Solution HW CH.5

Solution HW CH.5 - 96 CHAPTER 5 Fitting Curves to Data 5.1...

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CHAPTER 5 Fitting Curves to Data 5.1 Model Summaries: R-square Adjusted R-square Standard Error Linear Model 99.2 99.0 14.34 Second Order Model 100.0 99.9 3.54 The second-order model appears better than the first-order model. The p value on the second-order term, RDSQR, is 0.000, so the second-order term is significant at any reasonable level of significance. The adjusted R-square is higher and the standard error is lower. The R-square on the second-order model is stated as 100%. Note that not all of the variance in the y variable is explained, but the R-square rounds off to 100%. 5.4 Model Summaries: R-square Adjusted R-Square Standard Error Linear Model 95.1 94.8 68.41 Second-Order Model 99.8 99.7 15.14 The second-order model appears better than the first-order model. The p value on the second-order term, NUMSQR = NUMBER 2 , is 0.000, so the second-order term is significant at any reasonable level of significance. The adjusted R-square is higher and the standard error is lower. Note that the experience variable appears to be unnecessary in the model and could be omitted. NUMBER TIME 30 25 20 15 10 5 0 1000 800 600 400 200 0 Scatterplot of TI ME vs NUMBER 96
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EXPER TIME 11 10 9 8 7 1000 800 600 400 200 0 Scatterplot of TI ME vs EXPER Linear Model The regression equation is TIME = - 179 + 33.0 NUMBER + 10.2 EXPER Predictor Coef SE Coef T P Constant -179.3 125.6 -1.43 0.165 NUMBER 32.969 1.436 22.96 0.000 EXPER 10.19 13.12 0.78 0.444 S = 68.4118 R-Sq = 95.1% R-Sq(adj) = 94.8% Analysis of Variance Source DF SS MS F P Regression 2 2474190 1237095 264.33 0.000 Residual Error 27 126365 4680 Total 29 2600555 Source DF Seq SS NUMBER 1 2471367 EXPER 1 2823 Second-Order Model Using Square of NUMBER The regression equation is TIME = 65.7 + 3.89 NUMBER + 0.943 NUMSQR + 0.37 EXPER Predictor Coef SE Coef T P Constant 65.73 29.77 2.21 0.036 NUMBER 3.887 1.308 2.97 0.006 NUMSQR 0.94317 0.04114 22.93 0.000 EXPER 0.371 2.934 0.13 0.900 97
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S = 15.1350 R-Sq = 99.8% R-Sq(adj) = 99.7% Analysis of Variance Source DF SS MS F P Regression 3 2594599 864866 3775.58 0.000 Residual Error 26 5956 229 Total 29 2600555 Source DF Seq SS NUMBER 1 2471367 NUMSQR 1 123228 EXPER 1 4 Unusual Observations Obs NUMBER TIME Fit SE Fit Residual
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Solution HW CH.5 - 96 CHAPTER 5 Fitting Curves to Data 5.1...

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