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).

Gold Value ($ billions) Debt (% of GDP)
Country
China 63 17.7
France 146 81.7
Indonesia 203 83.2
Germany 33 69.2
Italy 147 119
Netherlands 36 63.7
Russia 50 9.9
Switzerland 62 55
United States 487 93.2
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 (to 4 decimals (to 4 decimals)

Answer 1

X`= -0.60872 Y + 176.4085

or X`= 176.4085-0.60872 Y

Explanation:

Country Gold Value Debt (% of GDP)

($ billions) X Y XY X² Y²

China 63 17.7 1115.1 3969 313.29

France 146 81.7 11928.2 21316 6674.89

Indonesia 203 83.2 16889.6 41209 6947.2

Germany 33 69.2 2283.6 1089 4788.64

Italy 147 119 17493 21609 14161

Netherlands 36 63.7 2293.2 1296 4057.69

Russia 50 9.9 495 2500 98.01

Switzerland 62 55 3410 3844 3025

United States 487 93.2 45,388.2 237169 8686.24

∑ 1227 592.6 101245.9 334001 48751.96

The estimated regression equation that can be used to predict the debt of a country given the total value of its gold holdings

X = a1 + bxy Y

wher e

bxy = n ∑XY -∑X∑Y/ n ∑Y²- (∑Y)²

= 9( 101245.9 )- (1227 *592.6)/ 48751.96-(592.6)²

911213.1 - 727120.2/ - 302422.8= - 0.60872

a1= X` -bxy Y`= 136.33- (-0.60872)(65.84)

= 136.33+ 40.07858= 176.4085

Hence X`= -0.60872 Y + 176.4085

or X`= 176.4085-0.60872 Y