Hw4_09fall sol

Hw4_09fall sol - Question1...

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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
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This note was uploaded on 12/25/2011 for the course ISYE 6413 taught by Professor Staff during the Spring '08 term at Georgia Tech.

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Hw4_09fall sol - Question1...

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