Question

TABLE 14-3

An economist is interested to see how consumption for an economy (in $ billions) is influenced by gross domestic product ($ billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.

SUMMARY OUTPUT

Regression Statistics
Multiple R  0.991
R Square  0.982
Adjusted R Square 0.976
Standard Error  0.299
Observations  10

ANOVA
            df      SS          MS           F       Signif F
Regsion 2    33.4163   16.7082    186.325   0.0001
Resdual 7     0.6277    0.0897
Total     9   34.0440

                Coeff     StdError   t Stat    P-value
Intcept   – 0.0861     0.5674     – 0.152    0.8837
GDP          0.7654     0.0574      13.340 0.0001
Price     – 0.0006     0.0028    – 0.219    0.8330

Referring to Table 14-3, when the economist used a simple linear regression model with consumption as the dependent variable and GDP as the independent variable, he obtained an r² value of 0.971. What additional percentage of the total variation of consumption has been explained by including aggregate prices in the multiple regression? In other words, the economist was explaining 97.1%, how much has that percentage or R-square increased after adding "price" as a second independent variable?

Question 6 options:

	.111 or 11.1%
	.028 or 2.8%
	.982 or 98.2%
	.011 or 1.1%

Answer 1

we have the summary of Regreession Analysis

SUMMARY OUTPUT

Regression Statistics
Multiple R  0.991
R Square  0.982
Adjusted R Square 0.976
Standard Error  0.299
Observations  10

ANOVA
            df      SS          MS           F       Signif F
Regsion 2    33.4163   16.7082    186.325   0.0001
Resdual 7     0.6277    0.0897
Total     9   34.0440

                Coeff     StdError   t Stat    P-value
Intcept   – 0.0861     0.5674     – 0.152    0.8837
GDP          0.7654     0.0574      13.340 0.0001
Price     – 0.0006     0.0028    – 0.219    0.8330

the value of R2 before adding the price was 0.971

the value of R2 after adding the price was 0.982

the percentage or R-square increased after adding "price" as a second independent variable is 0.982-0.971 = 0.011 ~1.1%

so option D is true