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Author Question: Civil engineers often use the straight-line equation, = 0 + 1x, to model the relationship between ... (Read 417 times)

newbem

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Civil engineers often use the straight-line equation, = β0 + β1x, to model the relationship between the mean shear strength 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 the estimate of the y-intercept of the least squares line.
◦ There is no practical interpretation since a triplet test with a precompression stress of 0 tons is outside the range of the sample data.
◦ For a triplet test with a precompression stress of 0 tons, we estimate the shear strength of the joint to increase 1.19 tons.
◦ For every 1 ton increase in precompression stress, we estimate the shear strength of the joint to increase by 0.987 ton.
◦ For a triplet test with a precompression stress of 0 tons, we estimate the shear strength of the joint to be 1.19 tons.


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Marked as best answer by newbem on Jan 16, 2020

elizabethrperez

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