Question

Many countries, especially those in Europe, have significant gold holdings. But many of these countries also have massive debts. The following data show the total value of gold holdings in billions of U.S. dollars and the debt as a percentage of the gross domestic product for nine countries (WordPress and Trading Economics websites, February 24, 2012).

Country Gold Value Debt
China 63 17.7
France 146 81.7
Germany 203 83.2
Indonesia 33 69.2
Italy 147 119
Netherlands 36 63.7
Russia 50 9.9
Switzerland 62 55
U.S. 487 93.2

Required:
a. Using the entire data set, develop the estimated regression equation that can be used to predict the debt of a country given the total value of its gold holdings.
b. Use residual analysis to determine whether any outliers or influential observations are present.
c. Compare the estimated slope for the new estimated regression equation to the estimated slope obtained in part (c).

Answer 1

Regression model = y = 0.123X + 49.077

Influential point = US ; 487 ; 93.2

Slope with influential point present = 0.123

Slope without influential point = 0.342

Explanation:

Given the data:

Gold value (X) :

63

146

203

33

147

36

50

62

487

Debt (Y) :

17.7

81.7

83.2

69.2

119

63.7

9.9

55

93.2

Using the online regression calculator :

The model obtained is :

y = 0.123X + 49.077

y = predicted variable ; debt

Slope = 0.123

x = predictor variable ; gold value

Intercept = 49.077

The influential observation :

US ; 487 ; 93.2

Dropping this observation from our data and fitting the model ;

Model without the influential point :

y = 0.342X+ 30.769

Slope with influential point present = 0.123

Slope without influential point = 0.342