Question

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 found in the file IRS.xlsx that accompanies this book listing the adjusted gross income (AGI) and charitable contributions for 11 taxpayers whose returns were audited and found to be correct.

Required:
a. Prepare a scatter plot of the data. Does there appear to be a linear relationship between 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?

Answer 1

ŷ = 195.698X - 6169.941 ;

R² = 0.9224 ; About 92% variation in the value of Charitable contribution can be explained by the best fit line.

Explanation:

The excel data:

AGI: (X) :

55

58

63

67

74

78

83

88

92

98

105

Charitable contribution Y:

4200

4800

6329

8017

7400

8600

12290

10406

11820

12090

14675

The scatter plot can b found in the picture attached below.

The estimated regression equation obtained is :

ŷ = 195.698X - 6169.941

Where ;

slope of the regression line = 195.698 ;

Intercept = - 6169.941

The R² value is called the Coefficient of determination which gives the proportion of variation due to the best fit line. Using the Coefficient determination calculator ; R² = 0.9224

About 92% variation in the value of Charitable contribution can be explained by the best fit line.