![]() The formula for a straight line is usually written like this: To do so, let’s start with a refresher of some high school maths. This is not highly surprising: the line that I’ve drawn in panel to the right doesn’t “fit” the data very well, so it doesn’t make a lot of sense to propose it as a way of summarising the data, right? This is a very simple observation to make, but it turns out to be very powerful when we start trying to wrap just a little bit of maths around it. In contrast, the panel to the right shows the same data, but with a very poor choice of regression line drawn over the top. Not surprisingly, the line goes through the middle of the data. 16.1 with the best fitting regression line drawn over the top. 16.2 The panel to the left shows the sleep-grumpiness scatterplot from Fig. close () glue ( "sleep_regressions_1-fig", fig, display = False )įig. set_ylabel ( "My grumpiness (0-10)" ) fig. set_title ( "Not the best-fitting regression line!" ) fig. scatterplot ( data = df, x = 'dan_sleep', y = 'dan_grump', ax = axes ) fig. set_title ( "The best-fitting regression line" ) fig. ![]() subplots ( 1, 2, figsize = ( 10, 5 ), sharey = True ) x = np. ols ( formula = "dan_grump ~ dan_sleep", data = df ). Import numpy as np import matplotlib.pyplot as plt import as smf # find the regression coefficients to allow manually plotting the line model = smf. We don’t find ourselves imagining anything like the rather silly plot shown in the right panel in Fig. Notice that – since we’re not idiots – the regression line goes through the middle of the data. In statistics, this line that we’re drawing is called a regression line. That is, we mentally draw a straight line through the middle of the data. 16.1, and as we saw previously this corresponds to a correlation of \(r=-.90\), but what we find ourselves secretly imagining is something that looks closer to the left panel in Fig. The actual scatterplot that we draw is the one shown in Fig. 16.1 Scatterplot showing grumpiness as a function of hours slept. close () glue ( "sleepycorrelation-fig", fig, display = False )įig. set ( title = 'Grumpiness and sleep', ylabel = 'My grumpiness (0-100)', xlabel = 'My sleep (hours)' ) sns. ![]() scatterplot ( data = df, x = 'dan_sleep', y = 'dan_grump' ) ax. Comparing two regression modelsįrom myst_nb import glue from matplotlib import pyplot as plt import seaborn as sns fig = plt. Checking the linearity of the relationship Calculating standardised regression coefficients Hypothesis tests for all pairwise correlations Hypothesis tests for a single correlation Testing the significance of a correlation The relationship between regression and correlation Quantifying the fit of the regression model
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