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 311 auger cast piles. The contractor was given bid information for cost-estimating 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?
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.
c. Give a point estimate for the Pile Length(ft.)-Actual for a pile with a Pile Length(ft.)-Estimated of 40 feet?