EPI811 Regression EPI811: Advanced Biostatistics Tutorial 3: Multiple Linear Regression Semester 1, 2016 Student name: Id number: Tutorial EPI811 Regression Tutorial Question 1 Suppose systolic blood pressure, birth weight (oz), and age (days) are measured for 16 infants and the data are shown in the following table ID Birth weight (oz) ( ) x1 Age in days ( ) x2 135 120 100 105 130 125 125 105 120 90 120 95 120 150 160 125 3 4 3 2 4 5 2 3 5 4 2 3 3 4 3 3 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 SBP mmHg (y) 89 90 83 77 92 98 82 85 96 95 80 79 86 97 92 88 a. Draw a scatter plot b. Fit a multiple regression equation. c. Calculate the predicted average systolic blood pressure of a baby with birth weight 8 128 oz measured at 3 days of life. d. Test the hypotheses that and at 5% level of significance. 1 0 2 0 e. Construct 95% C.I's for 1 and 2 and comment on regression. f. Carry out an analysis of variance and test the significance of the regression using . 0.05 g. Compute the coefficient of multiple determinations and multiple correlation coefficients for the above example. h. Carry out a residual analysis for the adequacy of the model estimated. Does any observation look like it could be influential? in its effect on the regression line? i. If yes, identify the influential points and reanalyze, excluding the influential observation. What have you noticed? EPI811 Regression Tutorial Question 2 Eight patients underwent an operation in a hospital. Measurement of weight (kg), duration of operation (minutes), and blood loss (ml) were taken. The hospital authorities would like to know whether the blood loss was related to weight and duration of operation. The data are as follows: (Hint: Use all concepts you have learned) Weight (X1) 44 42 70 45 50 51 36 53 Duration of Operation(X2) 108 85 88 114 110 101 97 121 Blood loss(Y) 505 492 472 506 484 492 515 466 a. Perform a multiple linear regression and describe your finding. b. Examine the model fit. c. Perform a residual analysis