The depth of wetting of a soil is the depth to which water content will increase
ID: 3173098 • Letter: T
Question
The depth of wetting of a soil is the depth to which water content will increase owing to external factors. The article "Discussion of Method for Evaluation of Depth of Wetting in Residential Areas" (J. Nelson, K. Chao, and D. Overton, Journal of Geotechnical and Geoenvironmental Engineering, 2011:293-296) discusses the relationship between depth of wetting beneath a structure and the age of the structure. The article presents measurements of depth of wetting, in meters, and the ages, in years, of 21 houses, as shown in the following table. Compute the least-squares line for predicting depth of wetting (y) from age (x). Identify a point with an unusually large x-value. Compute the least-squares line that results from deletion of this point. Identify another point which can be classified as an outlier. Compute the least-squares line that results from deletion of the outlier, replacing the point with the unusually large x-value. Which of these two points is more influential? Explain.Explanation / Answer
a. We do this in Excel. Following is the summary of regression results:
b. After deletion of one point with age = 14. The below are the summary of regression:
c.After deletion of age= 10 point, the below are the summary of regression:
d.Hence we can see that R squared after removing second outlier has increased the performance of the model
SUMMARY OUTPUT Regression Statistics Multiple R 0.707867493 R Square 0.501076387 Adjusted R Square 0.474817249 Standard Error 2.459792766 Observations 21 ANOVA df SS MS F Significance F Regression 1 115.4570667 115.4570667 19.0819819 0.000330735 Residual 19 114.9610286 6.050580451 Total 20 230.4180952 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 2.912190476 1.319189974 2.207559589 0.039769918 0.151094129 5.673286824 0.151094129 5.673286824 Age 0.877333333 0.200841238 4.36829279 0.000330735 0.45696779 1.297698876 0.45696779 1.297698876