This problem refers to the radial keratotomy study data from Problem 12 in Chapter 8. Suppose that we want to compare the average change in refraction for males and females, controlling for baseline refractive error and baseline curvature. To this end, we define the following dummy variable:

a. State an ANACOVA regression model that can be used to compare the mean change in refraction (Y) for males and females, controlling for baseline refractive error (X1) and baseline curvature (X2).
b. State the model that should be used to check whether the ANACOVA model in part (a) is appropriate. Using the computer output given next, carry out the appropriate test.
c. Using ANACOVA methods and the SAS output, determine adjusted mean changes in refractive error for males and females, and test whether they differ significantly from one another. (Unadjusted average change in refraction for males = 3.64 diopters; unadjusted average change in refraction for females = 3.965 diopters; overall mean baseline refraction = -4.03 diopters; overall mean baseline curvature = 44.02 diopters.)
Regression of Y on X1, X2, Z, X1 * Z, X2 * Z

Regression of Y on X1, X2, and Z

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1 0 if patient is male otherwise ANALYSIS OF VARIANCE Sum of Mean Source Model Error Corrected Total DF Squares Square F Value Pr> F 5 24.71516 494303 48 55.537781.1570 53 80.25294 4.27 0.0027 Root MSE Dependent Mean Coeff Var 1.07566 3.83343 28.05993 R-Square Adj R-Sq 0.3080 0.2359 PARAMETER ESTIMATES Parameter Standard Variable DF Estimate Intercept X1 X2 tValue | Pr>lt] 1.87 0.0671 0.10539 1,92 00610 0.15756 142 0.1618 -0.91427 10.01057 -0.09 0.9276 1.80 0.0775 10.02426 0.22572 0.11 0.9149 13.06563 6.97300 0.22389 X1z -0.35838 0.19864 X2Z ANALYSIS OF VARIANCE Sum of Mean DF Squares Square FValue Pr> F Source Model Error Corrected Total 3 20,90031 6.96677 5.87 0.0016 50 59 35263 1.18705 53 80.25294 Root MSE Dependent Mean Coeff Var 1.08952 3.83343 28.42156 R-Square Adj R-Sq 0.2604 0.2161 PARAMETER ESTIMATES Parameter Standard Error tValue Pr It 5.06713 Variable DF Estimate Intercept X1 X2 2.71 0.0093 0.30382 0.090413.36 0.0015 0 247700.11408 -2.17 00347 10.50859 0.30608 16 0.1028 13.71986