A hospital administrator studies the relationship between patient satisfaction Y

Question

A hospital administrator studies the relationship between patient satisfaction Y, age X_1, illness severity X_2, and anxiety level X_3. Larger indexed values indicate higher satisfaction, increased severity, and higher anxiety level. Data are collected from 46 patients. Write the estimated MR equation. Interpret b_2 in the context of the problem. Conduct a NATDRC model utility test at a 0.05 level of significance. Interpret the multiple coefficient of determination Estimate the satisfaction of a 45 year-old patient whose illness severity is 51 and anxiety level is 2.2.

Explanation / Answer

a) Estimated MR equation:

y = 158.49 -1.14 x1 - 0.44 x2 - 13.47 x3

b) Interpretation of b2:

As illness severity increases by 1 unit holding anxiety level and age constant, the patient satisfaction is estimated to decrease by 0.44 units.

c) Model utility test:

From the output, p - value = 1.5 * 10^(-10) = 0.000

This p - value is less than 0.05 so reject Ho.

We conclude that model is significant to predict the patient satisfaction.

d) Multiple coefficient of determination = 0.682

This indicates that 68.2% of the variability in patient satisfaction can be explained by the model.

e) For x1 = 45, x2 = 51, x3 = 2.2

y = 158.49 -1.14 (45) - 0.44 (51) - 13.47 (2.2)

y = 55.116

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