(Solution) - The article Ultimate Load Analysis of Plate Reinforced Concrete Beams -(2025 Original AI-Free Solution)

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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 steelreinforced 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 + ?, where ? is the measurement error. It is uncertain whether t is related to x by a linear model t = ?0 + ?1x or by a quadratic model t = ?0 + ?1x + ?2x2.

a. Fit the linear model y = ?0 + ?1x + ?. For each coefficient, find the P-value for the null hypothesis that the coefficient is equal to 0.
b. Fit the quadratic model y = ?0 + ?1x + ?2x2 + ?. 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 1500.
g. Using the more appropriate model, find a 95% confidence interval for the true strength if the theoretical strength is 1500.