Question
Many countries, especially those in Europe, have significant gold holdings. But, many of these countries also have massive debts. Suppose the following data show the
Many countries, especially those in Europe, have significant gold holdings. But, many of these countries also have massive debts. Suppose 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.
Country | Gold Value ($ billions) | Debt (% of GDP) |
---|---|---|
A | 63 | 15.7 |
B | 146 | 81.7 |
C | 203 | 83.2 |
D | 33 | 69.2 |
E | 147 | 117.0 |
F | 36 | 63.1 |
G | 50 | 9.9 |
H | 62 | 55.0 |
I | 487 | 93.2 |
(a)Develop a scatter diagram for the total value of a country's gold holdings ($ billions) as the independent variable.
A scatter diagram has 9 points plotted on it. The horizontal axis ranges from 0 to 600 and is labeled: Gold Value ($ billions). The vertical axis ranges from 0 to 140 and is labeled: Debt (% of GDP). The majority of the points are located between 30 to 210 on the horizontal axis and between 5 to 120 on the vertical axis and are plotted in an upward, diagonal direction from left to right. There is also a single point near (500, 90).
A scatter diagram has 9 points plotted on it. The horizontal axis ranges from 0 to 600 and is labeled: Gold Value ($ billions). The vertical axis ranges from 0 to 140 and is labeled: Debt (% of GDP). The majority of the points are scattered somewhat randomly between 30 to 210 on the horizontal axis and between 5 to 120 on the vertical axis; however, they become less scattered moving from left to right. There is also a single point near (500, 10).
A scatter diagram has 9 points plotted on it. The horizontal axis ranges from 0 to 600 and is labeled: Gold Value ($ billions). The vertical axis ranges from 0 to 140 and is labeled: Debt (% of GDP). The majority of the points are located between 30 to 210 on the horizontal axis and between 5 to 120 on the vertical axis and are plotted in a downward, diagonal direction from left to right. There is also a single point near (500, 10).
A scatter diagram has 9 points plotted on it. The horizontal axis ranges from 0 to 600 and is labeled: Gold Value ($ billions). The vertical axis ranges from 0 to 140 and is labeled: Debt (% of GDP). The majority of the points are located between 30 to 210 on the horizontal axis and between 5 to 120 on the vertical axis. In this group and between 60 to 120 on vertical axis, there are 6 points plotted in an upward, diagonal direction from left to right. There is also a single point near (500, 20).
(b)What does the scatter diagram developed in part (a) indicate about the relationship between the two variables?There appears to be a negative linear relationship between gold value ($ billions) and debt (% of GDP).There appears to be a positive linear relationship between gold value ($ billions) and debt (% of GDP). There appears to be no noticeable relationship between gold value ($ billions) and debt (% of GDP).Do there appear to be any outliers and/or influential observations?There appear to be no possible outliers or influential observations.There appear to be one or more possible outliers and/or influential observation. (c)Using the entire data set, develop the estimated regression equation that can be used to predict the debt of a country (as a % of GDP) given the total value of its gold holdings (in billions of U.S. dollars). (Round your numerical values to one decimal place.)=
(d)Use residual analysis to determine whether any outliers or influential observations are present. (Select all that apply.)Country D is a possible outlier because it has a large standardized residual (less than2 or greater than +2).Country D is a possible influential observation because it has high leverage (greater than 6/n).Country E is a possible outlier because it has a large standardized residual (less than2 or greater than +2).Country E is a possible influential observation because it has high leverage (greater than 6/n).Country I is a possible outlier because it has a large standardized residual (less than2 or greater than +2).Country I is a possible influential observation because it has high leverage (greater than 6/n).There are no possible outliers and/or influential observations present.
Step by Step Solution
There are 3 Steps involved in it
Step: 1
Get Instant Access to Expert-Tailored Solutions
See step-by-step solutions with expert insights and AI powered tools for academic success
Step: 2
Step: 3
Ace Your Homework with AI
Get the answers you need in no time with our AI-driven, step-by-step assistance
Get Started