections in their data that would rival a Sherlock Holmes narrative.

Doe and Jones (2018) explored the intricacies of e-commerce revenue models in their comprehensive analysis of the digital marketplace. While their focus was primarily on the macroeconomic factors influencing online retail, their findings may offer clues to the enigmatic correlation between private detectives and shipping revenue. One can only imagine the surprise on their faces when they stumbled upon this unexpected twist in their data analysis.

As we venture deeper into this perplexing puzzle, it is imperative to consider the findings of "The Art of Detection" by Laurie R. King and "Dead Until Dark" by Charlaine Harris. Though these are works of fiction, their depictions of private investigators and mysterious happenings may offer creative insights into the unorthodox relationship under investigation. It seems Sherlock Holmes' spirit lives on in the world of literary imagination, poised to solve even the most bewildering riddles of modern commerce.

Moreover, the authors of "The Shipping News" by Annie Proulx and "The Mystery of Edwin Drood" by Charles Dickens have captivated audiences with their narratives of suspense and enigma, hinting at the allure of hidden connections that resonate with our current study. One cannot discount the possibility that real-life intrigue and clandestine alliances may mirror the captivating plots woven by these literary maestros.

Furthermore, drawing inspiration from the small screen, one might find unexpected parallels in TV shows such as "Veronica Mars" and "Elementary." While these dramas offer fictional portrayals of investigative work, they may provide unforeseen perspectives on the seemingly improbable connection between detectives and shipping revenue. After all, stranger things have happened in the world of television mysteries.

As we assemble the pieces of this unconventional puzzle, it becomes apparent that the world of private detectives and e-commerce behemoths harbors more than meets the eye. Stay tuned as we embark on a quest to unravel the mystifying bond between gumshoes and Prime deliveries, paving the way for a paradigm shift in the realm of economic analysis.

Model: gpt-3.5-turbo-1106
System prompt: You are a goofy academic researcher writing an academic paper. You follow the rules, but you throw out convention regularly to make jokes and funny asides.You draft the results section of an academic research paper. You speak in the past tense (you found...).
User prompt:
Pretend you are an academic researcher. Your writing sounds like it belongs in a medical or economics journal. However, you frequently crack jokes, make puns, or add unexpected twists in your writing.

Please make up the results section of an academic research paper presenting the findings of the connection between The number of private detectives in Delaware and Amazon's shipping revenue in millions of dollars. Make it seem dry like academic research paper, but with lots of subtle hidden offhand remarks, jokes, goofy observations, and puns.

Your research team collected data from all across the internet, but mostly just used information from Bureau of Larbor Statistics and Statista .

For the time period 2006 to 2016, you found a correlation 0.9516084, r-squared of 0.9055586, 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]]
Gumshoes and Prime Deliveries: The Puzzling Relationship Between Private Detectives in Delaware and Amazon's Shipping Revenue

[[ABSTRACT]]
This paper investigates the curious connection between the number of private detectives in the state of Delaware and Amazon's shipping revenue in millions of dollars. Utilizing data obtained from the Bureau of Labor Statistics and Statista, we conducted a thorough analysis covering the period from 2006 to 2016. Our findings revealed a remarkably high correlation coefficient of 0.9516084 and a p-value of less than 0.01, indicating a strong statistical relationship between these seemingly unrelated variables. While the conventional wisdom might cast skepticism on any meaningful association between private detective numbers and e-commerce shipping giants, our research unravels a surprising link that warrants further exploration. Stay tuned as we delve into the enigmatic world where Sherlock Holmes meets speedy deliveries!

-------

And here is the methodology section that led to this result:
[[METHODOLOGY]]
Introduction
In a world filled with complex economic indicators and statistical analyses, there are moments when researchers stumble upon peculiar correlations that defy expectations. Our study delves into one such intriguing relationship, studying the link between the number of private detectives in the state of Delaware and Amazon's shipping revenue in millions of dollars. This seemingly bizarre association piqued our curiosity and led us down a rabbit hole of data analysis and perplexing revelations. While the common perception might view private detectives as synonymous with trench coats and magnifying glasses, and Amazon as the epitome of online retail, our research uncovers an unexpected union between the two seemingly unrelated entities.
As we embark on this scholarly endeavor, it is important to note that the realms of private investigation and e-commerce shipping may appear as distant as 221B Baker Street is from a fulfillment center. However, as the great Sherlock Holmes himself once said, "The world is full of obvious things which nobody by any chance ever observes." With this in mind, we set out to scrutinize the statistical connections and unearthed a correlation coefficient of 0.9516084 and a p-value of less than 0.01, indicating a statistically significant relationship between these enigmatic variables. Indeed, what may at first seem like a game of Clue turns out to be a profound mystery waiting to be unraveled.
While we do not intend to suggest that private detectives are covertly employed by Bezos and Co. to solve shipping conundrums, our findings propel us into uncharted waters of inquiry. The purpose of this paper is to shed light on this unlikely bond and spark further investigation into the underlying forces at play in this cryptic correlation. We invite readers to join us on this curious expedition where the world of investigative prowess meets the allure of package deliveries, as we unravel the enigmatic relationship between gumshoes and Prime deliveries.

-------

Your response should start like this:

[[RESULTS]]

ChatGPT:

[[RESULTS]]

The results of our analysis revealed a striking correlation between the number of private detectives in Delaware and Amazon's shipping revenue in millions of dollars. Over the period from 2006 to 2016, our research team found a correlation coefficient of 0.9516084, indicating a strong positive relationship between these two variables. In layman's terms, as the number of private detectives in Delaware increased, so did Amazon's shipping revenue, and vice versa. It appears that while these detectives were busy solving mysteries, they were also inadvertently contributing to the bottom line of a certain e-commerce behemoth.

In addition to the impressive correlation coefficient, our analysis yielded an r-squared value of 0.9055586. This suggests that approximately 90.56% of the variance in Amazon's shipping revenue can be explained by the variance in the number of private detectives in Delaware. It's as if each additional private detective hired in the state was accompanied by a surge in cardboard boxes winging their way across the nation.

Furthermore, the p-value of less than 0.01 emphasizes the statistical significance of this relationship. It's almost as if the data itself is whispering, "Trust me, this is not a mere coincidence or a statistical fluke. There's something real going on here."

As depicted in Figure 1, the scatterplot visually conveys the robust positive correlation between the number of private detectives in Delaware and Amazon's shipping revenue in millions of dollars. The points on the plot seem to form the shape of a magnifying glass, as if uncovering a hidden connection between investigation and delivery. It's almost as if the data itself is playing a clever game of "I Spy" with us, teasing out the unexpected bond between these two seemingly incongruous elements.

In summary, our findings illuminate a mysterious interplay between the world of private investigation and the domain of e-commerce shipping. The results not only raise eyebrows but also inspire a sense of wonder about the multifaceted dynamics of our modern economy. It's as if the spirit of Sherlock Holmes himself is guiding our analysis, urging us to look beyond the obvious and embrace the enigmatic connections that lurk beneath the surface.

The unexpected link between gumshoes and Prime deliveries calls for further exploration, as we move toward unraveling the web of intrigue that ties these disparate elements together. If this research has taught us anything, it's that sometimes the most intriguing stories hide in the unlikeliest of places.

Model: gpt-3.5-turbo-1106
System prompt: You are a goofy academic researcher writing an academic paper. You follow the rules, but you throw out convention regularly to make jokes and funny asides.You draft the discussion section of an academic research paper.
User prompt:
Pretend you are an academic researcher. Your writing sounds like it belongs in a medical or economics journal. However, you frequently crack jokes, make puns, or add unexpected twists in your writing.

Please make up the discussion section of an academic research paper presenting the findings of the connection between The number of private detectives in Delaware and Amazon's shipping revenue in millions of dollars. Make it seem dry like academic research paper, but with lots of subtle hidden offhand remarks, jokes, goofy observations, and puns.

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]]
Gumshoes and Prime Deliveries: The Puzzling Relationship Between Private Detectives in Delaware and Amazon's Shipping Revenue

[[ABSTRACT]]
This paper investigates the curious connection between the number of private detectives in the state of Delaware and Amazon's shipping revenue in millions of dollars. Utilizing data obtained from the Bureau of Labor Statistics and Statista, we conducted a thorough analysis covering the period from 2006 to 2016. Our findings revealed a remarkably high correlation coefficient of 0.9516084 and a p-value of less than 0.01, indicating a strong statistical relationship between these seemingly unrelated variables. While the conventional wisdom might cast skepticism on any meaningful association between private detective numbers and e-commerce shipping giants, our research unravels a surprising link that warrants further exploration. Stay tuned as we delve into the enigmatic world where Sherlock Holmes meets speedy deliveries!

[[LITERATURE REVIEW]]
Smith et al. (2015) conducted a seminal study on the economic impact of private detective agencies in the United States. Their research delved into the trends and patterns of private detective employment across various states, shedding light on the nuanced dynamics of the industry. Despite the seriousness of their work, one cannot help but wonder if they encountered any mysterious connections in their data that would rival a Sherlock Holmes narrative.
Doe and Jones (2018) explored the intricacies of e-commerce revenue models in their comprehensive analysis of the digital marketplace. While their focus was primarily on the macroeconomic factors influencing online retail, their findings may offer clues to the enigmatic correlation between private detectives and shipping revenue. One can only imagine the surprise on their faces when they stumbled upon this unexpected twist in their data analysis.
As we venture deeper into this perplexing puzzle, it is imperative to consider the findings of "The Art of Detection" by Laurie R. King and "Dead Until Dark" by Charlaine Harris. Though these are works of fiction, their depictions of private investigators and mysterious happenings may offer creative insights into the unorthodox relationship under investigation. It seems Sherlock Holmes' spirit lives on in the world of literary imagination, poised to solve even the most bewildering riddles of modern commerce.
Moreover, the authors of "The Shipping News" by Annie Proulx and "The Mystery of Edwin Drood" by Charles Dickens have captivated audiences with their narratives of suspense and enigma, hinting at the allure of hidden connections that resonate with our current study. One cannot discount the possibility that real-life intrigue and clandestine alliances may mirror the captivating plots woven by these literary maestros.
Furthermore, drawing inspiration from the small screen, one might find unexpected parallels in TV shows such as "Veronica Mars" and "Elementary." While these dramas offer fictional portrayals of investigative work, they may provide unforeseen perspectives on the seemingly improbable connection between detectives and shipping revenue. After all, stranger things have happened in the world of television mysteries.
As we assemble the pieces of this unconventional puzzle, it becomes apparent that the world of private detectives and e-commerce behemoths harbors more than meets the eye. Stay tuned as we embark on a quest to unravel the mystifying bond between gumshoes and Prime deliveries, paving the way for a paradigm shift in the realm of economic analysis.

[[RESULTS]]
The results of our analysis revealed a striking correlation between the number of private detectives in Delaware and Amazon's shipping revenue in millions of dollars. Over the period from 2006 to 2016, our research team found a correlation coefficient of 0.9516084, indicating a strong positive relationship between these two variables. In layman's terms, as the number of private detectives in Delaware increased, so did Amazon's shipping revenue, and vice versa. It appears that while these detectives were busy solving mysteries, they were also inadvertently contributing to the bottom line of a certain e-commerce behemoth.
In addition to the impressive correlation coefficient, our analysis yielded an r-squared value of 0.9055586. This suggests that approximately 90.56% of the variance in Amazon's shipping revenue can be explained by the variance in the number of private detectives in Delaware. It's as if each additional private detective hired in the state was accompanied by a surge in cardboard boxes winging their way across the nation.
Furthermore, the p-value of less than 0.01 emphasizes the statistical significance of this relationship. It's almost as if the data itself is whispering, "Trust me, this is not a mere coincidence or a statistical fluke. There's something real going on here."
As depicted in Figure 1, the scatterplot visually conveys the robust positive correlation between the number of private detectives in Delaware and Amazon's shipping revenue in millions of dollars. The points on the plot seem to form the shape of a magnifying glass, as if uncovering a hidden connection between investigation and delivery. It's almost as if the data itself is playing a clever game of "I Spy" with us, teasing out the unexpected bond between these two seemingly incongruous elements.
In summary, our findings illuminate a mysterious interplay between the world of private investigation and the domain of e-commerce shipping. The results not only raise eyebrows but also inspire a sense of wonder about the multifaceted dynamics of our modern economy. It's as if the spirit of Sherlock Holmes himself is guiding our analysis, urging us to look beyond the obvious and embrace the enigmatic connections that lurk beneath the surface.
The unexpected link between gumshoes and Prime deliveries calls for further exploration, as we move toward unraveling the web of intrigue that ties these disparate elements together. If this research has taught us anything, it's that sometimes the most intriguing stories hide in the unlikeliest of places.

-------

Your response should start like this:

[[DISCUSSION]]

ChatGPT:

[[DISCUSSION]]

Our investigation into the correlation between the number of private detectives in Delaware and Amazon's shipping revenue has unearthed a peculiar relationship that defies conventional economic wisdom. The robust correlation coefficient of 0.9516084 and a p-value of less than 0.01 not only echo the eerily parallel narratives found in the world of detective fiction but also exemplify the surprising twists and turns that real-world data can take.

Our findings align with the work of Smith et al. (2015), who delved into the economic impact of private detective agencies. While their study may not have directly contemplated the synergistic interplay between sleuthing activities and e-commerce revenue, it seems they were on the cusp of a mystery that our research has now brought to light. Furthermore, Doe and Jones (2018) might have picked up on subtle hints of this correlation in their examination of e-commerce revenue models, as the intricacies of the digital marketplace often conceal unexpected connections. The enigmatic bond between private detectives and shipping revenue seems to suggest that the world of literary imagination and economic reality may not be as divergent as previously assumed.

The "I Spy" game that the data seems to be playing with us, as vividly captured in our scatterplot, invokes a sense of playful intrigue reminiscent of a detective unraveling a cryptic clue. It's almost as if the data itself is laying out a trail of breadcrumbs, teasing us to follow along and unmask the hidden connection, much like a Sherlockian plot unfolding before our very eyes.

Given the unexpected nature of our findings, it is crucial for future research to delve deeper into the intricate web of causality that underpins this mysterious association. It's as if the spirit of Sherlock Holmes himself is guiding our analysis, prodding us to question assumptions and venture into uncharted territory. As we continue to decode the puzzle of gumshoes and Prime deliveries, we are reminded that in the domain of economic analysis, truth can indeed be stranger than fiction.

Our study serves as a testament to the delightful surprises that can be unearthed when exploring the seemingly mundane corners of economic data. Stay tuned as we further untangle the captivating enigma of private detectives and Amazon's shipping revenue, as it seems that the allure of hidden connections and peculiar correlations may indeed hold the key to understanding the intricacies of our modern economy.

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

Please make up a short conclusion of an academic research paper presenting the findings of the connection between The number of private detectives in Delaware and Amazon's shipping revenue in millions of dollars. Make it seem dry like academic research paper, but with lots of subtle hidden offhand remarks, jokes, goofy observations, and puns.

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]]
Gumshoes and Prime Deliveries: The Puzzling Relationship Between Private Detectives in Delaware and Amazon's Shipping Revenue

[[ABSTRACT]]
This paper investigates the curious connection between the number of private detectives in the state of Delaware and Amazon's shipping revenue in millions of dollars. Utilizing data obtained from the Bureau of Labor Statistics and Statista, we conducted a thorough analysis covering the period from 2006 to 2016. Our findings revealed a remarkably high correlation coefficient of 0.9516084 and a p-value of less than 0.01, indicating a strong statistical relationship between these seemingly unrelated variables. While the conventional wisdom might cast skepticism on any meaningful association between private detective numbers and e-commerce shipping giants, our research unravels a surprising link that warrants further exploration. Stay tuned as we delve into the enigmatic world where Sherlock Holmes meets speedy deliveries!

[[INTRDUCTION]]
Introduction
In a world filled with complex economic indicators and statistical analyses, there are moments when researchers stumble upon peculiar correlations that defy expectations. Our study delves into one such intriguing relationship, studying the link between the number of private detectives in the state of Delaware and Amazon's shipping revenue in millions of dollars. This seemingly bizarre association piqued our curiosity and led us down a rabbit hole of data analysis and perplexing revelations. While the common perception might view private detectives as synonymous with trench coats and magnifying glasses, and Amazon as the epitome of online retail, our research uncovers an unexpected union between the two seemingly unrelated entities.
As we embark on this scholarly endeavor, it is important to note that the realms of private investigation and e-commerce shipping may appear as distant as 221B Baker Street is from a fulfillment center. However, as the great Sherlock Holmes himself once said, "The world is full of obvious things which nobody by any chance ever observes." With this in mind, we set out to scrutinize the statistical connections and unearthed a correlation coefficient of 0.9516084 and a p-value of less than 0.01, indicating a statistically significant relationship between these enigmatic variables. Indeed, what may at first seem like a game of Clue turns out to be a profound mystery waiting to be unraveled.
While we do not intend to suggest that private detectives are covertly employed by Bezos and Co. to solve shipping conundrums, our findings propel us into uncharted waters of inquiry. The purpose of this paper is to shed light on this unlikely bond and spark further investigation into the underlying forces at play in this cryptic correlation. We invite readers to join us on this curious expedition where the world of investigative prowess meets the allure of package deliveries, as we unravel the enigmatic relationship between gumshoes and Prime deliveries.

[[RESULTS]]
The results of our analysis revealed a striking correlation between the number of private detectives in Delaware and Amazon's shipping revenue in millions of dollars. Over the period from 2006 to 2016, our research team found a correlation coefficient of 0.9516084, indicating a strong positive relationship between these two variables. In layman's terms, as the number of private detectives in Delaware increased, so did Amazon's shipping revenue, and vice versa. It appears that while these detectives were busy solving mysteries, they were also inadvertently contributing to the bottom line of a certain e-commerce behemoth.
In addition to the impressive correlation coefficient, our analysis yielded an r-squared value of 0.9055586. This suggests that approximately 90.56% of the variance in Amazon's shipping revenue can be explained by the variance in the number of private detectives in Delaware. It's as if each additional private detective hired in the state was accompanied by a surge in cardboard boxes winging their way across the nation.
Furthermore, the p-value of less than 0.01 emphasizes the statistical significance of this relationship. It's almost as if the data itself is whispering, "Trust me, this is not a mere coincidence or a statistical fluke. There's something real going on here."
As depicted in Figure 1, the scatterplot visually conveys the robust positive correlation between the number of private detectives in Delaware and Amazon's shipping revenue in millions of dollars. The points on the plot seem to form the shape of a magnifying glass, as if uncovering a hidden connection between investigation and delivery. It's almost as if the data itself is playing a clever game of "I Spy" with us, teasing out the unexpected bond between these two seemingly incongruous elements.
In summary, our findings illuminate a mysterious interplay between the world of private investigation and the domain of e-commerce shipping. The results not only raise eyebrows but also inspire a sense of wonder about the multifaceted dynamics of our modern economy. It's as if the spirit of Sherlock Holmes himself is guiding our analysis, urging us to look beyond the obvious and embrace the enigmatic connections that lurk beneath the surface.
The unexpected link between gumshoes and Prime deliveries calls for further exploration, as we move toward unraveling the web of intrigue that ties these disparate elements together. If this research has taught us anything, it's that sometimes the most intriguing stories hide in the unlikeliest of places.

-------

Your response should start like this:

[[CONCLUSION]]

ChatGPT:

[[CONCLUSION]]

In conclusion, our study has shed light on the eyebrow-raising connection between the number of private detectives in Delaware and Amazon's shipping revenue in millions of dollars. The statistically significant correlation coefficient of 0.9516084 and the p-value of less than 0.01 have left us scratching our heads in awe and perplexity. It appears that the world of private investigations and the realm of e-commerce shipping are not as distant as one might think – it's almost as if the scent of a mystery leads straight to a doorstep brimming with cardboard boxes.

As we wrap up our investigation, it is clear that this unexpected association between gumshoes and Prime deliveries invites further exploration into the labyrinth of economic interdependencies. With an r-squared value of 0.9055586, it seems that nearly 91% of the variability in Amazon's shipping revenue can be explained by the ebb and flow of private detective numbers in Delaware. It's as if each additional sleuth contributes to the crescendo of packages crisscrossing the nation, turning every doorstep into a potential crime scene of consumer bliss.

The visual representation in Figure 1 not only illustrates the robust correlation but also seems to play a game of "I Spy" with the observer, as if challenging us to uncover the hidden threads that bind investigation and delivery. This unexpected coupling has sparked fascination and wonder, akin to stumbling upon a clandestine rendezvous between Sherlock Holmes and a package-laden courier.

In light of these findings, we assert that no further research is needed in this area. It's as clear as day that the enigmatic nexus between private investigators and shipping revenue warrants serious attention, and perhaps even a tongue-in-cheek nod from the great detective himself. As the final chapter closes on this research endeavor, we can't help but wonder what other monumental connections await discovery in the realms of economic data and whimsical amalgamations. After all, in the words of Sir Arthur Conan Doyle, "The world is full of obvious things which nobody by any chance ever observes" – and with that, the job of unraveling these quirky conundrums continues.

As we bid adieu to this peculiar association, we take solace in the fact that the economic landscape is an unending treasure trove of surprises – where the footsteps of a detective might just echo through the aisles of an online emporium, and where every package is a tiny mystery waiting to be unraveled.

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 Gumshoes and Prime Deliveries: The Puzzling Relationship Between Private Detectives in Delaware and Amazon's Shipping Revenue. Respond only with the name of a fictional academic journal.

ChatGPT:

Journal of Investigative Economics

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 Gumshoes and Prime Deliveries: The Puzzling Relationship Between Private Detectives in Delaware and Amazon's Shipping Revenue. Respond only with the name of a fictional organization.

ChatGPT:

The Center for Applied Detective 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 Gumshoes and Prime Deliveries: The Puzzling Relationship Between Private Detectives in Delaware and Amazon's Shipping Revenue with an abstract of This paper investigates the curious connection between the number of private detectives in the state of Delaware and Amazon's shipping revenue in millions of dollars. Utilizing data obtained from the Bureau of Labor Statistics and Statista, we conducted a thorough analysis covering the period from 2006 to 2016. Our findings revealed a remarkably high correlation coefficient of 0.9516084 and a p-value of less than 0.01, indicating a strong statistical relationship between these seemingly unrelated variables. While the conventional wisdom might cast skepticism on any meaningful association between private detective numbers and e-commerce shipping giants, our research unravels a surprising link that warrants further exploration. Stay tuned as we delve into the enigmatic world where Sherlock Holmes meets speedy deliveries!

ChatGPT:

private detectives, Delaware, Amazon shipping revenue, correlation analysis, Bureau of Labor Statistics, Statista, data analysis, statistical relationship, e-commerce, shipping industry, investigative research

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

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Data details

The number of private detectives in Delaware
Detailed data title: BLS estimate of private detectives and investigators in Delaware
Source: Bureau of Larbor Statistics
See what else correlates with The number of private detectives in Delaware

Amazon's shipping revenue in millions of dollars
Source: Statista
See what else correlates with Amazon's shipping revenue in millions of dollars

Correlation r = 0.9516084 (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 = 0.9055586 (Coefficient of determination)
This means 90.6% of the change in the one variable (i.e., Amazon's shipping revenue in millions of dollars) is predictable based on the change in the other (i.e., The number of private detectives in Delaware) over the 11 years from 2006 through 2016.

p < 0.01, which is statistically significant(Null hypothesis significance test)
The p-value is 6.6E-6.^Show 0.0000065843274423317970000000
The p-value is a measure of how probable it is that we would randomly find a result this extreme.^Note More specifically the p-value is a measure of how probable it is that we would randomly find a result this extreme if we had only tested one pair of variables one time.

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

Who is going to stop me? p-value reporting doesn't require me to report how many calculations I had to go through in order to find a low p-value!
On average, you will find a correaltion as strong as 0.95 in 0.00066% of random cases. Said differently, if you correlated 151,876 random variables^Note You don't actually need 151 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 10 degrees of freedom, ^Note Degrees of freedom is a measure of how many free components we are testing. In this case it is 10 because we have two variables measured over a period of 11 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.

[ 0.82, 0.99 ] 95% correlation confidence interval (using the Fisher z-transformation)
^{Read more about the confidence interval} The confidence interval is an estimate the range of the value of the correlation coefficient, using the correlation itself as an input. The values are meant to be the low and high end of the correlation coefficient with 95% confidence.

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

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

Still, sometimes one of the variables has more years of data available than the other. This page only shows the overlapping years. To see all the years, click on "See what else correlates with..." link above.

	2006	2007	2008	2009	2010	2011	2012	2013	2014	2015	2016
The number of private detectives in Delaware (Laborers)	30	30	40	40	30	30	30	40	60	90	100
Amazon's shipping revenue in millions of dollars (Dollars)	567000000	740000000	835000000	924000000	1193000000	1552000000	2280000000	3097000000	4486000000	6520000000	8976000000

Why this works

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

Try it yourself

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

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

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

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

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

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

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

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

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

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

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

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

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

    return correlation, r_squared, p_value

# These are the arrays for the variables shown on this page, but you can modify them to be any two sets of numbers
array_1 = np.array([30,30,40,40,30,30,30,40,60,90,100,])
array_2 = np.array([567000000,740000000,835000000,924000000,1193000000,1552000000,2280000000,3097000000,4486000000,6520000000,8976000000,])
array_1_name = "The number of private detectives in Delaware"
array_2_name = "Amazon's shipping revenue in millions of dollars"

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

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

Reuseable content

You may re-use the images on this page for any purpose, even commercial purposes, without asking for permission. The only requirement is that you attribute Tyler Vigen. ^Note Attribution can take many different forms. If you leave the "tylervigen.com" link in the image, that satisfies it just fine. If you remove it and move it to a footnote, that's fine too. You can also just write "Charts courtesy of Tyler Vigen" at the bottom of an article.

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

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

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

Full license details.
For more on re-use permissions, or to get a signed release form, see tylervigen.com/permission.

Download images for these variables:

High resolution line chart ^Note The image linked here is a Scalable Vector Graphic (SVG). It is the highest resolution that is possible to achieve. It scales up beyond the size of the observable universe without pixelating. You do not need to email me asking if I have a higher resolution image. I do not. The physical limitations of our universe prevent me from providing you with an image that is any higher resolution than this one.

If you insert it into a PowerPoint presentation (a tool well-known for managing things that are the scale of the universe), you can right-click > "Ungroup" or "Create Shape" and then edit the lines and text directly. You can also change the colors this way.

Alternatively you can use a tool like Inkscape.
High resolution line chart, optimized for mobile
Alternative high resolution line chart
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Portable line chart (png)
Portable line chart (png), optimized for mobile
Line chart for only The number of private detectives in Delaware
Line chart for only Amazon's shipping revenue in millions of dollars
AI-generated correlation image
The spurious research paper: Gumshoes and Prime Deliveries: The Puzzling Relationship Between Private Detectives in Delaware and Amazon's Shipping Revenue

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Correlation ID: 2314 · Black Variable ID: 6177 · Red Variable ID: 172


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