Author Question: Civil engineers often use the straight-line equation, E(y) = 0 + 1x, to model the relationship ... (Read 196 times)

jc611 · **on:** Jan 16, 2020

Civil engineers often use the straight-line equation, E(y) = β₀ + β₁x, to model the relationship between the mean shear strength E(y) of masonry joints and precompression stress, x. To test this theory, a series of stress tests were performed on solid bricks arranged in triplets and joined with mortar. The precompression stress was varied for each triplet and the ultimate shear load just before failure (called the shear strength) was recorded. The stress results for n = 7 triplet tests is shown in the accompanying table followed by a SAS printout of the regression analysis.

Analysis of Variance

Sum of Mean
Source DF Squares Square F Value Prob > F

Model 1 2.39555 2.39555 47.732 0.0010
Error 5 0.25094 0.05019
C Total 6 2.64649

Root MSE 0.22403 R-square 0.9052
Dep Mean 2.32857 Adj R-sq 0.8862
C.V. 9.62073

Parameter Estimates

Parameter Standard T for HO:
Variable DF Estimate Error Parameter=0 Prob > |T|

INTERCEP 1 1.191930 0.18503093 6.442 0.0013
X 1 0.987157 0.14288331 6.909 0.0010

Give a practical interpretation of R², the coefficient of determination for the least squares model. Express R² to the nearest whole percent.
◦ About 91% of the total variation in the sample of y-values can be explained by (or attributed to) the linear relationship between shear strength and precompression stress.
◦ In repeated sampling, approximately 91% of all similarly constructed regression lines will accurately predict shear strength.
◦ We expect about 91% of the observed shear strength values to lie on the least squares line.
◦ We expect to predict the shear strength of a triplet test to within about .91 ton of its true value.

Joy Chen · **Reply #1 on:** Jan 16, 2020

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