Civil engineers often use the straight-line equation, = b 0 + b 1x, to model the relationship between the shear strength 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 resulted in a Coefficient of Determination of 0.8436. Given that r 2= 0.8436, give a practical interpretation of r 2, the coefficient of determination for the least squares model. a. We expect to predict the shear strength of a triplet test to within about 0.8436 tons of its true value. b. About 84.36% 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. c. In repeated sampling, approximately 84.36% of all similarly constructed regression lines will accurately predict shear strength. d. We expect about 84.36% of the observed shear strength values to lie on the least squares line.
Civil engineers often use the straight-line equation, = b 0 + b 1x, to model the relationship between the shear strength 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 resulted in a Coefficient of Determination of 0.8436. Given that r 2= 0.8436, give a practical interpretation of r 2, the coefficient of determination for the least squares model.
a. We expect to predict the shear strength of a triplet test to within about 0.8436 tons of its true value.
b. About 84.36% 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.
c. In repeated sampling, approximately 84.36% of all similarly constructed regression lines will accurately predict shear strength.
d. We expect about 84.36% of the observed shear strength values to lie on the least squares line.
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