A computer game. A multimedia statistics learning system includes a test of skill in using the computer's mouse. The software displays a circle at a random location on the computer screen. The subject clicks in the circle with the mouse as quickly as possible. A new circle appears as soon as the subject clicks the old one. Table 5.3 (text page 155) gives data for one subject's trials, 20 with each hand. Distance is the distance from the cursor location to the center of the new circle, in units whose actual size depends on the size of the screen. Time is the time required to click in the new circle, in milliseconds.

(a) Specify the population multiple regression model for predicting time from distance separately for each hand. Make sure you include the interaction term that is necessary to allow for the possibility of having different slopes. Explain in words what each ß in your model means.

(b) Use statistical software to find the estimated multiple regression equation for predicting time from distance separately for each hand. What percent of variation in the distances is explained by this multiple regression model?

(c) Explain how to use the estimated multiple regression equation in part (b) to obtain the least-squares line for each hand. Draw these lines on a scatterplot of time versus distance.