Timber piles are often used to

Timber piles are often used to buttress multiplespan simply supported (MSSS) bridges that are commonly found in rural areas. The authors of “Bridge Timber Piles Load Rating under Eccentric Loading Conditions” (J. Bridge Engr., 2012: 700–710) examined the effect of various geometric and structural characteristics on the critical rating (an overall structural assessment score) of MSSS bridges. The article reported the following data (read from a graph) for  timber pile length (m) and y  critical rating for a particular timber profile at various damage levels.

a. Create the scatterplots for the pairs  and  Does each scatterplot suggest that a simple linear regression model holds for the respective variables?

b. For each pair, calculate point estimates of the slope and intercept of the respective population regression line and determine the corresponding coefficients of determination.

c. Given the slope coefficients from the regression, summarize the relationship between criticalrating and pile length as timber damage changes from 0%, to 20%, and to 40%.

d. Calculate a point estimate of the error standard deviation   for each of the pairs. How do these point estimates change as timber damage increases from 0% to 20% and then to 40%?

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