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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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 denote the measured strength, the theoretical strength, and the true strength, which is unknown. Assume that ε, where ε is the measurement error. It is uncertain whether is related to by a linear model β0 + β1or by a quadratic model β0 + β1x + β2x2

Fit the linear model  β0 + β1ε. 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.

Theoretical
Measured
Theoretical
Measured
991
1118
1516
1550
785
902
1071
1167
1195
1373
1480
1609
1021
1196
1622
1756
1285
1609
2032
2119
1167
1413
2032
2237
1519
1668
660
640
530
893
1314
1491
565
1743
1952
738
791
844
682
775
Transcribed Image Text:Theoretical Measured Theoretical Measured 991 1118 1516 1550 785 902 1071 1167 1195 1373 1480 1609 1021 1196 1622 1756 1285 1609 2032 2119 1167 1413 2032 2237 1519 1668 660 640 530 893 1314 1491 565 1743 1952 738 791 844 682 775
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