A psychologist made a small scale study to examine the nature of the relation between an employee's emotional stability (Y) and the employee's ability to perform in a task group (X). Emotional stability was measured by a written test and ability to perform in a task group (X = 1 if able, X = 0 if unable) was evaluated by the supervisor. The results were as follows:
i: 1 2 3 4 5 6 7 8
Y_i 479 619 584 638 399 481 624 582
X_i 0 1 0 1 0 1 1 1
a) Fit a linear regression and write down the fitted model.
b) Write down separate estimated regression equations for "able" employees and "unable" employees.
c) Is there a linear relationship between X and Y? Test at 5% level.