Question

The accompanying computer excel output (please see attachment on Blackboard) provides details of data and analysis on the topic of “patient satisfaction”. A hospital administrator wished to study the relation between patient satisfaction (Y) and patients’ age (X1, in years) , severity of illness (X2), and anxiety level (X3).

The output includes a listing of all 46 observations; descriptive statistics for each variable; and, the results of a regression analysis that uses patient satisfaction as the dependent variable, and patient’s age, severity of illness, and anxiety level as independent variables.

1. a. Write out the regression equation, with specific intercept and slope estimates. Remember that the regression is already estimated for you so you only need to write the equation of the estimated model. For example: Y=….
2. b. For the first row of actual data from the excel file, use the equation in (a) to “predict” the value of Y. For this row, also compute the “residual” (actual value minus the predicted value). Note: Only use the first raw of data and not the whole data set.
3. c. Evaluate the statistical significance of each of the three slope estimates. This can be done in a very summary way. Use a significance level of 0.05. Note: You can either use the p-value or t-statistics to determine whether the coefficients are significant or not.
4. d. Use the R-square and F-test to evaluate the overall reliability of the regression.

Patient Satisfaction Patient Age Severity of illness Anxiety Level 48 50 51 2.3 57 36 46 2.3 66 40 48 2.2 70 41 44 1,8 89 28 43 1.8 36 49 54 2.9 46 42 50 2.2 54 45 48 2.4 26 52 62 2.9 77 29 50 2.1 89 29 48 2.4 67 43 53 2.4 47 38 55 2.2 51 34 51 2.3 57 53 54 2.2 66 36 49 2 79 33 56 2.5 88 29 46 1.9 60 33 49 2.1 49 55 51 2.4 77 29 52 2.3 52 44 58 2.9 60 43 50 2.3 86 23 41 1.8 43 47 53 2.5 34 55 54 2.5 63 25 49 2 72 32 46 2.6 57 32 52 2.4 55 42 51 2.7 59 33 42 2 83 36 49 1.8 76 31 47 2 47 40 48 2.2 36 53 57 2.8 80 34 49 2.2 82 29 48 2.5 64 30 51 2.4 37 47 60 2.4 42 47 50 2.6 66 43 53 2.3 83 51 2 37 44 51 2.6 68 45 51 2.2 59 37 53 2.1 92 28 46 1.8 22

Answer 1

a). Using Excel, go to Data, select Data Analysis, choose Regression. Put Patient Satisfaction in y inputrange and other values in x input range

	Coefficients	standard error	t stat	P-value
Intercept	158.491	18.126	8.744	0.000
Patient age	-1.142	0.215	-5.315	0.000
Severity of illness	-0.442	0.492	-0.898	0.374
Anxiety level	-13.470	7.100	-1.897	0.065

Y=158.491-1.142x1-0.442x2-13.470x3