Question

A deep-foundation engineering contractor has bid on a foundation system for a new building housing the world headquarters for a Fortune 500 company. A part of the project consists of installing auger cast piles. The contractor was given bid information for cost-estimation purposes which consisted of the estimated depth of each pile; however, actual drill footage of each pile could not be determined exactly until construction was performed. The contractor developed a linear regression model to estimate the actual pile length as a function of the estimated pile lengths. Use a significance level of 0.05 for all hypothesis tests and intervals.

Source	DF	Sum of Squares	Mean Square	F Ratio	Prob>F
Model	1	52569.023	52569	537.7953	<0.0001*
Error	309	30204.481	97.7
C. Total	310	82773.505
Parameter Estimates
Term	Estimate	Std. Error	t ratio	Prob>t	Lower 95%	Upper 95%
Intercept	11.614377	1.137095	10.21	<0.0001*	9.3769485	13.851806
Pile Length (ft.) Estimated	0.8141892	0.035109	23.19	<0.0001*	0.7451065	0.8832719

a. What proportion of the variation in the Pile Length(ft.)-Actual is “explained” by the simple linear relationship with Pile Length(ft.)-Estimated?

b. What is the correlation coefficient between Pile Length(ft.)-Estimated and the Pile Length(ft.)-Actual?

c. Multiple Choice: Choose 1

1. as the Pile Length(ft.)-Estimated increases by 1, the Pile Length(ft.)-Actual is expected to decrease by about 0.8141892.

2. as the Pile Length(ft.)-Estimated increases by 1, the Pile Length(ft.)-Actual is expected to increase by about 0.035109.

  3. as the Pile Length(ft.)-Estimated increases by 1, the Pile Length(ft.)-Actual is expected to decrease by about 0.035109.

4. it is not appropriate since the simple regression coefficient for Pile Length(ft.)-Estimated is not significant based on its large t Ratio.

5.  as the Pile Length(ft.)-Estimated increases by 1, the Pile Length(ft.)-Actual is expected to increase by about 0.8141892.

d. Give a point estimate for the Pile Length(ft.)-Actual for a pile with a Pile Length(ft.)-Estimated of 40 feet?

Answer 1

A) Proportion of the variation explained by the linear model is given by R squared.

Therefore, 63.5% variation is explained by the model.

B) The correlation coefficient is given by:-

C) As the Pile Length(ft.)-Estimated increases by 1, the Pile Length(ft.)-Actual increase by 0.8141892. The regression equation is

.

So, option (D) is correct.

D) The point estimate is given by:-