here are the data question:
Posted: Mon Apr 11, 2022 6:21 am
here are the data
question:
Y 20.19 27 51.75 51.36 28.98 21.7 14.4 15.14 50 23.73 29.33 19.98 13.28 X1 3.11 4.9 5.72 7.82 2.62 1.48 0.57 0.6 6.29 1.94 0.52 1.11 1.61 X2 4.51 6.03 7.98 9.58 7.54 3.96 8.6 5.46 13.03 7.12 8.94 5.85 3.73 X3 2.05 0.67 0.96 1.06 1.42 1.09 2.16 1.58 1.48 0.91 1.58 1.19 1.58 X4 0.67 0.65 0.6 0.42 0.36 0.23 0.83 0.85 0.28 0.57 0.88 0.62 0.62 X5 53 51 54 56 66 37 41 55 43 58 39 41 54
2. The data (Assignment2-Q2.txt) include the total triglyceride level, in mmol/L(Y) and five potential predictor variables are defined as shown below. X1 : Chylomicrons X2 : Very low-density lipoprotein (VLDL) X3 : Low-density lipoprotein (LDL) X4 : High-density lipoprotein (HDL) X5 : Age of patient Consider the multiple regression model : Y; = Bo + B1Xi1 + B2X2 + Ej. Calculate parts (a) and (b) by hands. : == = = (a) Find r12 (b) Find (VIF), and (VIF)2. (c) What is the coefficients and MSE of the following models? i. Y; = Bo + B1Xi1 + B2X 2 + B3X:3 + B4X14 + B5X15 + Ei ii. Yị = Bo + B1X11 + B2X12 + B4X14 + B5X15 + Ei iii. Y; = Bo + B1Xi1 + B2X2 + B3X:3 + Ei iv. Y; = Bo + BiXi1 + B2X2 + Ei (d) Find SSR(X3|X1, X2, X4, X5) and SSR(X3|X1, X2). (e) Perform hypothesis testing for Ho : B3 = 0 vs Ha: B3 + 0 at 5% significance level by 5 F-test in the following models: i. Y; = Bo + B1X11 + B2X12 + B3X13 + B4X 4 + B5X15 + £i; and ii. Y; = Bo + B1X,1 + B2X/2 + B3X;3 + Ej. (f) Find the 95% prediction interval for Yh when Xh1 = 4 and Xh2 = 6. . = = =
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2. The data (Assignment2-Q2.txt) include the total triglyceride level, in mmol/L(Y) and five potential predictor variables are defined as shown below. X1 : Chylomicrons X2 : Very low-density lipoprotein (VLDL) X3 : Low-density lipoprotein (LDL) X4 : High-density lipoprotein (HDL) X5 : Age of patient Consider the multiple regression model : Y; = Bo + B1Xi1 + B2X2 + Ej. Calculate parts (a) and (b) by hands. : == = = (a) Find r12 (b) Find (VIF), and (VIF)2. (c) What is the coefficients and MSE of the following models? i. Y; = Bo + B1Xi1 + B2X 2 + B3X:3 + B4X14 + B5X15 + Ei ii. Yị = Bo + B1X11 + B2X12 + B4X14 + B5X15 + Ei iii. Y; = Bo + B1Xi1 + B2X2 + B3X:3 + Ei iv. Y; = Bo + BiXi1 + B2X2 + Ei (d) Find SSR(X3|X1, X2, X4, X5) and SSR(X3|X1, X2). (e) Perform hypothesis testing for Ho : B3 = 0 vs Ha: B3 + 0 at 5% significance level by 5 F-test in the following models: i. Y; = Bo + B1X11 + B2X12 + B3X13 + B4X 4 + B5X15 + £i; and ii. Y; = Bo + B1X,1 + B2X/2 + B3X;3 + Ej. (f) Find the 95% prediction interval for Yh when Xh1 = 4 and Xh2 = 6. . = = =