Civil engineers often use the straight-line equatin y=A0+A1x, to model the relat
ID: 3132918 • Letter: C
Question
Civil engineers often use the straight-line equatin y=A0+A1x, to model the relationship between the mean shear strenth 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 was recorded. The stress results for n=7 triplet test is shows in the table along with an SAS printout regression analysis.
1.75
Analysis of Varience
Source DF Sum of Squares Mean Square FValue 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-Sqaure 0.9052
Dep Mean 2.32857 Adj R-sq 0.8862
CV 9.62073
Parameter Estimates
Variable DF Parameter Estimate Standard Error T for HO: Parameter=0 Prob> I T I
Intercept 1 1.191930 0.18503093 6.442 0.0013
X 1 0.987157 0.14288331 6.909 0.0010
a) Give a practical interpretation of the estimate of y-intercept of the least squares line.
b) Give a practical interpretation of the slope of the least squares line
c) Give a practical interpretation of r^2 = .905
d) Find r
Triplet Test 1 2 3 4 5 6 7 Shear Strength (tons), y 1.00 2.18 2.24 2.41 2.59 2.82 3.06 Precomp. Stress (tons), x 0 0.60 1.20 1.33 1.43 1.751.75
Explanation / Answer
a)y-intercept=1.192,tells us that even when the precompression stress is 0,we find a shear strength of 1.192.
It can also be interpreted as the starting value,the value you may have started with. Or the initial value(if t=0)
b)slope=0.987,it tells us that for every 1ton increase in precompression stress,the shear strength increases by 0.987tons.
c)R^2=0.905 tells us that about 90.5% of the response variation is explained by the model.
d)r=sqrt(0.905)=0.951