Question

TABLE 7

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.

1. 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 .971. What additional percentage of the total variation of consumption has been explained by including aggregate prices in the multiple regression?

1. 98.2

2. 1.1

3. 2.8

4. 11.1

B. The p-value for GDP is

1. 0.05

2. 0.01

3. 0.001

4. None of the above

C. What is the predicted consumption level for an economy with GDP equal to $4 billion and an aggregate price index of 150?

1. $4.75 billion

2. $9.45 billion

3. $2.89 billion

4. $1.39 billion

D. One economy in the sample had an aggregate consumption level of $4 billion, a GDP of $6 billion, and an aggregate price level of 200, What is the residual for this data point?

1. $-0.39 billion

2. $0.39 billion

3. -$1.33 billion

4. $4.39 billion

E. To test for the significance of the coefficient on aggregate price index, the value of the relevant T statistic is ____.

1. 2.365

2. -1.960

3. 0.143

4. -0.219

F. To test for the significance of the coefficient on aggregate price index, the p value is _____.

5. .9999

6. 0.0001

7. 0.8330

8. 0.8837

Answer 1

Solution(A)
Given that R^2 value for model is 0.982
While if we use one variable as independent variable(GDP) than R^2 value is 0.971 than variable Variance explained by other variable is ( 0.982-0.971) = 0.011 so 1.1% variance explained by other variable so its answer is B. i.e. 1.1

Solution(b)

from the coefficient table we found that p-value for GDP is 0.0001 so its answer is D. i.e. None of the above.

Solution(c)

Regression model can be written as
Economy = -0.0861 + 0.7654*GDP - 0.0006*Price
at GDP = 4, and Price = 150
Economy = -0.0861 + 0.7654*4 - 0.0006*150 = 0.0861 + 3.0616 - 0.09 =2.8855 or 2.89 billion
so its answer is C. i.e. $ 2.89bn

Solution(d)
GDP = 6
Price = 200
So Economy = -0.0861 + 0.7654*6 - 0.0006*200 = 4.3863
So residual = 4-4.3863 = - 0.39
So its answer is A.

Solution(e)
To test for the significance of the coefficient on the aggregate price index, the value of the relevant T statistic is -0.219 so its answer is D.

Solution(f)

P-value for Aggregate price index is 0.8330. so its answer is C. i.e. 0.8330