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3. A hospital administrator wished to study the relation between patient satisfaction (Y) and patients age (Xi, in years), se
below is pat data
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
3. A hospital administrator wished to study the relation between patient satisfaction (Y) and patients age (Xi, in years), severity of illness (X2, an index) and anxiety level (X3, an index). The administrator randomly selected 23 patients and collected the data in pat, where larger values of Y, X2 and X3 are, respectively, associated with more satisfaction, increased severity of illness and more anxiety. The data is saved in Moodle2 as pat. (a) Obtain the scatterplot matrix and the correlation matrix. Interpret these and state your principal findings (b) Fit the regression model, to the data and state the estimated regression function. How is here? interpreted (c) Test whether there is a regression relation here: use α = 0.10. State the alterna- tives, decision rule (the rule that determines rejection of thenu hypothesis) and conclusion. What does your test imply about A, and A? (d) Obtain joint 90% interval estimates of A, and β3. Interpret your results. (e) Obtain a 90% confidence interval estimate of mean satisfaction when X10-35, X20 45 and X30 2.2. Interpret your confidence interval. (f) Obtain the analysis of variance table that decomposes the regression sum of squares into regression sum of squares associated with X2; with X1 given X2; and with X3 given X2 and X1. (g) Test whether X3 can be dropped from the regression model given that X1 and X2 are retained. Use the F statistic and α-, 0.025. State the alternatives, decision rule and conclusion (h) Test whether both X2 and X3 can be dropped from the model given that X1 is retained using α-0.025. State the alternatives, decision rule and conclusion
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 2.0 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 2.0 72 32 46 2.6 57 32 52 2.4 55 42 51 2.7 59 33 42 2.0 83 36 49 1.8 76 31 47 2.0 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 22 51 2.0 37 44 51 2.6 68 45 51 2.2 59 37 53 2.1 92 28 46 1.8
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