Civil engineers often use the straight-line equation,
= β
0 + β
1x, 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.
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 slope of the least squares line.
◦ 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 1 ton, we estimate the shear strength of the joint to be 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.
◦ For every 0.987 ton increase in precompression stress, we estimate the shear strength of the joint to increase by 1 ton.
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