13.22 ● The accompanying data were read from a plot (and are a subset of the complete data set) given in the article “Cognitive Slowing in Closed-Head Injury” (Brain and Cognition [1996]: 429– 440). The data represent the mean response times for a group of individuals with closed-head injury (CHI) and a matched control group without head injury on 10 different tasks.

Each observation was based on a different study, and used different subjects, so it is reasonable to assume that the observations are independent.

Mean Response Time Study Control CHI 1 250 303 2 360 491 3 475 659 4 525 683 5 610 922 6 740 1044 7 880 1421 8 920 1329 9 1010 1481 10 1200 1815

a. Fit a linear regression model that would allow you to predict the mean response time for those suffering a closed-head injury from the mean response time on the same task for individuals with no head injury.

b. Do the sample data support the hypothesis that there is a useful linear relationship between the mean response time for individuals with no head injury and the mean response time for individuals with CHI?

Test the appropriate hypotheses using a 5 .05.

c. It is also possible to test hypotheses about the y intercept in a linear regression model. For these data, the null hypothesis H0: a 5 0 cannot be rejected at the .05 significance level, suggesting that a model with a y intercept of 0 might be an appropriate model. Fitting such a model results in an estimated regression equation of CHI 5 1.48(Control)

Interpret the estimated slope of 1.48.