Question

Question 16

1. Exhibit 3

   Below you are given a partial computer output based on a sample of 19 countries relating their debt (Y in billion dollars), GDP (X₁ in billion dollars) and the score on a corruption index (X₂). The higher the corruption index, the more corrupt a country is.

   Source of Variation	Sum of Squares	Degrees of Freedom	Mean Square	F
   Regression	150
   Error
   TOTAL	200	18

   	Coefficient	Standard Error
   Intercept	6.25	7.865
   GDP (X1)	0.5	0.5
   Corruption Index (X2)	2.00	0.5

   If a country has a GDP of 100 billion dollars and a corruption index of 80, what would you expect that country’s debt to be?

   _____

Question 17

1. To answer this question, refer to Exhibit 3 in question 16.

   We would like to determine if the Corruption Index belongs in the regression. What is the 95% critical value from this test (to 2 decimal places)?

Question 18

1. To answer this question, refer to Exhibit 3 in question 16.

   What is the value of the test statistic for the test in question 17. (to 2 decimal places)?

Question 19

1. To answer this question, refer to Exhibit 3 in question 16.

   What is your conclusion? Type 1 if you find that Corruption Index belongs in the regression and 0 if it does not.

Question 20

1. To answer this question, refer to Exhibit 3 in question 16.

   We would like to test for the significance of the whole regression. What is the 95% critical value from this test (to 2 decimal places)?

Question 21

1. To answer this question, refer to Exhibit 3 in question 16.

   What is the value of the test statistic for the test in question 20 (the question immediately above this one) (to 2 decimal places)?

  

Question 22

1. To answer this question, refer to Exhibit 3 in question 16.

   Based on information in questions 20 and 21, what do you conclude? Type 1 if the regression is significant and 0 if the regression is not significant.

Answer 1

16.
The estimated regression equation is,
Y = 6.25 + 0.5 X1 + 2.00 X2

Given,
X1 = 100, X2 = 80
The estimated country's debt is,
Y = 6.25 + 0.5 * 100 + 2.00 * 80 = 216.25 billion dollars

17.
Degree of freedom = n - k - 1 = 19 - 2 - 1 = 16
where n is number of observations and k is number of predictor variables
Critical value of t at 95% confidence level and df = 16 is 2.12

18.
The value of the test statistic = Estimated coefficient / Standard error
= 2.00 / 0.5
= 4.00

19.
Since the observed test statistic is greater than the critical value, the variable Corruption Index belongs in the regression.
Answer is 1

20.
Numerator df = k = 2
Denominator df = n - k - 1 = 19 - 2 - 1 = 16
Critical value of F at 95% confidence level and df = 2,16 is 3.89

21.
Sum of Squares Error = Sum of Squares Total - Sum of Squares Regression = 200 - 150 = 50
Mean Square Regression = Sum of Squares Regression / Numerator df = 150 / 2 = 75
Mean Square Error = Sum of Squares Error / Denominator df = 50 / 16 = 3.125
Test statistic F = Mean Square Regression / Mean Square Error
= 75 / 3.125
= 24

22.
Since the observed test statistic (F = 24) is greater than the critical value, the regression is significant.
Answer is 1