In a study about beer froth, a researcher poured beer into a cylindrical beer mug and recorded the heights of the froth at the start and then every minute for the first 6 minutes. For each of three brands of beer, the researcher ran the experiment several times and computed the mean height of beer froth at each of the 7 times (see Table 56).

Let y be the mean height (in centimeters) of froth for an Erdinger Weissbier x minutes after having been poured.
a. Construct a scatterplot that compares values of x and y.
b. Find the regression equation that models the association between x and y.
c. Describe the four characteristics of the association between x and y. Compute and interpret an appropriate correlation coefficient as part of your analysis.
d. Use the model to predict the mean height of froth 1 minute after an Erdinger Weissbier is poured.
e. Find the residual for your prediction in part (d). What does it mean in this situation?

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Table 56 Times and Mean Heights of Beer Froth Mean Height of Froth (centimeters) Erdinger Time (minutes) Weissbier Augustinerbräu Budweiser 170 13.2 10.7 8.9 München 14.0 6.0 Budvar 14.0 9.3 70 6.3 5.2 13 0.7 3.5 2.0 0.9