Response to the following question:
1. The IRS wants to develop a method for detecting whether or not individuals have overstated their deductions for charitable contributions on their tax returns. To assist in this effort, the IRS supplied data disk listing the adjusted gross income (AGI) and charitable contributions for 11 tax payers whose returns were audited and found to be correct.
| AGI |
Charitable |
| (in $1,000s) |
Contributions |
| $55 |
$4,200 |
| $58 |
$4,800 |
| $63 |
$6,329 |
| $67 |
$8,017 |
| $74 |
$7,400 |
| $78 |
$8,600 |
| $83 |
$12,290 |
| $88 |
$10,406 |
| $92 |
$11,820 |
| $98 |
$12,090 |
| $105 |
$14,675 |
a. Prepare a scatter plot of the data. Does there appear to be a linear relationship be-tween these variables?
b. Develop a simple linear regression model that can be used to predict the level of charitable contributions from a return's AGI. What is the estimated regression equation?
c. Interpret the value of R2.
d. How might the IRS use the regression results to identify returns with unusually high charitable contributions?