(Continues Exercise 7 in Section 8.1.) To try to improve the prediction of FEV, additional independent variables are included in the model. These new variables are Weight (in kg), the product (interaction) of Height and Weight, and the ambient temperature (in °C). The following MINITAB output presents results of fitting the mode FEV, = b, + P Last FEV, + ß; Gender + , Height + B, Weight + ß; Height - Weight + P. Temperature + ß, Pressure + E The regression equation is FEV1 = -0.257 + 0.778 Last FEV – 0.105 Gender + 1.213 Height - 0.00624 Weight + %3D 0.00386 Height*Weight – 0.00740 Temp - 0.00148 Pressure Predictor Coef SE Coef тР Constant -0.2565 0.7602 -0.340.736 Last FEV 0.77818 0.05270 14.770.000 Gender -0.10479 0.03647-2.870.005 Height Weight Height*Weight 0.0038642 0.008414 0.460.647 Temp 1.2128 0.4270 2.840.005 -0.0062446 0.01351-0.460.645 -0.007404 0.009313 -0.790.428 Pressure -0.00147730.0005170 -2.860.005 S = 0.22189 R-Sq = 93.5% R-Sq(adj) = 93.2% Analysis of Variance Source DF MS Regression 7111.35 15.907323.060.000 Residual 1577.73020.049237 Error Total 164119.08 The following MINITAB output, reproduced from Exercise 7 in Section 8.1, is for a reduced model in which Weight, Height · Weight, and Temp have been dropped. Compute the F statistic for testing the plausibility of the reduced model. a. The regression equation is FEV1 = -0.219 + 0.779 Last FEV – 0.108 Gender + 1.354 Height – 0.00134 Pressure Predictor Coef SE Coef тР Constant -0.21947 0.4503-0.490.627 0.779 0.04909 15.870.000 Last FEV Gender Height Pressure -0.00134310.0004722-2.840.005 -0.10827 0.0352 -3.080.002 1.3536 0.2880 4.700.000 R-Sq = 93.5% R-Sq(adj) = 93.3% 0.22039 Analysis of Variance Source DF MS Regression 4111.31 27.826572.890.000 Residual 1607.77160.048572 Error Total 164119.08 How many degrees of freedom does the F statistic have? Find the P-value for the F statistic. Is the reduced model plausible? d. Someone claims that since each of the variables being dropped had large P-values, the reduced model must be plausible, and it was not necessary to perform an F test. Is this correct? Explain why or why not. b. C. The total sum of squares is the same in both models, even though the independent variables are different. Is there a mistake? Explain. e.

(Continues Exercise 7 in Section 8.1.) To try to improve the prediction of FEV, additional independent variables are included in the model. These new variables are Weight (in kg), the product (interaction) of Height and Weight, and the ambient temperature (in °C). The following MINITAB output presents results of fitting the mode FEV, = b, + P Last FEV, + ß; Gender + , Height + B, Weight + ß; Height - Weight + P. Temperature + ß, Pressure + E The regression equation is FEV1 = -0.257 + 0.778 Last FEV – 0.105 Gender + 1.213 Height - 0.00624 Weight + %3D 0.00386 HeightWeight – 0.00740 Temp - 0.00148 Pressure Predictor Coef SE Coef тР Constant -0.2565 0.7602 -0.340.736 Last FEV 0.77818 0.05270 14.770.000 Gender -0.10479 0.03647-2.870.005 Height Weight HeightWeight 0.0038642 0.008414 0.460.647 Temp 1.2128 0.4270 2.840.005 -0.0062446 0.01351-0.460.645 -0.007404 0.009313 -0.790.428 Pressure -0.00147730.0005170 -2.860.005 S = 0.22189 R-Sq = 93.5% R-Sq(adj) = 93.2% Analysis of Variance Source DF MS Regression 7111.35 15.907323.060.000 Residual 1577.73020.049237 Error Total 164119.08 The following MINITAB output, reproduced from Exercise 7 in Section 8.1, is for a reduced model in which Weight, Height · Weight, and Temp have been dropped. Compute the F statistic for testing the plausibility of the reduced model. a. The regression equation is FEV1 = -0.219 + 0.779 Last FEV – 0.108 Gender + 1.354 Height – 0.00134 Pressure Predictor Coef SE Coef тР Constant -0.21947 0.4503-0.490.627 0.779 0.04909 15.870.000 Last FEV Gender Height Pressure -0.00134310.0004722-2.840.005 -0.10827 0.0352 -3.080.002 1.3536 0.2880 4.700.000 R-Sq = 93.5% R-Sq(adj) = 93.3% 0.22039 Analysis of Variance Source DF MS Regression 4111.31 27.826572.890.000 Residual 1607.77160.048572 Error Total 164119.08 How many degrees of freedom does the F statistic have? Find the P-value for the F statistic. Is the reduced model plausible? d. Someone claims that since each of the variables being dropped had large P-values, the reduced model must be plausible, and it was not necessary to perform an F test. Is this correct? Explain why or why not. b. C. The total sum of squares is the same in both models, even though the independent variables are different. Is there a mistake? Explain. e.

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015

1st Edition

ISBN:9781680331141

Author:HOUGHTON MIFFLIN HARCOURT

Publisher:HOUGHTON MIFFLIN HARCOURT

Chapter1: Solving Linear Equations

Section1.5: Rewriting Equations And Formula

Problem 49E

See similar textbooks