# hw6 - Homework 6(due March 25 1 Corrosion of still...

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Homework 6 (due March 25) 1. Corrosion of still reinforcing bars is the most important durability problem for reinforced concrete structures. Carbonation of concrete results from a chemical reaction that lowers the pH value enough to to initiate cor- rosion. The table below shows a sample dependence of the strength in MPa ( y ) on the carbonation depth in mm ( x ) taken from a particular building. x 8.0 15.0 16.5 20.0 20.0 27.5 30.0 30.0 35.0 y 22.8 27.2 23.7 17.1 21.5 18.6 16.1 23.4 13.4 x 38.0 40.0 45.0 50.0 50.0 55.0 55.0 59.0 65.0 y 19.5 12.4 13.2 11.4 10.3 14.1 9.7 12.0 6.8 a) Fit a linear regression model to the data. What is the estimated expected value of the strength if the carbonation depth is 25.0 mm? b) Do the data suggest that the regression is significant? (Use the t-test). Assume that α = 0 . 01. What is the corresponding P-value? c) Use the analysis of variance approach to test the significance of regres- sion. Find the P-value. Compare with problem b). d) A civil engineering graduate student develops a theoretical model that predicts a linear relationship between strength and carbonation depth with

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