This problem involves the PERK study data discussed in Problem 12 in Chapter 8. Suppose that we want to compare the relationship between changes in refraction five years after surgery and baseline refractive error, for males and females. To this end, we define the following dummy variable:

a. State a single regression model that defines straight-line models relating change in refraction five years after surgery and baseline refractive error for both males and females.
b. Using the computer output given next, test whether the straight lines for males and females coincide.
c. Test H0: "The lines are parallel" versus HA: "The lines are not parallel."
d. In light of your answers to parts (b) and (c), comment on differences and similarities in the change in refraction-baseline refractive error relationship for males and females.
Regression of Y on X1, Z, and X1Z

Regression of Y on X1 and Z

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1 0 if patient is male otherwise ANALYSIS OF VARIANCE Sum of DF Squares Mean Square F Value Pr> F 5.40 00027 Source Model Error Corrected Total 3 19.65170 6.55057 50 6060124 1.21202 53 80.25294 Root MSE Dependent Mean Cooff Var 1.10092 3.83343 28.71896 R-Square Adj R-Sq 0.2449 0.1996 PARAMETER ESTIMATES ParameterStandard DF Estimate t Value Pr> t Variable Intercept X1 3.17821 6.84 <0001 0.10786 1.86 0.0683 -1.99513 0.88972 -2.24 0.0294 1 0.38383 0.202661.89 00640 0.46488 -0.20101 x12 ANALYSIS OF VARIANCE Sum of Mean DF Squares Square F Value Pr> F Source Model Error Corrected Total 2 15.30414 7.65207 51 64.94880 1.27351 53 80.25294 6.01 0.0045 0.1907 Root MSE Dependent Mean Coeff Var 1.12850 3.83343 29.43835 R-Square Adj R-Sq 0.1590 PARAMETER ESTIMATES Parameter Standard | Variable Intercept X1 DFI Estimate t Value Pr > It <0001 Error 2.75265 041717 0.09360 3.31 0.0017 0.31372 1.32 0.1940 6.60 0.41288