Values of modulus of elasticity (MOE, the ratio of stress, i.e., force per unit
ID: 3177769 • Letter: V
Question
Values of modulus of elasticity (MOE, the ratio of stress, i.e., force per unit area, to strain, i.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: Fitting the simple linear regression model to the n = 27 observations on x = modulus of elasticity and y = flexural strength given in the data above resulted in y = 7.642, sy = 0.179 when x = 40 and y = 9.789, sy = 0.253 for x = 60. (a) Explain why sy is larger when x = 60 than when x = 40. The closer x is to x, the smaller the value of sy. The closer x is to y, the smaller the value of sy. The farther x is from y, the smaller the value of sy. The farther x is from x, the smaller the value of sy. (b) Calculate a confidence interval with a confidence level of 95% for the true average strength of all beams whose modulus of elasticity is 40. (Round your answers to three decimal places.) (7.208 7.916) MPa (c) Calculate a prediction interval with a prediction level of 95% for the strength of a single beam whose modulus of elasticity is 40. (Round your answers to three decimal places.) (5.815) MPaExplanation / Answer
(b) answer: 95% confidence interval: (7.290, 8.016)
(c) Answer: 95% prediction interval: (5.858, 9.448)
Since
Regression Analysis: Strength versus MOE
The regression equation is
Strength = 3.36 + 0.107 MOE
Predictor Coef SE Coef T P
Constant 3.3578 0.5902 5.69 0.000
MOE 0.10738 0.01258 8.53 0.000
S = 0.853475 R-Sq = 74.4% R-Sq(adj) = 73.4%
Analysis of Variance
Source DF SS MS F P
Regression 1 53.059 53.059 72.84 0.000
Residual Error 25 18.210 0.728
Total 26 71.270
Unusual Observations
Obs MOE Strength Fit SE Fit Residual St Resid
26 79.4 11.700 11.884 0.462 -0.184 -0.26 X
27 80.1 10.900 11.959 0.470 -1.059 -1.49 X
X denotes an observation whose X value gives it large leverage.
Predicted Values for New Observations
New Obs Fit SE Fit 95% CI 95% PI
1 7.653 0.176 (7.290, 8.016) (5.858, 9.448)
Values of Predictors for New Observations
New Obs MOE
1 40.0
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