Question

To the Internal Revenue Service, the reasonableness of total itemized deductions depends on the taxpayer’s adjusted gross income. Large deductions, which include charity and medical deductions, are more reasonable for taxpayers with large adjusted gross incomes. If a taxpayer claims larger than average itemized deductions for a given level of income, the chances of an IRS audit are increased. Data (in thousands of dollars) on adjusted gross income and the average or reasonable amount of itemized deductions follow.

Adjusted Gross Income ($1000s)	Reasonable Amount of Itemized Deductions ($1000s)
22	9.6
27	9.6
32	10.1
48	11.1
65	13.5
85	17.7
120	25.5

Use Excel - no hand calculations.

1. Write the regression equation.

2. Interpret the regression constant and regression coefficient.

3. Forecast a value for the dependent variable, test the significance of the regression coefficient at an alpha level of .05

4.Test the overall significance of the regression model, and Interpret the coefficient of determination.

Answer 1

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.9772
R Square	0.9549
Adjusted R Square	0.9458
Standard Error	1.3716
Observations	7
ANOVA
	df	SS	MS	F	Significance F
Regression	1.0000	199.0083	199.0083	105.7884	0.0001
Residual	5.0000	9.4060	1.8812
Total	6.0000	208.4143
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	4.6768	1.0334	4.5256	0.0063	2.0203	7.3332
Adjusted Gross Income ($1000s), X	0.1613	0.0157	10.2854	0.0001	0.1210	0.2016

1. Regression equation can be represented as Y = a+bx
Y = 4.68+0.16X
Where Y is Reasonable Amount of Itemized Deductions ($1000s), X is Adjusted Gross Income ($1000s)
2. The regression constant is 4.68, the average Reasonable Amount of Itemized Deductions ($1000s) when X is zero
The regression constant is 0.16, means for 1 unit increase in Adjusted Gross Income ($1000s), Reasonable Amount of Itemized Deductions ($1000s) increases by 0.16
3. For value of X =120, the value of Y = 4.68+0.16*120 = 23.88
As the P-value of the coefficient is less than 0.05, the regression coefficient is significant
4. The overall model is significant as the calculated F value is greater than significance F value in the ANOVA table
Coefficient of determination or R^2 is 0.9772, which means the model is able to capture 97.72 percent of variation