Radial keratotomy is a type of refractive surgery in which radial incisions are made in the cornea of myopic (nearsighted) patients in an effort to reduce their myopia. Theoretically, the incisions allow the curvature of the cornea to become less steep, thereby reducing the refractive error of the patient. This and other vision correction surgery grew in popularity in the 1980s and 1990s, both among the public and among ophthalmologists.

The Prospective Evaluation of Radial Keratotomy (PERK) study began in 1983 to investigate the effects of radial keratotomy. Lynn et al. (1987) examined the factors associated with the 5-year postsurgical change in refractive error (Y, measured in diopters, D). Two independent variables under consideration were baseline refractive error (X1) in diopters) and baseline curvature of the cornea (X2, in dioptets).
The accompanying computer output is based on data adapted from the PERK study. Use it to answer the following questions.
a. State the estimated least-squares equation for the regression of change in refractive error (Y) on baseline refractive error (X1) and baseline curvature (X2).
b. Using your answer to part (a), give a point estimate for the change in refractive error for a patient who, at baseline, has a refractive error of €“ 8.00D and a corneal curvature of 44D.
c. Find the R2-value for the regression in part (a), and comment on the fit of the model.

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Regression of Y on X1 and X2 Source Model Error Corrected Total DF Sum of Squares Mean Square F Value Pr>F 17.62277191 62.63016929 80 25294120 8.81138596 7.18 0.0018 2 51 53 1.22804254 R-Square Coeff Var Root MSE Y Mean 0.219590 28.90811 1.108171 3833426 Portion of output omitted Estimate Standard Error tValue Pr> It Parameter Intercept X1 X2 12.36001523 -0.29160125 0.09165295 3,18 0.0025 0.22039615 0.11482391 1.92 0.0605 5.08621177 2.43 0.0187