Hw4_09fall sol - Question1 .10(1 and thetypeoffilm....

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Question 1 We first fit the model given in Section 3.10: (1) This model assumes the relationship of and is a linear relationship that does not depend on the type of film. The MINITAB output is shown below. Regression Analysis: y versus x, tau2, tau3 The regression equation is y = 158 + 62.5 x - 83.7 tau2 + 70.4 tau3 Predictor Coef SE Coef T P Constant 158.3 179.8 0.88 0.383 x 62.50 17.06 3.66 0.001 tau2 -83.67 86.10 -0.97 0.336 tau3 70.36 67.78 1.04 0.305 S = 164.650 R-Sq = 68.1% R-Sq(adj) = 66.0% PRESS = 1428711 R-Sq(pred) = 62.70% Analysis of Variance Source DF SS MS F P Regression 3 2610082 870027 32.09 0.000 Residual Error 45 1219940 27110 Total 48 3830022 Source DF Seq SS x 1 2553357 tau2 1 27513 tau3 1 29212 Unusual Observations Obs x y Fit SE Fit Residual St Resid 39 10.8 1282.0 903.6 44.6 378.4 2.39R 40 10.1 1233.8 859.9 51.1 373.9 2.39R 41 12.7 1660.0 1022.4 41.9 637.6 4.00R R denotes an observation with a large standardized residual.
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Residual Percent 500 250 0 -250 -500 99 90 50 10 1 Fitted Value Residual 1200 1000 800 600 400 600 400 200 0 -200 Residual Frequency 600 400 200 0 -200 24 18 12 6 0 Normal Probability Plot of the Residuals Residuals Versus the Fitted Values Histogram of the Residuals Residual Plots for y (Common Slope Model) A model with three separate intercept and slope terms is given by (2) where , , . Fitting the model with MINITAB gives the results shown below. Regression Analysis: y versus d1, d2, d3, d1x, d2x, d3x The regression equation is y = 191 d1 - 751 d2 + 587 d3 + 59.3 d1x + 189 d2x + 32.5 d3x Predictor Coef SE Coef T P Noconstant d1 191.0 234.9 0.81 0.421 d2 -751.0 323.3 -2.32 0.025 d3 587.5 307.9 1.91 0.063 d1x 59.29 22.65 2.62 0.012 d2x 188.91 49.20 3.84 0.000 d3x 32.51 25.54 1.27 0.210
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S = 154.664 PRESS = 1287347 Analysis of Variance Source DF SS MS F P Regression 6 29414933 4902489 204.95 0.000 Residual Error 43 1028601 23921 Total 49 30443534 Source DF Seq SS d1x 1 8370407 d2x 1 4652848 d3x 1 16159726 d1 1 15817 d2 1 129071 d3 1 87063 Obs d1 y Fit SE Fit Residual St Resid 2 1.00 610.0 564.5 98.1 45.5 0.38 X 39 0.00 1282.0 938.6 47.9 343.4 2.34R 40 0.00 1233.8 915.8 60.6 318.0 2.23R 41 0.00 1660.0 1000.3 42.0 659.7 4.43R R denotes an observation with a large standardized residual. X denotes an observation whose X value gives it large influence. Residual Percent 800 400 0 -400 99 90 50 10 1 Fitted Value Residual 1000 800 600 400 200 600 400 200 0 -200 Residual Frequency 600 400 200 0 -200 20 15 10 5 0 Normal Probability Plot of the Residuals Residuals Versus the Fitted Values Histogram of the Residuals Residual Plots for y (Model with Different Slopes)
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The residual plots above indicate that there are three large outliers: observations 39, 40, and 41. After removal of outliers, we obtain the results shown below. Regression Analysis: y versus d1x, d2x, d3x, d1, d2, d3 The regression equation is y = 59.3 d1x + 189 d2x + 55.9 d3x + 191 d1 - 751 d2 + 209 d3 Predictor Coef SE Coef T P Noconstant d1x 59.29 11.17 5.31 0.000 d2x 188.91 24.27 7.78 0.000 d3x 55.95 13.72 4.08 0.000 d1 191.0 115.8 1.65 0.107 d2 -751.0 159.5 -4.71 0.000 d3 208.8 167.7 1.25 0.220 S = 76.2782 PRESS = 333176 Analysis of Variance Source DF SS MS F P Regression 6 24289413 4048236 695.77 0.000 Residual Error 40 232734 5818 Total 46 24522148 Source DF Seq SS d1x 1 8370407 d2x 1 4652848 d3x 1 11112242 d1 1 15817 d2 1 129071 d3 1 9028 Obs d1x y Fit SE Fit Residual St Resid 1 7.7 791.7 647.5 35.0 144.2 2.13R 2 6.3 610.0 564.5 48.4 45.5 0.77 X 20 0.0 400.0 552.4 19.7 -152.4 -2.07R 38 0.0 950.0 751.5 39.1 198.5 3.03R R denotes an observation with a large standardized residual. X denotes an observation whose X value gives it large influence.
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Residual Percent 200 100 0 -100 -200 99 90 50 10 1 Fitted Value Residual 1000 800 600 400 200 200 100 0 -100 -200 Residual Frequency 200 150 100 50 0 -50 -100 -150 12 9 6 3 0 Normal Probability Plot of the Residuals Residuals Versus the Fitted Values Histogram of the Residuals Residual Plots for y (Model
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