Values of modulus of elasticity (MOE, the ratio of stress, e., force per unit ar

Question

Values of modulus of elasticity (MOE, the ratio of stress, e., force per unit area, to strain, e., deformation per unit length, in GPa) and flexural strength (a measure of the ability to resist failure in bending, in MPa) were determined for a sample of concrete beams of a certain type, resulting in the following data: MOE 29.8 33.3 33.8 35.4 35.5 36.0 36.4 36.4 37.5 37.7 38.8 38.9 39.6 41.2 Strength 5.9 7.1 7.2 6.3 8.1 6.7 6.9 7.4 7.0 6.6 7.2 6.2 7.8 9.1 MOE 42.6 42.8 43.5 45.4 45.9 46.8 48.2 49.2 51.6 62.7 69.6 79.7 79.9 Strength 8.0 8.9 7.9 9.8 7.4 7.7 9.9 7.7 7.7 11.4 11.1 11.8 10.7 Fitting the simple near regression model to the n 27 observations on X modulus of elasticity and y flexural strength given in the data above resulted in y 7.584 sp 0.180 when X 40 and y 9.716, sp 0.255 for X 60

Explanation / Answer

Sol:

Regression equation is

flexural strngth=3.319+0.107(MOE)

for MOE=40

predicted flexural strngth=3.319+0.107(40)

=7.599

df=n-2=27-2=25

alpha=0.05

alpha/2=0.025

t crit for 25 df and 0.025 los is

=2.060

Multiple R 0.855542 R Square 0.731953 Adjusted R Square 0.721231 Standard Error 0.871615 Observations 27 ANOVA df SS MS F Significance F Regression 1 51.86346 51.86346 68.26716 1.3E-08 Residual 25 18.99283 0.759713 Total 26 70.8563 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 3.319018 0.605912 5.477725 1.09E-05 2.071119 4.566917 MOE 0.106622 0.012904 8.262394 1.3E-08 0.080044 0.133199

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