The data from a patient satisfaction survey in a hospital are in Table E12-1.

The regressor variables are the patient€™s age, an illness severity index (higher values indicate greater severity), an indicator variable denoting whether the patient is a medical patient (0) or a surgical patient (1), and an anxiety index (higher values indicate greater anxiety).

(a) Fit a multiple linear regression model to the satisfaction response using age, illness severity, and the anxiety index as the regressors.

(b) Estimate σ².

(c) Find the standard errors of the regression coefficients.

(d) Are all of the model parameters estimated with nearly the same precision? Why or why not?

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Satis- Obser- vation Age Severity Surg-Med Anxiety faction 55 2.1 1 50 68 2 46 24 1 2.8 77 3.3 3 30 46 96 4 35 48 1 4.5 80 43 59 58 2.0 61 60 5.1 44 74 65 5.5 26 38 42 1 3.2 88 27 42 3.1 75 10 51 50 2.4 57 11 53 38 1 2.2 56 12 41 30 2.1 88 13 37 31 1.9 88 14 24 34 3.1 102 15 3.0 88 16 50 48 4.2 70 17 58 61 4.6 52 18 60 71 1 5.3 43 19 62 62 7.2 46 20 68 38 7.8 56 21 70 41 7.0 59 22 79 66 6.2 26 23 63 31 4.1 52 83 24 39 42 3.5 25 49 40 1 2.1 75