A+ Answers

A mortgage department of a large bank is studying its recent loans. Of particular interest is how such factors as the value of the home (in thousands of dollars) X1, education level X2, and age X3, are related to annual income (Y).         

A random sample or 25 recent loans is obtained.

            Income            Value of Home          Years of Education        Age

            ($ thousands)  ($thousands)

            Y                     X1                              X2                                  X3

            40.3                 190                             14                                   53

            39.6                 121                             15                                   49

            40.8                 161                             14                                   44

            40.3                 161                             14                                   39

            40.0                 179                             14                                   53

            38.1                 99                               14                                   46

            40.4                 114                             15                                   42

            40.7                 202                             14                                   49

            40.8                 184                             13                                   37

            37.1                 90                               14                                   43

            39.9                 181                             14                                   48

            40.4                 143                             15                                   54

            38.0                 132                             14                                   44

            39.0                 127                             14                                   37

            39.5                 153                             14                                   50

            40.6                 145                             14                                   50

            40.3                 174                             15                                   52

            40.1                 177                             15                                   47

            41.7                 188                             15                                   49

            40.1                 153                             15                                   53

            40.6                 150                             16                                   58

            40.4                 173                             13                                   42

            40.9                 163                             14                                   46

            40.1                 150                             15                                   50

            38.5                 139                             14                                   45

Conduct a multiple regression analysis to find the best predicator(s) of income (Y).

(a) What is the expected relationship between income and each explanatory variable?

(b) Develop scatterplots between income and each of the explanatory variables. Evaluate each scatterplot.

(c) Estimate correlation coefficients between income and each explanatory variable and provide interpretations.

(d) Estimate simple regressions between income (Y) and each explanatory variable (X). Provide full evaluations of each estimated simple regression equation. Make sure you include hypothesis tests on the slope coefficients (.05 alpha or one-sided p value).

(e) Estimate a multiple regression equation including all explanatory variables. Provide a full evaluation of the estimated multiple regression equation. Make sure you include hypothesis tests on the slope coefficients (.05 alpha or one-sided p value).

(f)  Are there any variables that should be dropped? Justify your answer.

(g) Redefine (re-estimate) the multiple regression equation if necessary so the remaining variables are significant? Provide a full evaluation of the final estimated multiple regression equation. Make sure you include hypothesis tests on the slope coefficients (.05 alpha or one-sided p value).

(h) Use your final estimated regression equation to predict income using the following values of the explanatory variables. Use only the variables applicable to your final estimated regression equation.