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In this lesson, we're going to apply all our Python programming knowledge to do the regression and analyze
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the data from a 1968 American study on how drugs affect math test scores.
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So we're going to be writing some Python code to visualize and plot our data and then we're going to
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run a linear regression to look at how well drug concentration in the tissue affects test performance.
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But before we do that, let's chat a little bit about the dataset that we're going to be using for this
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exercise.
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I was actually genuinely surprised when I found out that research like this even exists.
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But then again, maybe the late 1960s where a different time in the United States. In the original research
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paper the three academics by the names of Wagner, Aghajanian and Bing get five male volunteers
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to sit math tests after being injected with drugs.
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Now I reckon the fact that these drugs were administered intravenously speaks way more for the commitment
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of these five blokes than sitting math tests voluntarily. Anyhow, the specific drug in question is
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called, and I hope I pronounced this right -
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the lysergic acid diethylamide, or LSD 25, which Google tells me is a pretty potent hallucinogen. And
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the way that this experiment worked is that these five blokes had to give seven blood samples after
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being injected with LSD.
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The amount of drugs that each dude was injected was actually proportional to their body weight so that
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each volunteer should be roughly affected more or less equally.
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The blood samples were taken from the volunteers after five minutes, half an hour, two hours, four hours
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and again after eight hours.
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Now if you remember this is what you see in the first column of our data
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dataframe. The second column labelled LSD_ppm is the tissue concentration of the drug measured
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in parts per million. And after each blood sample was taken,
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the volunteers were sat down for a total of three minutes to solve as many arithmetic math problems
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as possible.
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And this brings me to our third column in the data frame.
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I've labeled this Avg_Math_Test_Score and the way these numbers
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are calculated is that, first off the number shown in the column is actually the average of the five
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guys in the experiment.
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The second thing to note about these numbers is that the score is expressed as a percentage value and
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it's not like the number of questions that they got right.
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But it's a percentage of the control value.
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In other words, the researchers knew how well people fared on average on their arithmetic tests and they
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compared the performance of the volunteers against that, against the control test scores.
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Another way to think about this is that if there were 10 questions and the control group got around
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nine of them right, then the volunteers got about three or 32.9 percent of the questions
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right, 240 minutes or four hours into the experiment.
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Okay, so we've imported pandas in our notebook and then we called the read_csv function to store our
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data in a data frame called data.
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Now we've been messing around with our data quite a bit.
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So if you're curious what your data frame looks like, at the bottom of your notebook then type data and
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press Shift+Enter.
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If you just started this lesson and have not run the cells above then the Jupyter notebook will not
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recognize this variable. In this case,
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you'll get a name error which means you have to go to "Cell" and go to "Run All".
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So that's a good thing to check if you're coming back to the Python intro
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after taking a break. Here we can see what our data looks like, right?
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We've got three columns and we're going to extract each column and put it into a separate variable.
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The first column I'm going to extract is gonna be called time.
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And I'm gonna set it equal to data[] and then when I pass in the name, I'm going to say
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Time_Delay_in_Minutes, and hit Shift+Enter to see what it looks like.
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If I want to know what it looks like I can simply say print(time).
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And here it is - our variable called time now contains a series containing the values of the first column.
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Let's do the same thing with the other two columns.
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So I'm gonna create a variable called LSD set it equal to data[] and it was
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LSD_ppm. And the third variable I'm going to create, I'm gonna call score, I'm going to set equal
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to data[] and then 
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Avg_Math_Test_Score. I'm going to hit Shift+Enter to make sure I haven't made any typos and this gives me confidence
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that my Python code is working.
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Now we're ready to start looking at our data in a graphical way.
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If you recall from previous lessons we've imported our plotting module as plt so we can refer to
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our pyplot as plt and visualize the data in these variables.
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So the easiest way to do this is to type plt.plot and supply into two things that we want to
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see.
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Let's say we want to look at the time vs. the amount of LSD in people's tissues, hitting Shift+Enter doesn't
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show me anything.
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And that's because we need to give our pyplot the instruction to show us the graph, so I'm going to write
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plt.show()
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and this gives me a graph that looks like this. What this plot is showing us is the amount of LSD
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tissue concentration over time.
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So we've got eight data points and we're simply plotting a line chart. For the x-axis on this chart we
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have supplied our time and for the y axis we have supplied our LSD variable.
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Now, check this out - at the moment our plot takes two arguments, right, time and LSD.
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However, we're not limited to just providing these two. We can actually provide more arguments including
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an argument for the color of the graph.
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So I'm going to put a comma here and write
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"color=" and then 'G'. If I hit Shift+Enter now, we see the line color change to
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green.
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Now, a reasonable question to ask is "How did you know that you can supply a color argument with a keyword
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just like this?"
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And the answer is - I didn't know until I looked at the official documentation that's available for
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pyplot.
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Being able to read and interpret the official documentation that's available for each of these components
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is one of the key skills at getting good at Python programming. So check this out,
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we're gonna head down to the part of the documentation that gives us information on the plotting method.
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This is the part of the documentation where we can find out more about the plotting method.
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We've got the name of our method up here, namely plot and inside the parentheses,
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we can see it takes some arguments.
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Now the documentation provides some examples as well as information about what these arguments could
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be.
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The first thing that we did was that we plotted time vs. drug concentration in tissue, so we just had
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two arguments. And in the documentation,
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we can see that this is the way to create a plot using the default styles and colors.
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However, in addition to these standard x and y arguments we can supply some additional arguments.
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This is where we come across this term called kwargs, kwargs is an abbreviation for keyword arguments.
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And an example of a keyword argument is our color. Scrolling down,
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we can also see that G is a supported color abbreviation. And scrolling down even further, we can see
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a handy list of the keyword arguments that we can use on our plot method. So right here, we can see that
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color is one of these keyword arguments, but there are others too.
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For example, line style or line width.
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Let's add the line with keyword argument to our Python code,
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now. Here's how we can do it.
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We'll just add a comma and then write
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linewidth =
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I don't know, say 10
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Hitting Shift+Enter updates the chart. And,
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voila! We can see that now it has a very, very thick green line in it.
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Ten is probably a little bit too thick for my taste,
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I'm going to go with three.
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There you go.
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This is not so bad.
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The other thing to think about with visualization and looking at data is that design is actually quite
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important in data visualization because, if you think about it, the end goal is showing our data to people
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and that's why we both need to make it look clear and we need to make it look pretty because typically,
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you and I are gonna be in a position where we're going to have to impress both our bosses and our customers.
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Everybody judges a book by its cover I'm afraid, so our chant is going to have to look a lot better
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than it is right now.
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The first thing to note is that we're going to add text to our chart.
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We have to add labels to these axes and a title to the chart, so that people know what it is they're
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actually looking at.
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The second thing is that we don't actually have to stick to the default colors.
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We don't have to stick to a generic green or red.
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We can add a custom color and we do that by supplying a color's hex code.
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So here's a mini crash course in design. A hex code looks something like this:
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it has a little hash tag and then it has one, two, three, four, five numbers or digits that come after it.
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In other words, a hex code is just like a particular ID for a color.
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Now what you'll want to do is you'll want to go to a Web site, like say flat ui colors, to grab these
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hex codes of colors that have already been curated for you, because, quite frankly, these colors look really,
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really good.
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So let's grab the hex code for this
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red, this alizarin here and then, when we go back to our plot, we can supply this hex code instead of
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this G. Hitting Shift+Enter,
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I can see that now my line has been updated to this beautiful red.
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A great resource to be aware of to find beautiful colors, by the way, is a website called material
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palette.
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If you want to include more than one color in your chart, you can click on two of these,
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and you'll get an eight color color palette that you can use in your designs. These kind of tricks are
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really handy for making something look beautiful really, really quickly.
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So let's add some text to our graph.
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First off, I'm going to give this graph a title, so I'm going to say 
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plt.title('Tissue concentration of LSD over time')
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and then I'll Shift+Enter. Excellent!
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But I do think that this title is a little bit small.
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So again, we're gonna use a keyword argument to set the font size here.
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So the argument's name is fontsize,
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no surprises there. And I'm going to set the font size to 17. Hitting Shift+Enter updates
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my chart.
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Now let's put some labels on these axes.
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For the x-axis, we will write plt.xlabel('Time in Minutes') and we'll set
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the font size for that equal to, say 14. Hitting Shift+Enter, we can see our change right away.
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So now our x-axis has a nice looking label. We're going to do the same thing for our y-axis.
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And notice how every time we write plt, which is our object, put a dot after it and then we're calling
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a method on our object.
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So to put that y label on there, we're going to say 
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plt.ylabel('Tissue LSD ppm'),
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font size equals 14.
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There you go.
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Now, these aren't the only ways of adding text to our graph by the way.
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We can also add text in freeform, more or less. So if you want to add a little footer to the graph, we
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can do that and have it display where our data came from.
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So, let's take a look at the documentation for adding arbitrary text to our graph.
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Here we can see that our text method has multiple arguments that it takes - some of these are optional
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and some of these are required.
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The first thing you'll notice is that we have to supply an x value and a y value.
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These are the coordinates of where the text should be in the picture. And the second thing that you'll
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notice is that the s stands for string.
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And this is just the piece of text that should be displayed.
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So we have to supply coordinates for the text as well as what the text should be.
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Let's try this out.
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So coming back here we can see
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plt.text()
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Now, I don't know exactly where the text should go so I'm going to say x is gonna be equal to zero,
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y is gonna be equal to zero and our string, our text itself, is gonna read "Wagner, et al.,
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1968.
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Maybe some parentheses here as well.
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Let's press Shift+Enter now and see where these 0,0 coordinates actually are. Scrolling down,
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I can see that it places the text right here
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if x is equal to zero and y is equal to zero. Let's see what happens when y is equal to, say 5. When y
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is equal to 5 if it moves our text up here, and when y is equal to say negative 1 I can see that it
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moves our text down here.
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So this is pretty good, we know where the origin is.
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We know that positive number moves the text up and a negative number on the y value moves the text down.
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I reckon that a good amount for this y value might be something like 0.5. Let's try that. This arranges
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it very nicely.
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Now, at the moment our font size for this piece of text is the default font size.
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We can set our own value again by providing the font size argument and say setting it to 12. There
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we go. Now, since we're setting the font size on a lot of things,
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we can also specify the font size of these numbers that are on the axes.
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Say we wanted the numbers on the axes to be the same font size as the label here.
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So I could write something like plt.xticks(fontsize=14) and 
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plt.yticks(fontsize=14)
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If a hit Shift+Enter now, we can see that the numbers now have the same size as our labels. Another
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thing that we can do on these axes is to set hard values for the range that they should cover.
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So for example, we know that our time delay in minutes is going to be between 0 and 500.
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And we also know that the parts per million are going to be between 1 and say 6.5 or 7.
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To set a hard range
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we can write something like plt.ylim(), lim for limit and provide two values - a lower bound which is,
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say, 1 and an upper bound which is to say, I don't know, 7. Hitting Shift+Enter,
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we can now see that our chart has updated, so it's no longer determining automatically what the range
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of values should be
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that should be displayed on the y axis.
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We have now specified our own range that we'd like to show, namely we'd like to have the chart to show
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the values between 1 and 7. We can do the same thing for the x axis by writing plt.xlim() and
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providing a lower bound of 0 and an upper bound of 500.
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The reason I'm trying to show all this is to get this idea across that we're kind of breaking up our
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Python code into two sections, if you will, for the chart. We're doing the styling and then down here we're
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actually plotting the data.
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And what's interesting to note about this is that the amount of code that's written to style the chart
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is actually getting longer and longer and longer.
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This is one of the reasons why matplotlib comes with something called built-in styles these built-in
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styles can act as a shortcut or a template to help you reduce the amount of code that you need to
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write to make something look pretty.
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In our previous lessons, we've used the 'fivethirtyeight' style for our chart, but there is actually many other styles
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that you can choose from. One of the handy things to look at is actually the style of gallery.
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And here you can see for example the name of the style;
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so the first one it's called 'bmh' and the second one's called 'classic',
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and the third one is called 'dark_background' and you can scroll down to see what these
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different styles translate into if you're actually going to plot a chart.
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Now mind you this is actually an unofficial style guide that I found very, very helpful.
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The official one looks something like this. Now I find both of these really, really helpful in deciding
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what kind of template I should go with for my charts. To apply any of these particular styles to your
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chart,
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all you have to do is write plt.style.use
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and then provide the name of the particular template.
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So say we use 'classic'. If I hit Shift+Enter,
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I can see my chart update.
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This is what it would look like using the 'classic' style.
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Of course you can put anything you want in here.
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So if you wanted to use say 'dark_background' which is the name of another style then we'll
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get this.
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I think one of the other names that I saw on the gallery was 'ggplot'.
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So let me just hit Shift+Enter here.
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Now one thing you'll notice is that maybe the style won't be applied right away.
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So if you see that happen to you, just click into the cell and it Shift+Enter again.
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Then you should see the style applied.
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So I'm going to go with 'classic'.
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Now the last thing we'll do with our plotting code is add a line of code into the cell so that our beautiful
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charts can be exported when we export our notebook.
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You see, at the moment our chants are generated when this code is run but if we add a percentage sign and
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then write 'matplotlib inline', then we are telling Jupyter notebook to export these charts
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along with the notebook when we go to File > Download as > Notebook.
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In other words, this line of code here is Jupyter notebook specific.
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Now it's time to run our regression.