1Bears.MTW With Calc > Calculator Z = Sex-1 (from 1,2 to 0,1) With Graph > Plot • Y=Weight, X=Length • Symbol by group, variable Z • Lowess bygroup, variable Z (smoothing param 0.5) (With “Edit attributes”, use different symbols and line types, or colors) 0 1 0 1 8575655545355004003002001000LengthWeight2With Calc > Calculator • ZL = Z times Length With Stat > Regression > Regression • response = Weight • predictors = Length, Z, ZL • With “Storage”, Residuals and Fits • With “Results”, second option The regression equation isWeight = - 450 + 10.6 Length + 158 Z - 3.01 ZLPredictor Coef SE Coef T PConstant -450.40 33.79 -13.33 0.000Length 10.5663 0.5307 19.91 0.000Z 157.62 79.69 1.98 0.050ZL -3.012 1.352 -2.23 0.027S = 52.58 R-Sq = 77.9% R-Sq(adj) = 77.4%Analysis of VarianceSource DF SS MS F PRegression 3 1351010 450337 162.91 0.000Residual Error 139 384243 2764Total 142 17352533With Graph > Plot • Y=RESI1, X=Length • Symbol by group, variable Z • Lowess by group, variable Z (With “Edit attributes”, use different symbols and line types, or colors) 0 1 0 1 8575655545352001000-100LengthRESI1 With Calc > Calculator • LogW = logarithm of Weight4Now, proceeding as before… 0 1 0 1 8575655545356543LengthLogW The regression equation isLogW = 1.54 + 0.0582 Length - 0.806 Z + 0.0132 ZLPredictor Coef SE Coef T PConstant 1.5384 0.1331 11.56 0.000Length 0.058173 0.002091 27.82 0.000Z -0.8056 0.3140 -2.57 0.011ZL 0.013211 0.005326 2.48 0.014S = 0.2072 R-Sq = 88.5% R-Sq(adj) = 88.3%Analysis of VarianceSource DF SS MS F PRegression 3 45.949 15.316 356.93 0.000Residual Error 139 5.965 0.043Total 142 51.91450 1 0 1 8575655545350.50.0-0.5LengthRESI2 With Stat > Basic Statistics > Display descriptive statistics By variable Z Variable Z N Mean Median TrMean StDevLength 0 99 62.88 64.00 63.22 10.011 44 57.693 58.750 58.063 6.449Variable Z SE Mean Minimum Maximum Q1 Q3Length 0 1.01 37.00 83.00 57.00 70.501 0.972 36.000 70.000 56.250 61.375 With Stat > Regression > Regression > Options Lack of fit test, Data subsetting Prediction intervals for new observations, for example at: Length=70, Z=0, ZL=0 Length=60, Z=1, ZL = 60 Predicted Values for New ObservationsNew Obs Fit SE Fit 95.0% CI 95.0% PI1 5.6106 0.0256 ( 5.5599, 5.6612) ( 5.1979, 6.0233)2 5.0158 0.0332 ( 4.9502, 5.0815) ( 4.6010, 5.4306)Values of Predictors for New ObservationsNew Obs Length Z ZL1 70.0 0.000000 0.0000002 60.0 1.00 60.0Possible lack of fit at outer X-values (P-Value = 0.066)Overall lack of fit test is significant at P = 0.0666With Graph > Plot • Y=LogW, X=Length • Symbol by group, variable Z (With “Edit attributes”, use different symbols, or colors) • Annotation > Line, through points (using equation 1.54 + 0.0582 Length - 0.806 Z + 0.0132 ZL) 35 3.577 85 6.487 (for Z=0) 35 3.237 85 6.803 (for Z=1) (use different line types, or colors) 0 1 85756555453576543LengthLogW7Now eliminate both terms relative to the effect of Gender (fit a nested model) The regression equation isLogW = 1.37 + 0.0606 LengthPredictor Coef SE Coef T PConstant 1.3746 0.1172 11.73 0.000Length 0.060628 0.001891 32.07 0.000S = 0.2107 R-Sq = 87.9% R-Sq(adj) = 87.9%Analysis of VarianceSource DF SS MS F PRegression 1 45.655 45.655 1028.39 0.000Residual Error 141 6.260 0.044Total 142 51.914 With the usual Stat > Regression > Fitted line plot 8575655545356.56.05.55.04.54.03.53.0LengthLogWS = 0.210699 R-Sq = 87.9 % R-Sq(adj) = 87.9 %LogW = 1.37463 + 0.0606279 LengthRegression Plot8F ratio for comparison of nested models: [(6.260 - 5.965) / 2] / 0.043 = 3.4302 Use null distribution F(2,139) With Calc > Probability distributions > F Cumulative probability Non-centrality parameter 0 Num dof 2 Den dof 139 Input constant 3.4302 F distribution with 2 DF in numerator and 139 DF in denominatorx P(X<=x)3.4302 0.9649 p-value for our test 1-0.9649 = 0.0351 (reject the nested model in favor of the larger
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