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, 2011:293296) 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.Age Depth Age Depth 3 7.6 4 5.5 4 4.6 3 6.1 6 6.1 8 10.7 6 9.1 6 10.4 3 4.3 4 4.6 8 7.3 7 7.0 5 5.2 6 6.1 8 10.4 14 16.8 6 15.5 10 9.1 2 5.8 7 8.8 6 10.7 a. Compute the least-squares line for predicting depth of wetting (y) from age (x). b. Identify a point with an unusually large x-value. Compute the least-squares line that results from deletion of this point. c. 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. d. Which of these two points is more influential? Explain.
Ch. 3 Statistical Descriptions of Data • Measures of Central Tendency & Dispersion: these show the center and variability and are calculated for numerical summaries • Measures of Central Tendency: describe the typical values of the data o Show the center of gravity/middle of the data • Mean (Average): add all the values and then divide by the number of values o Sample Mean: sum of the observations divided by the sample size (n) ̅ o A bar over a letter means the average, so X means the average of all values of X Σx o Equation: X= i n o The mean is not resistant to outliers; outliers will sway the mean •
