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 2.4 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.34

(a) We suspect that time depends on distance. Make a scatterplot of time against distance, using separate symbols for each hand.

(b) Describe the pattern. How can you tell that the subject is right-handed?

(c) Find the regression line of time on distance separately for each hand. Draw these lines on your plot. Which regression does a better job of predicting time from distance? Give numerical measures that describe the success of the two regressions.

(d) It is possible that the subject got better in later trials due to learning. It is also possible that he got worse due to fatigue.

Plot the residuals from each regression against the time order of the trials (down the columns in Table 2.4). Is either of these systematic effects of time visible in the data?