The article “Ultimate Load Analysis of Plate Reinforced Concrete Beams” (N. Subedi and P. Baglin, Engineering Structures, 2001:1068–1079) presents theoretical and measured ultimate strengths (in kN) for a sample of steel reinforced concrete beams. The results are presented in the following table (two outliers have been deleted). Let y denote the measured strength, x the theoretical strength, and t the true strength, which is unknown. Assume that y = t + ε, where ε is the measurement error. It is uncertain whether t is related to x by a linear model t = β0 + β1x or by a quadratic model t = β0 + β1x + β2x2. Fit the linear model y = β0 + β1x + ε. For each coefficient, find the P-value for the null hypothesis that the coefficient is equal to 0. a) The fitted linear model is? b) Since (select one) P < 0.001 , 0.001 < P < 0.002 , 0.002 < P < 0.01 , 0.01 < P < 0.02 , 0.02 < P < 0.05 , 0.05 < P < 0.10 , 0.10 < P < 0.20 , 0.20 < P < 0.50 , 0.50 < P < 0.80 , P > 0.80 , we conclude that β0 (select one) differs/may not differ from 0. c) Since (select one) P < 0.001 , 0.001 < P < 0.002 , 0.002 < P < 0.01 , 0.01 < P < 0.02 , 0.02 < P < 0.05 , 0.05 < P < 0.10 , 0.10 < P < 0.20 , 0.20 < P < 0.50 , 0.50 < P < 0.80 , P > 0.80 , we conclude that β1 (select one) differs/may not differ from 0.
The article “Ultimate Load Analysis of Plate Reinforced Concrete Beams” (N. Subedi and P. Baglin, Engineering Structures, 2001:1068–1079) presents theoretical and measured ultimate strengths (in kN) for a sample of steel reinforced concrete beams. The results are presented in the following table (two outliers have been deleted). Let y denote the measured strength, x the theoretical strength, and t the true strength, which is unknown. Assume that y = t + ε, where ε is the measurement error. It is uncertain whether t is related to x by a linear model t = β0 + β1x or by a quadratic model t = β0 + β1x + β2x2.
Fit the linear model y = β0 + β1x + ε. For each coefficient, find the P-value for the null hypothesis that the coefficient is equal to 0.
a) The fitted linear model is?
b) Since (select one) P < 0.001 , 0.001 < P < 0.002 , 0.002 < P < 0.01 , 0.01 < P < 0.02 , 0.02 < P < 0.05 , 0.05 < P < 0.10 , 0.10 < P < 0.20 , 0.20 < P < 0.50 , 0.50 < P < 0.80 , P > 0.80 , we conclude that β0 (select one) differs/may not differ from 0.
c) Since (select one) P < 0.001 , 0.001 < P < 0.002 , 0.002 < P < 0.01 , 0.01 < P < 0.02 , 0.02 < P < 0.05 , 0.05 < P < 0.10 , 0.10 < P < 0.20 , 0.20 < P < 0.50 , 0.50 < P < 0.80 , P > 0.80 , we conclude that β1 (select one) differs/may not differ from 0.
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