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Q-2) The article "Ultimate Load Analysis of Plate Reinforced Concrete Beams" 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 + E, where & is the measurement error. It is uncertain whether it is related to x by a linear model t = 30 + 1x, or by quadratic model t = 30 + B1x +32 x 2 Theoretical 991 785 1195 1021 1285 1167 1519 1314 1743 791 Measured 1118 902 1373 1196 1609 1413 1668 1491 1952 844 Theoretical 1516 1071 1480 1622 2032 2032 660 565 738 682 Measured 1550 1167 1609 1756 2119 2237 640 530 893 775 a. Fit the linear model y = 30 + 31 x + E. For each coefficient, find the P-value for the null hypothesis that the coefficient is equal to 0. b. Fit the quadratic model y = 60+ B1x + 2x 2 + E. For each coefficient, find the P-value for the null hypothesis that the coefficient is equal to 0. c. Plot the residuals versus the fitted values for the linear model. d. Plot the residuals versus the fitted values for the quadratic model. e. Based on the results in parts (a) through (d), which model seems more appropriate? Explain. f. Using the more appropriate model, estimate the true strength if the theoretical strength is 1450. g. Using more appropriate model, find a 95% confidence interval for the true strength if the theoretical strength is 1450.

Q-2) The article "Ultimate Load Analysis of Plate Reinforced Concrete Beams" 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 + E, where & is the measurement error. It is uncertain whether it is related to x by a linear model t = 30 + 1x, or by quadratic model t = 30 + B1x +32 x 2 Theoretical 991 785 1195 1021 1285 1167 1519 1314 1743 791 Measured 1118 902 1373 1196 1609 1413 1668 1491 1952 844 Theoretical 1516 1071 1480 1622 2032 2032 660 565 738 682 Measured 1550 1167 1609 1756 2119 2237 640 530 893 775 a. Fit the linear model y = 30 + 31 x + E. For each coefficient, find the P-value for the null hypothesis that the coefficient is equal to 0. b. Fit the quadratic model y = 60+ B1x + 2x 2 + E. For each coefficient, find the P-value for the null hypothesis that the coefficient is equal to 0. c. Plot the residuals versus the fitted values for the linear model. d. Plot the residuals versus the fitted values for the quadratic model. e. Based on the results in parts (a) through (d), which model seems more appropriate? Explain. f. Using the more appropriate model, estimate the true strength if the theoretical strength is 1450. g. Using more appropriate model, find a 95% confidence interval for the true strength if the theoretical strength is 1450.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Q-2) The article "Ultimate Load Analysis of Plate Reinforced Concrete Beams" 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 + E, where & is the measurement error. It is uncertain whether t is related to x by a linear model t = ß0 + B1x, or by quadratic model t = 30 + B1x + 32 x 2 Theoretical 991 785 1195 1021 1285 1167 1519 1314 1743 791 Measured 1118 902 1373 1196 1609 1413 1668 1491 1952 844 Theoretical 1516 1071 1480 1622 2032 2032 660 565 738 682 Measured 1550 1167 1609 1756 2119 2237 640 530 893 775 a. Fit the linear model y = 60+ ß1 x + E. For each coefficient, find the P-value for the null hypothesis that the coefficient is equal to 0. b. Fit the quadratic model y = 30 + B1x + 32x 2 + ε. For each coefficient, find the P-value for the null hypothesis that the coefficient is equal to 0. c. Plot the residuals versus the fitted values for the linear model. d. Plot the residuals versus the fitted values for the quadratic model. e. Based on the results in parts (a) through (d), which model seems more appropriate? Explain. f. Using the more appropriate model, estimate the true strength if the theoretical strength is 1450. g. Using more appropriate model, find a 95% confidence interval for the true strength if the theoretical strength is 1450.
Transcribed Image Text:Q-2) The article "Ultimate Load Analysis of Plate Reinforced Concrete Beams" 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 + E, where & is the measurement error. It is uncertain whether t is related to x by a linear model t = ß0 + B1x, or by quadratic model t = 30 + B1x + 32 x 2 Theoretical 991 785 1195 1021 1285 1167 1519 1314 1743 791 Measured 1118 902 1373 1196 1609 1413 1668 1491 1952 844 Theoretical 1516 1071 1480 1622 2032 2032 660 565 738 682 Measured 1550 1167 1609 1756 2119 2237 640 530 893 775 a. Fit the linear model y = 60+ ß1 x + E. For each coefficient, find the P-value for the null hypothesis that the coefficient is equal to 0. b. Fit the quadratic model y = 30 + B1x + 32x 2 + ε. For each coefficient, find the P-value for the null hypothesis that the coefficient is equal to 0. c. Plot the residuals versus the fitted values for the linear model. d. Plot the residuals versus the fitted values for the quadratic model. e. Based on the results in parts (a) through (d), which model seems more appropriate? Explain. f. Using the more appropriate model, estimate the true strength if the theoretical strength is 1450. g. Using more appropriate model, find a 95% confidence interval for the true strength if the theoretical strength is 1450.
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