Question

Many countries, especially those in Burope, 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).

a. Develop a scatter diagram for the total value of a country's gold holdings ($ billions) as the independent variable. 

b. What does the scatter diagram developed in part (a) indicate about the relationship between the two variables? Does there appear to be any outliers and/or influential observations? Explain. 

c. 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. 

d. Suppose that after looking at the scatter diagram in part (a) that you were able to visually identify what appears to be an influential observation. Drop this observation from the data set and fit an estimated regression equation to the remaining data. Compare the estimated slope for the new estimated regression equation to the estimated slope obtained in part (c). Does this approach confirm the conclusion you reached in part (d)? Explain

Answer 1

a)

b)

The scatter diagram in a) indicate a positive relationship between the variables Gold value and Debt. Also, there appears to be an outlier or influential observation by the value (487, 93.2).

c)

b) After dropping the outlier values (487, 93.2) looking in scatter plot a), the estimated regression model is

Regression Analysis: Debt versus Gold value The regression equation is Debt 30.80.342 Gold value Predictor Constant Gold value 0.3422 0.1804 1.90 0.107 Coef SE Coef T 30.77 19.85 1.55 0.172 S= 30.3907 R-Sq 37.5% R-Sq (adj ) =27.1% =

Comparing the slope from the c) fitting in original data, the slope estimated after dropping the outlier is bigger.

But the prediction of Debt using the Gold values does not have a significant effect at 0.05 level of significance at both c) and d). Because the estimated p-values of the slope in original and dropping outlier are more than 0.05 level of significance.