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Unformatted text preview: CHAPTER 7 Notes to the Instructor: The normal probability plots are constructed in Minitab using the command ‘Normality Test’ under “Basic Statistics”. The analysis of variance is carried out using “ANOVA” under ‘Stat’ in Minitab. In cases where there are exactly two levels for each factor of interest, use “DOE” under ‘Stat’. Hierarchial models are used throughout. To use “Regression” to find an appropriate model, the interactions must be entered by hand. The data files on disk contain the design shown in each problem and columns for the corresponding interactions. Section 73 71. a) Predictor Coef StDev T P Constant 105.438 7.730 13.64 0.000 Material 9.313 7.730 1.20 0.252 Temp 33.938 7.730 4.39 0.001 Mat*Temp 4.687 7.730 0.61 0.556 b) 11 11 145 135 125 115 105 95 85 75 65 55 Temp Material Mean Interaction Plot  Data Means for Life The interaction plot does not indicate a strong interaction between temperature and material. c) The tratios are given in the output shown in part a. The tratios indicate that temperature is significant, but material and the interaction material*temperature are not at the α = 0.05 level. d) The 95% confidence intervals are given by effect estimate ± 2(s.e.(effect)) where effect = 2(coefficient). The coefficient is given in the Minitab output of part a. s.e.(effect) = 2[s.e.(coefficient)]. The s.e.(coefficient) is given in the Minitab output of part a. Temperature: effect = 2(coefficient) = 2(33.938) = 67.876 s.e.(effect) = 2(7.73) = 15.46 Approximate 95% confidence interval on the effect of Temperature:67.876 ± 2(15.46) ( 98.796, 36.956) Material: effect = 2(coefficient) = 2(9.313) = 18.626 s.e.(effect) = 2(7.73) = 15.46 Approximate 95% confidence interval for the effect of Material: 18.626 ± 2(15.46) (12.294, 49.546) Material*Temperature: effect = 2(coefficient) = 2(4.687 )= 9.374 s.e.(effect) = 2(7.73) = 15.46 Approximate 95% confidence interval for the effect of Material*Temperature: 9.374 ± 2(15.46) ( 21.546, 40.294) e) Life = 105 + 9.31 Material  33.9 Temp + 4.69 Mat*Temp Predictor Coef StDev T P Constant 105.438 7.730 13.64 0.000 Material 9.313 7.730 1.20 0.252 Temp 33.938 7.730 4.39 0.001 Mat*Temp 4.687 7.730 0.61 0.556 Based on the regression analysis, only temperature appears to be the significant factor. This result is equivalent to that obtained in part c. The final regression analysis and model are Life = 105  33.9 Temp Predictor Coef StDev T P Constant 105.438 7.680 13.73 0.000 Temp 33.938 7.680 4.42 0.001 S = 30.72 RSq = 58.2% RSq(adj) = 55.3% Analysis of Variance Source DF SS MS F P Regression 1 18428 18428 19.53 0.001 Residual Error 14 13212 944 Total 15 31640 The analysis of variance indicates the final regression model is adequate for this set of data. This is evident by pvalue = 0.001....
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This note was uploaded on 12/11/2009 for the course CSE IEE taught by Professor Chattin during the Summer '09 term at ASU.
 Summer '09
 chattin

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