{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Plotting and Correlation\n",
"\n",
"## Learning Goals\n",
"\n",
"After this week, the student will be able to:\n",
"- Create different types of plots\n",
"- Calculate the correlation coefficient\n",
"- Relate the concepts of correlation and causation\n",
"- Examine data using the concepts of expected value, standard deviation and correlation"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Correlation\n",
"\n",
"Before the lecture you should read these excerpts covering An Introduction to Correlations and Causes.\n",
"\n",
"The lecture will focus on how we calculate correlation from measurements, so you should first have some grasp on what correlation means, and how we should treat a correlation result."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Plotting"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Visualization is a powerful tool for interpreting data. As you have already seen, finding the expected value, variance and standard deviation does not always tell you the whole story. Python has a plethora of tools for plotting. The standard one, called `matplotlib` is the one we will be using. We import it differently from how we have been importing `randint`, since the module `matplotlib` has many different functions we want to access without having to import each seperately."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"from random import randint\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Line plot\n",
"\n",
"We can create a line plot with the function `plot()`. The function `plot()` takes the x-coordinates and the y-coordinates of our data as arguments. Here we are plotting the gross domestic product of Norway from 1973 to 2019. (Source: https://www.ssb.no/nasjonalregnskap-og-konjunkturer/faktaside/norsk-okonomi)"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"year = [1973, 1974, 1975, 1976, 1977, 1978, 1979, 1980, 1981, 1982, 1983, 1984, 1985, 1986, 1987, 1988, 1989, 1990, 1991, 1992, 1993, 1994, 1995, 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019]\n",
"bnp = [32810, 37736, 42887, 48713, 54654, 60086, 66061, 77895, 89028, 98256, 108929, 122340, 135421, 139648, 151634, 157759, 167649, 176792, 185391, 189691, 198377, 206900, 220945, 240719, 259092, 262482, 283665, 335626, 346565, 343978, 354965, 388296, 430427, 475536, 499065, 546765, 502924, 530036, 563827, 590617, 604552, 611359, 599389, 591684, 624484, 664483, 660400]\n",
"\n",
"plt.plot(year, bnp)\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Bar Plot\n",
"\n",
"Bar plots are useful for comparing the values or quantities of things. We can create one using the function `bar()`. `bar()` takes two arguments, the names of the bars, and the heights of the corresponding bars.\n",
"\n",
"We can illustrate the population of Norway, Finland and Denmark with a bar plot:"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
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"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"country = [\"Norway\", \"Finland\", \"Denmark\"]\n",
"population = [5.415001, 5.539463, 5.789215] #millions\n",
"plt.bar(country, population)\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Histogram\n",
"\n",
"A histogram counts how many times each number appears in a list and plots the results. Histograms are made with the function `hist()`. The first argument should be the list we want to make a histogram of, the rest are optional, but are needed to make the columns properly centered.\n",
"\n",
"We can illustrate the results of 1000 dice throws using a histogram. We can also add a title to our plot with `plt.title()`:"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"diceResults = []\n",
"\n",
"for i in range(1000):\n",
" dice = randint(1, 6)\n",
" diceResults.append(dice)\n",
" \n",
"plt.hist(diceResults, bins = [1,2,3,4,5,6,7], align=\"left\", rwidth=0.8)\n",
"plt.title(\"Occurences of dice throw results\")\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can expand on the idea in the previous example to plot the sum of two dice throws.\n",
"\n",
"Let's plot 1000 sums of two dice throws."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"diceResults = []\n",
"\n",
"for i in range(1000):\n",
" dice1 = randint(1, 6)\n",
" dice2 = randint(1, 6)\n",
" total = dice1 + dice2\n",
" diceResults.append(total)\n",
" \n",
"plt.hist(diceResults, bins=range(2,14), align=\"left\", rwidth=0.8)\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As you might expect, a sum of 7 is much more common than a sum of 12.\n",
"\n",
"### Scatter plot\n",
"\n",
"If we want to plot the age of death and yearly ice cream consumption of indivudual people to see how the two values are related we might want to make a scatter plot with `scatter()`.\n",
"\n",
"Here is an example of how to do that with made-up data. It seems like labeling the x- and y-axis would be useful here. We can do that with `plt.xlabel()` and `plt.ylabel()`:"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"age = [65, 75, 67, 59, 54, 67, 62, 54, 56, 58, 60, 61, 73, 66, 64, 61, 71, 75, 74, 66, 65, 59, 59, 58, 63]\n",
"iceCream = [6, 6, 6, 8, 9, 4, 11, 9, 10, 9, 8, 9, 5, 8, 10, 11, 6, 6, 6, 5, 6, 11, 8, 10, 8]\n",
"\n",
"plt.scatter(age, iceCream)\n",
"plt.title(\"Ice cream consumption vs. Age of death\")\n",
"plt.xlabel(\"Ice cream consumption\")\n",
"plt.ylabel(\"Age of death\")\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Each dot represents one person. It looks like people who eat more ice cream die sooner. Such a connection is called a correlation, which is the topic of the next section."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---\n",
"\n",
"### In-Class Plotting Exercises\n",
"\n",
"Plot these data with the suitable plotting function\n",
"\n",
"**a)** Temperature in Oslo and Bergen on certain days. (Made-up data)\n",
"\n",
" osloTemp = [0, -1.71, -3.05, -4.33, -5.15, -4.15, -2.09, 0, 1.83, 4.49, 5.53, 4.31, 2.77, 1.45]\n",
" bergenTemp = [-5, -3.72, -2.24, -0.4, 2.26, 4.18, 4.36, 3, 4.16, 4.66, 2.06, -0.48, -2.36, -4.04]\n",
"\n",
"**b)** 2017 Norwegian parliamentary election. (Source: https://en.wikipedia.org/wiki/2017_Norwegian_parliamentary_election)\n",
"\n",
" party = [\"Ap\", \"H\", \"FrP\", \"Sp\", \"SV\", \"V\", \"KrF\", \"MDG\", \"R\"]\n",
" votes = [800949, 732897, 444683, 302017, 176222, 127911, 122797, 94788, 70522]\n",
"\n",
"---"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Recognizing Types of Correlation"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Two events are correlated if they tend to happen at the same time, or if they tend to not happen at the same time. If two events are not correlated, there are no such patterns. One measure of correlation is the pearson correlation coefficient. It will be explained at the end of this section, and you will be shown how it is calculated in the next section. In the following examples it will simply be given in the title of the scatter plots.\n",
"\n",
"First let's look at an example of positive correlation:\n",
"\n",
"\n",
"\n",
"Both figures show the same data. The left figure is a line plot where grades and hours studied have seperate lines which we see have a strong correlation since they mostly move up together and down together. The right figure is a scatter plot where the correlation is apparent due to all of the data points almost forming a line. Higher grades coincide with more hours studied. Lower grades coincide with less hours studied.\n",
"\n",
"Now let's look at an example of negative correlation:\n",
"\n",
"\n",
"\n",
"We see that fun and hours studied are negatively correlated. This can be recognized from how the lines mostly move opposite of each other. When one moves down the other moves up. And on the scatter plot we see that the data forms a line which tends downwards. Higher grades coincide with *less* fun.\n",
"\n",
"The final example shows data with almost no correlation:\n",
"\n",
"\n",
"\n",
"The lines seem to move independently from each other, and the scatter plot is spread out, not forming a line at all. This is an example of data with close to no correlation.\n",
"\n",
"The pearson correlation coefficient takes values from -1 to 1. A value of 1 means a perfect linear correlation, a value of 0 means no correlation and a value of -1 means a perfect negative correlation. If a number inbetween (ie. 0.7) means a strong or weak correlation depends entirely on context. If you're trying to prove a law in physics, 0.9 is very low, but in the social sciences 0.9 can be a very strong correlation.\n",
"\n",
"**Extra:** The pearson correlation coefficient only has any meaning when we are looking at linearly correlated, normally distributed data. Linearly correlated means that one value does not start increasing faster or slower in relation to the other when they both grow. An example on a non-linear relation is the year and population of the world, as the population is currently growing much faster than before. Normally distributed data appear in many real world examples, like peoples height, where most are around the average while fewer people are much shorter or taller. (Further reading to know when to use the pearson correlation coefficient: https://en.wikipedia.org/wiki/Pearson_correlation_coefficient, https://en.wikipedia.org/wiki/Normal_distribution)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Calculating Correlation"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now that you know the difference between positive, negative and no correlation, it is time to calculate the correlation coefficient. The calculation consists of three steps: Scale, multiply, average.\n",
"\n",
"We want to find out if ice cream consumption is correlated with age of death. We have recorded the ice cream consumption and age of death of 25 individuals, which we will analyze. First, we plot the data like we did in the previous examples.\n",
"\n",
"We use a library called `numpy` to turn our lists into arrays. Arrays are basically lists which we can use for maths, like for multiplying an array of numbers by 2, or adding 100 to every element of an array. You are not expected to know how to use numpy or arrays yet (this is covered much later in this course), just try to follow the maths."
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"\n",
"age = np.array([65, 75, 67, 59, 54, 67, 62, 54, 56, 58, 60, 61, 73, 66, 64, 61, 71, 75, 74, 66, 65, 59, 59, 58, 63])\n",
"iceCream = np.array([6, 6, 6, 8, 9, 4, 11, 9, 10, 9, 8, 9, 5, 8, 10, 11, 6, 6, 6, 5, 6, 11, 8, 10, 8])\n",
"\n",
"plt.figure(figsize=(12,8))\n",
"plt.subplot(221)\n",
"plt.plot(age, label = \"Age of Death\")\n",
"plt.plot(iceCream, label = \"Ice Cream Consumption\")\n",
"plt.legend()\n",
"\n",
"plt.subplot(222)\n",
"plt.scatter(age, iceCream)\n",
"plt.xlabel(\"Age of Death\")\n",
"plt.ylabel(\"Ice Cream Consumption\")\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The scatter plot seems to form some sort of line, but it is impossible to tell what the correlation coefficient should be just from looking at it.\n",
"\n",
"The line plot is even less useful, the lines are at totally different scales. The age of death is much higher, and has much larger variations than ice cream consumption. This is a big problem when we want to compare the two values for different individuals. The first step to remedy this problem, and to calculate the correlation coefficient, is to scale the data."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Step 1 - Scale"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Imagine that you drag the age of death line (the blue one) straight down to the ice cream line (orange). Then, it would be much easier to see whether the lines move together, opposite or independently. The age of death line would still move up and down much further however, which we can fix by just squeezing the line until it varies as much as the ice cream line. If we dragged the age of death line down, and squeezed it the right amount we would get a line plot much more like the examples in the previous section, with the hours studied plots.\n",
"\n",
"This is not a very systematic approach however. What we do instead is drag *both* lines (blue and orange) down until they have a mean of 0, and then squeeze them until they have a standard deviation of 1.\n",
"\n",
"For this we need the mean and standard deviation of the data. You learned how to calculate this with for-loops in the previous lecture, but we will here just use the function `np.mean()` and `np.std()`, as should you, given that you know how the functions work and are not asked not to use them. You should become used to reading the documentation of functions you wish to use. Open these links to read how [np.mean()](https://numpy.org/doc/stable/reference/generated/numpy.mean.html) and [np.std()](https://numpy.org/doc/stable/reference/generated/numpy.std.html) work and are used.\n",
"\n",
"Below is a plot of the age of death data scaled by its mean and standard deviation. Note how the shape of the line is the same as before the scaling, just that the values are now around 0 and don't vary too much."
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [],
"source": [
"age_scaled = (age - np.mean(age)) / np.std(age)"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {
"tags": [
"hide-input"
]
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(20, 12))\n",
"\n",
"plt.subplot(331)\n",
"plt.plot(age)\n",
"plt.title(\"Original Data\")\n",
"\n",
"plt.subplot(332)\n",
"plt.plot(age - np.mean(age))\n",
"plt.title(\"Data - Mean\")\n",
"\n",
"plt.subplot(333)\n",
"plt.plot((age - np.mean(age)) / np.std(age))\n",
"plt.title(\"(Data - Mean) / Standard Deviation\")\n",
"\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"When we scale both the age of death data and the ice cream data and plot them together, we get this plot:"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"iceCream_scaled = (iceCream - np.mean(iceCream)) / np.std(iceCream)\n",
"\n",
"plt.plot(age_scaled, label = \"Age of Death\")\n",
"plt.plot(iceCream_scaled, label = \"Ice Cream Consumption\")\n",
"plt.legend()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now it is easier (but still not fun!) to see whether the data is correlated."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Step 2 - Multiply"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now comes a very important observation: If the scaled age of death and ice cream consumption are both high at the same time, their product is positive. If they are both low, their product is *still* positive, since a negative times a negative gives a positive. **This means that (scaled) values which vary together always give a positive product.**\n",
"\n",
"When we have a high age of death and a low ice cream consumption, we get a negative product. Positive age, negative ice cream. We also get a negative product when the age of death is low and the ice cream consumption of an individual is high. **This means that (scaled) values which vary in opposite directions always give a negative product.**\n",
"\n",
"Below we have plotted the product of the scaled age of death and ice cream consumption. Look at the y-axis, are the values mostly negative or mostly positive?"
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.plot(age_scaled * iceCream_scaled)\n",
"plt.hlines(np.mean(age_scaled * iceCream_scaled), xmin = 0, xmax = 24, color=\"red\", linestyle=\"--\")\n",
"plt.title(\"Scaled values multiplied together (mean shown in red)\")\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Step 3 - Average"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"It looks like the product is mostly negative. Following the observation that scaled values which vary in opposite directions give a negative product, we can conclude that the data are negatively correlated. If the data varied together as much as they were opposite, the average would be close to zero, and there would be no correlation.\n",
"\n",
"But \"mostly negative\" is not a very good measure. We instead take the mean value of the product, as shown by the red dashed line in the figure above."
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"-0.705955340971355\n"
]
}
],
"source": [
"corr = np.mean(age_scaled * iceCream_scaled)\n",
"print(corr)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This mean of the product of the scaled values is the pearson correlation coefficient! -0.7 is a pretty strong negative correlation in this case.\n",
"\n",
"All of the steps we took to find it can be condensed into these three very dense lines of code. If you were to calculate the means and standard deviations yourself like you did in the previous lecture, it would be much more of a hassle."
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"-0.705955340971355\n"
]
}
],
"source": [
"age_scaled = (age - np.mean(age)) / np.std(age)\n",
"iceCream_scaled = (iceCream - np.mean(iceCream)) / np.std(iceCream)\n",
"\n",
"print(np.mean(age_scaled * iceCream_scaled))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Even these three lines are a hassle though, when we can just use the `pearsonr()` function from `scipy.stats.stats`. You should just use this when calculating the correlation coefficient, no need to reinvent the wheel, as long as you understand how to use it."
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(-0.7059553409713553, 8.051146825575674e-05)\n",
"-0.7059553409713553\n"
]
}
],
"source": [
"from scipy.stats.stats import pearsonr\n",
"\n",
"print(pearsonr(age, iceCream))\n",
"print(pearsonr(age, iceCream)[0]) # if you only want the correlation coefficient"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Extra**: The second number returned by `pearsonr()` is a two-sided p-value. It is the probability that a population with no correlation would give us a sample with a correlation greater than or equal to the one we found in magnitude.)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Controlling for a variable"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In our case -0.7 is a pretty strong correlation. So why are these variables correlated? Is it because eating more ice cream causes you to die sooner? Proving that this is true is impossible, the only thing you can do to support such a claim is show that the correlation is not random, that dying sooner does not cause eating more ice cream, and that the correlation is not caused by a third, common-causal variable, among other things.\n",
"\n",
"We expand our example so that we also know the gender of the people we are looking at. Maybe being male causes you to die sooner *and* eat more ice cream? If this is the case, eating more ice cream and dying sooner will not be correlated within the male population.\n",
"\n",
"Let's first sort the data into a male population and a female population."
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {},
"outputs": [],
"source": [
"male = [False, False, False, True, True, False, True, True, True, True, True, True, False, True, True, True, False, False, False, False, False, True, True, True, True]\n",
"\n",
"age_Male = []\n",
"iceCream_Male = []\n",
"\n",
"age_Female = []\n",
"iceCream_Female = []\n",
"\n",
"for i in range(len(age)):\n",
" if male[i] == True:\n",
" age_Male.append(age[i])\n",
" iceCream_Male.append(iceCream[i])\n",
" else:\n",
" age_Female.append(age[i])\n",
" iceCream_Female.append(iceCream[i])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now, let's use the `pearsonr()` function to calculate the correlation between eating ice cream and dying sooner in each of the populations seperately."
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(-0.06109050664155455, 0.82877185216734)\n",
"(0.23396392997339183, 0.515311044747241)\n"
]
}
],
"source": [
"print(pearsonr(age_Male, iceCream_Male))\n",
"print(pearsonr(age_Female, iceCream_Female))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"There is almost no correlation! We have now shown that this made-up data shows no causal relation between ice cream consumption and dying sooner. Being male is simply correlated with both eating more ice cream and dying sooner, and being female correlates with eating less ice cream and dying later. Note that the data shows that eating more ice cream is not making men die sooner than men eating less ice cream!\n",
"\n",
"If we scatter-plot again and color code the genders this becomes readily apparent."
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.scatter(age_Male, iceCream_Male, label=\"Male\")\n",
"plt.scatter(age_Female, iceCream_Female, label=\"Female\")\n",
"plt.title(\"More ice cream does not kill you\")\n",
"plt.xlabel(\"Age of death\")\n",
"plt.ylabel(\"Ice cream consumption\")\n",
"plt.legend()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---\n",
"\n",
"### In-Class Calculating Correlation Exercises\n",
"\n",
"**a)** There is clearly a very strong relation visible in this scatter plot. Why is the pearson correlation coefficient so low?\n",
"\n",
"\n",
"\n",
"---"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.8.5"
}
},
"nbformat": 4,
"nbformat_minor": 4
}