Section 26.8 Section 5.3 Summary
In this section you considered the association between two quantitative variables. Because this was your first encounter with this type of analysis scenario, we returned to several themes from Chapter 1, including starting with graphical displays and numerical summaries. You learned that the relevant graphical display for describing the association between two quantitative variables is a scatterplot, and that some features to look for in a scatterplot are the direction, strength, and linearity of the association. The most common numerical summary of a linear association is the correlation coefficient, and you studied some properties of this measure. Then you turned your attention to fitting a linear model to the data, useful for predicting the value of the response variable based on an explanatory variable outcome. You studied the least squares criterion for determining this regression line and derived the equations for estimating the coefficients from sample data. With the regression line in hand, you can make predictions for the response variable outcome based on the explanatory variable value. Just keep in mind that these predictions should be made only for \(x\) values within the range of the original data (and not extrapolating beyond the original explanatory variable values). Finally, you examined properties of regression lines, such as the coefficient of determination, which reveals how much of the variability in the response variable is explained by the regression line, and influential observations, which have substantial effect on the regression line and typically arise from observations with extreme explanatory variable values.
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