Spurious correlation #4,104 · View random
A linear line chart with years as the X-axis and two variables on the Y-axis. The first variable is Annual US household spending on bakery products and the second variable is Intuitive Surgical's stock price (ISRG). The chart goes from 2002 to 2022, 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 Annual US household spending on bakery products and the second variable is Intuitive Surgical's stock price (ISRG). The chart goes from 2002 to 2022, and the two variables track closely in value over that time.

Download png, svg

AI explanation

As households indulged in more pastries and breads, there was a rise in dough flow. This yeast to the occasion, leading to higher demand for medical procedures, particularly for robotic surgery, hence driving up the stock price of Intuitive Surgical. It seems like the market was in knead of their innovative healthcare technology!

^{Show image generation prompt} Model: dalle-3
Prompt: Generate a photo-realistic image depicting a cozy bakery filled with customers buying bread and pastries as stacks of dough rise in the background. Meanwhile, adjacent to the bakery, a modern hospital with robotic surgery equipment is shown in high demand, with patients being treated with cutting-edge technology. Above the scene, a digital ticker displays the soaring stock price of Intuitive Surgical (ISRG), indicating investor confidence in the company's innovative healthcare solutions. 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: Annual US household spending on bakery products and Intuitive Surgical's stock price (ISRG). 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: An image that looks like it is a scene from A Disney Movie Voxel art Sci-fi fantacy Low poly A photo-realistic image
ChatGPT: A photo-realistic image

Model: gpt-3.5-turbo-1106
System prompt: You describe simple visual scenes that depict the two variables stated. You combine both variables into one scene.
User prompt: Please describe a visual scene that prominently depicts both Annual US household spending on bakery products and Intuitive Surgical's stock price (ISRG), in the following situation: As households indulged in more pastries and breads, there was a rise in dough flow. This yeast to the occasion, leading to higher demand for medical procedures, particularly for robotic surgery, hence driving up the stock price of Intuitive Surgical. It seems like the market was in knead of their innovative healthcare technology!. Keep the description simple.
ChatGPT: In the scene, there is a cozy bakery bustling with customers buying bread and pastries, with stacks of dough rising in the background. Adjacent to the bakery, a modern hospital with robotic surgery equipment is in high demand, as patients are being treated with cutting-edge technology. Meanwhile, on a digital ticker above, the stock price of Intuitive Surgical (ISRG) is soaring upwards, indicating investor confidence in the company's innovative healthcare solutions.

Model: gpt-3.5-turbo-1106
System prompt: You write and improve image generation prompts for DALLE-3. You maintain the same subjects, but enhance the visuals.
User prompt: Please respond with an image generation prompt that would be likely to create an interesting visual using DALLE-3, using the following style: [ A photo-realistic image ] and depicting this scene: In the scene, there is a cozy bakery bustling with customers buying bread and pastries, with stacks of dough rising in the background. Adjacent to the bakery, a modern hospital with robotic surgery equipment is in high demand, as patients are being treated with cutting-edge technology. Meanwhile, on a digital ticker above, the stock price of Intuitive Surgical (ISRG) is soaring upwards, indicating investor confidence in the company's innovative healthcare solutions. Keep the visual depiction simple. Do not include any words or speech bubbles.
ChatGPT: Generate a photo-realistic image depicting a cozy bakery filled with customers buying bread and pastries as stacks of dough rise in the background. Meanwhile, adjacent to the bakery, a modern hospital with robotic surgery equipment is shown in high demand, with patients being treated with cutting-edge technology. Above the scene, a digital ticker displays the soaring stock price of Intuitive Surgical (ISRG), indicating investor confidence in the company's innovative healthcare solutions.

*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 Annual US household spending on bakery products caused Intuitive Surgical's stock price (ISRG) to increase. Include one good pun.

AI academic paper

(Because p < 0.01)

Dough Nation: Exploring the Rise of Bakery Spending and Intuitive Surgical's Stock Price

The Journal of Culinary Economics and Financial Analysis

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 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 Annual US household spending on bakery products and Intuitive Surgical's stock price (ISRG). Make lots of jokes, goofy observations, and puns.

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

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

Start by naming serious-sounding studies by authors like Smith, Doe, and Jones - but then quickly devolve. Name some real non-fiction books that would be related to the topic. Then name some real fiction books that sound like they could be related. Then 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]]
Dough Nation: Exploring the Rise of Bakery Spending and Intuitive Surgical's Stock Price

[[ABSTRACT]]
Bread, dough, and stock prices - the trifecta of economic analysis! This paper delves into the unexpectedly buttery relationship between annual US household spending on bakery products and Intuitive Surgical's stock price (ISRG). By crunching data from the Bureau of Labor Statistics and LSEG Analytics (Refinitiv), our research team discovered a correlation coefficient of 0.9631457 and p < 0.01 for the period spanning from 2002 to 2022. The aroma of this correlation is as tantalizing as a freshly baked loaf, and the statistical significance is as clear as the connection between a baguette and brie. Join us in unraveling the layers of this unexpected linkage, as we knead our way through the doughy world of economics and stock market trends.

-------

And here is the introduction section that led to this literature review:
[[INTRODUCTION]]
The intersection of bakery products and stock prices may seem as unlikely as finding a croissant in a cookie jar. However, the tantalizing aroma of correlation has drawn our attention to the unexpectedly buttery relationship between annual US household spending on bakery products and Intuitive Surgical's stock price (ISRG). As we delve into this doughy world of economic analysis, we must resist the temptation to get too wrapped up in bread puns, though it may be quite a challenge!
The global financial market is like a baker's oven, filled with the heat of speculation and the need to rise to the occasion. Just as a baker meticulously measures ingredients for the perfect loaf, investors carefully weigh market trends and consumer behaviors to forecast stock performance. The tantalizing smell of freshly baked goods may have more to do with the stock market than one might initially assume.
In this paper, we aim to explore the statistical connection between annual US household spending on bakery products and Intuitive Surgical's stock price. Our approach is as subtle as the scent of a perfectly proofed sourdough and as precise as the cuts made to shape a beautifully braided challah. Through rigorous data analysis and statistical methods, we seek to unravel the layers of this unexpected linkage, finding the grain of truth in what may seem like a half-baked hypothesis.

-------

Your response should start like this:

[[LITERATURE REVIEW]]

ChatGPT:
[[LITERATURE REVIEW]]

Empirical studies have examined the relationship between consumer spending habits and stock prices, shedding light on the intricate dynamics of economic decision-making. Smith et al. (2015) find a positive correlation between household spending on baked goods and the stock prices of companies within the food industry. Similarly, Doe and Jones (2018) analyze consumer preferences for artisanal bakery products and its impact on stock market trends, revealing intriguing insights into the interconnectedness of consumer behavior and financial markets.

Moreover, in "The Economics of Bread: A Crustworthy Analysis" (Baker, 2019), the author explores the economic implications of bread production and consumption, offering a yeastful perspective on the broader economic landscape. In a similar vein, "The Sourdough Stock Exchange" (Yeastman, 2020) provides a whimsical yet insightful examination of the historical parallels between sourdough bread making and stock market dynamics, inviting readers to rise to the occasion of understanding financial fluctuations through a doughy lens.

However, as we delve deeper into the literature, the unconventional sources become apparent. "The Baguette Chronicles: A Tale of Flour and Fortune" (Fictional, 2000) presents a fictional narrative that intertwines the fate of a bakery with the fluctuations of a mythical stock market, blurring the lines between reality and imagination. Similarly, "The Croissant Conundrum" (Imaginary, 2015) offers a fantastical exploration of pastry-driven economic theories, challenging traditional notions of causality and correlation.

As scrutiny intensifies, it becomes necessary to consider an array of unconventional sources. After combing through the literature, the research team stumbled upon an unexpected treasure trove of insight and wisdom that defied conventional expectations. The back of a shampoo bottle, with its cryptic promises of silkier hair and untold botanical secrets, offered a surprising perspective on consumer decision-making processes and the elusive nature of market trends. While this source may have initially been viewed as an eccentric departure from traditional scholarship, its unconventional wisdom proved to be a shampoo-rising revelation in the pursuit of understanding the enigmatic bond between bakery spending and stock prices.

The literature thus presents a diverse palette of perspectives, ranging from the rigorously empirical to the delightfully imaginative, as well as the unexpectedly ordinary yet strangely insightful. These varied sources lay the groundwork for our own examination of the doughy landscape where economic analysis and stock market trends collide.

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 Annual US household spending on bakery products and Intuitive Surgical's stock price (ISRG). Make lots of 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]]
Dough Nation: Exploring the Rise of Bakery Spending and Intuitive Surgical's Stock Price

[[ABSTRACT]]
Bread, dough, and stock prices - the trifecta of economic analysis! This paper delves into the unexpectedly buttery relationship between annual US household spending on bakery products and Intuitive Surgical's stock price (ISRG). By crunching data from the Bureau of Labor Statistics and LSEG Analytics (Refinitiv), our research team discovered a correlation coefficient of 0.9631457 and p < 0.01 for the period spanning from 2002 to 2022. The aroma of this correlation is as tantalizing as a freshly baked loaf, and the statistical significance is as clear as the connection between a baguette and brie. Join us in unraveling the layers of this unexpected linkage, as we knead our way through the doughy world of economics and stock market trends.

[[LITERATURE REVIEW]]
Empirical studies have examined the relationship between consumer spending habits and stock prices, shedding light on the intricate dynamics of economic decision-making. Smith et al. (2015) find a positive correlation between household spending on baked goods and the stock prices of companies within the food industry. Similarly, Doe and Jones (2018) analyze consumer preferences for artisanal bakery products and its impact on stock market trends, revealing intriguing insights into the interconnectedness of consumer behavior and financial markets.
Moreover, in "The Economics of Bread: A Crustworthy Analysis" (Baker, 2019), the author explores the economic implications of bread production and consumption, offering a yeastful perspective on the broader economic landscape. In a similar vein, "The Sourdough Stock Exchange" (Yeastman, 2020) provides a whimsical yet insightful examination of the historical parallels between sourdough bread making and stock market dynamics, inviting readers to rise to the occasion of understanding financial fluctuations through a doughy lens.
However, as we delve deeper into the literature, the unconventional sources become apparent. "The Baguette Chronicles: A Tale of Flour and Fortune" (Fictional, 2000) presents a fictional narrative that intertwines the fate of a bakery with the fluctuations of a mythical stock market, blurring the lines between reality and imagination. Similarly, "The Croissant Conundrum" (Imaginary, 2015) offers a fantastical exploration of pastry-driven economic theories, challenging traditional notions of causality and correlation.
As scrutiny intensifies, it becomes necessary to consider an array of unconventional sources. After combing through the literature, the research team stumbled upon an unexpected treasure trove of insight and wisdom that defied conventional expectations. The back of a shampoo bottle, with its cryptic promises of silkier hair and untold botanical secrets, offered a surprising perspective on consumer decision-making processes and the elusive nature of market trends. While this source may have initially been viewed as an eccentric departure from traditional scholarship, its unconventional wisdom proved to be a shampoo-rising revelation in the pursuit of understanding the enigmatic bond between bakery spending and stock prices.
The literature thus presents a diverse palette of perspectives, ranging from the rigorously empirical to the delightfully imaginative, as well as the unexpectedly ordinary yet strangely insightful. These varied sources lay the groundwork for our own examination of the doughy landscape where economic analysis and stock market trends collide.

[[RESULTS]]
The analysis of the relationship between annual US household spending on bakery products and Intuitive Surgical's stock price (ISRG) revealed a remarkably robust correlation coefficient of 0.9631457. This finding suggests a strong positive association between these seemingly unrelated variables. The R-squared value of 0.9276496 further underscores the close relationship between bakery spending and ISRG stock price movement, indicating that approximately 92.7% of the variability in ISRG stock price can be explained by changes in annual bakery expenditure. Notably, the p-value of less than 0.01 indicates a high level of statistical significance, affirming the credibility of the observed relationship.
As shown in Fig. 1, the scatterplot vividly illustrates the striking correlation between annual US household spending on bakery products and Intuitive Surgical's stock price. The data points form a tightly clustered pattern, resembling the texture of a well-kneaded dough, affirming the strength of the association between these variables.
The implications of these findings are as intriguing as discovering a hidden pastry in a bread basket. While the direct causal mechanism underlying this relationship remains to be fully elucidated, it is evident that there is more to the dynamics of stock prices and consumer behavior than meets the eye. The aroma of correlation emanating from this analysis is as satisfying as the smell of freshly baked bread and invites further exploration into the intertwined world of consumer spending and stock market movements.

-------

Your response should start like this:

[[DISCUSSION]]

ChatGPT:

[[DISCUSSION]]

The results of our study have produced a confection of unexpected findings, as the statistical analysis has unveiled a correlation of 0.9631457 between annual US household spending on bakery products and Intuitive Surgical's stock price (ISRG). This robust statistical relationship lovingly kneads together seemingly unrelated variables, affirming the existence of a significant bond that rises like dough in a warm oven. These findings build upon the previous research conducted by Smith et al. (2015) and Doe and Jones (2018), which also toasted the idea of a positive correlation between bakery spending and stock prices within the food industry. Indeed, our results provide further support for these earlier studies, ensuring that the topic remains as fresh as a just-baked baguette.

Our findings also echo the yeastful contemplations of Baker (2019) and Yeastman (2020), who harmoniously blend the worlds of bread economics and stock market dynamics. The surprising parallels between bread production and stock market activity are akin to finding the perfect ratio of flour to water in a recipe – unexpected, yet undoubtedly satisfying. As such, our results reflect the whimsical yet insightful aspects of their analyses, eagerly rising to the occasion of expanding our understanding of financial markets through a doughy lens.

Moreover, the unanticipated emergence of unconventional sources, such as the fictional narratives of "The Baguette Chronicles" (Fictional, 2000) and "The Croissant Conundrum" (Imaginary, 2015), has added a distinct zest to our understanding of bakery spending and stock prices. While initially dismissed as fantastical musings, these unconventional works have proven to be as essential as a pinch of salt in our recipe for comprehending the enigmatic relationship between consumer spending on baked goods and stock market trends. The unexpected wisdom gained from a shampoo bottle adds another layer of richness to our analysis, showing that insight can be found in the most surprising of places – much like finding a cherry in a loaf of bread.

In conclusion, our research has uncovered a substantial correlation between annual US household spending on bakery products and Intuitive Surgical's stock price (ISRG), demonstrating that the aroma of correlation emanating from these seemingly distinct variables is as irresistible as the scent of freshly baked bread. These findings open up new avenues for future research, inviting scholars to delve deeper into the doughy landscape where economic analysis and stock market trends converge.

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 Dough Nation: Exploring the Rise of Bakery Spending and Intuitive Surgical's Stock Price. Respond only with the name of a fictional academic journal.

ChatGPT:

The Journal of Culinary Economics and Financial Analysis

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 Dough Nation: Exploring the Rise of Bakery Spending and Intuitive Surgical's Stock Price. Respond only with the name of a fictional organization.

ChatGPT:

Society for Culinary and Economic Research

Model: gpt-3.5-turbo-1106
System prompt: You provide potential search keywords separated by commas. You say nothing else, and you do not chat with the user.
User prompt: Please provide potential search keywords for a paper titled Dough Nation: Exploring the Rise of Bakery Spending and Intuitive Surgical's Stock Price with an abstract of Bread, dough, and stock prices - the trifecta of economic analysis! This paper delves into the unexpectedly buttery relationship between annual US household spending on bakery products and Intuitive Surgical's stock price (ISRG). By crunching data from the Bureau of Labor Statistics and LSEG Analytics (Refinitiv), our research team discovered a correlation coefficient of 0.9631457 and p < 0.01 for the period spanning from 2002 to 2022. The aroma of this correlation is as tantalizing as a freshly baked loaf, and the statistical significance is as clear as the connection between a baguette and brie. Join us in unraveling the layers of this unexpected linkage, as we knead our way through the doughy world of economics and stock market trends.

ChatGPT:

Dough Nation, bakery spending, Intuitive Surgical, ISRG stock price, US household spending, correlation coefficient, statistical significance, Bureau of Labor Statistics, LSEG Analytics, economic analysis, stock market trends, bakery products, annual household spending, Refinitiv, bread and stock prices

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

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Data details

Annual US household spending on bakery products
Detailed data title: Average annual household spend on bakery products
Source: Bureau of Labor Statistics
See what else correlates with Annual US household spending on bakery products

Intuitive Surgical's stock price (ISRG)
Detailed data title: Opening price of Intuitive Surgical (ISRG) on the first trading day of the year
Source: LSEG Analytics (Refinitiv)
Additional Info: ^{See full details} Via Microsoft Excel Stockhistory function

See what else correlates with Intuitive Surgical's stock price (ISRG)

Correlation r = 0.9631457 (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 = 0.9276496 (Coefficient of determination)
This means 92.8% of the change in the one variable (i.e., Intuitive Surgical's stock price (ISRG)) is predictable based on the change in the other (i.e., Annual US household spending on bakery products) over the 21 years from 2002 through 2022.

p < 0.01, which is statistically significant(Null hypothesis significance test)
The p-value is 2.7E-12.^Show 0.0000000000027305508336434622
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 0.96 in 2.7E-10% of random cases. Said differently, if you correlated 366,226,472,578 random variables^Note You don't actually need 366 billion 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 20 degrees of freedom, ^Note Degrees of freedom is a measure of how many free components we are testing. In this case it is 20 because we have two variables measured over a period of 21 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.

[ 0.91, 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.

	2002	2003	2004	2005	2006	2007	2008	2009	2010	2011	2012	2013	2014	2015	2016	2017	2018	2019	2020	2021	2022
Annual US household spending on bakery products (Household spend)	296	292	307	302	304	317	337	334	337	356	356	359	343	346	353	388	392	400	428	462	497
Intuitive Surgical's stock price (ISRG) (Stock price)	2.18	1.37	1.9	4.45	13.21	10.78	35.96	14.04	34.13	29.09	52.33	56.28	42.63	58.99	60.79	70.66	122.63	156.5	198.56	275.28	358.65

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.
Y-axis doesn't start at zero: I truncated the Y-axes of the graph above. I also used a line graph, which makes the visual connection stand out more than it deserves. ^Note Nothing against line graphs. They are great at telling a story when you have linear data! But visually it is deceptive because the only data is at the points on the graph, not the lines on the graph. In between each point, the data could have been doing anything. Like going for a random walk by itself!
Mathematically what I showed is true, but it is intentionally misleading. Below is the same chart but with both Y-axes starting at zero.

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([296,292,307,302,304,317,337,334,337,356,356,359,343,346,353,388,392,400,428,462,497,])
array_2 = np.array([2.18,1.37,1.9,4.45,13.21,10.78,35.96,14.04,34.13,29.09,52.33,56.28,42.63,58.99,60.79,70.66,122.63,156.5,198.56,275.28,358.65,])
array_1_name = "Annual US household spending on bakery products"
array_2_name = "Intuitive Surgical's stock price (ISRG)"

# 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.

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

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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
Scatterplot
Portable line chart (png)
Portable line chart (png), optimized for mobile
Line chart for only Annual US household spending on bakery products
Line chart for only Intuitive Surgical's stock price (ISRG)
AI-generated correlation image
The spurious research paper: Dough Nation: Exploring the Rise of Bakery Spending and Intuitive Surgical's Stock Price

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Correlation ID: 4104 · Black Variable ID: 19887 · Red Variable ID: 1634


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