51. Consider the following data for two variables, x and y.

xi 4 5 7 8 10 12 12 22 yi 12 14 16 15 18 20 24 19

a. Compute the standardized residuals for these data. Do the data include any outliers?

Explain.

b. Compute the leverage values for these data. Do there appear to be any influential observations in these data? Explain.

c. Develop a scatter diagram for these data. Does the scatter diagram indicate any influential observations? Explain.

Administrative Fundraising Program Total Expenses Expenses Expenses Expenses Charity ($) (%) (%) (%)
Volunteers of America 929,158,968 8.6 1.9 89.4 Dana-Farber Cancer Institute 877,321,613 13.1 1.6 85.2 AmeriCares 854,604,824 .4 .7 98.8 ALSAC—St. Jude Children’s 829,662,076 9.6 16.9 73.4 Research Hospital City of Hope 736,176,619 13.7 3.0 83.1

a. Develop a scatter diagram with fundraising expenses (%) on the horizontal axis and program expenses (%) on the vertical axis. Looking at the data, do there appear to be any outliers and/or influential observations?

b. Develop an estimated regression equation that could be used to predict program expenses (%) given fundraising expenses (%).

c. Does the value for the slope of the estimated regression equation make sense in the context of this problem situation?

d. Use residual analysis to determine whether any outliers and/or influential observations are present. Briefly summarize your findings and conclusions.