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In: Statistics and Probability

Question 1. The Institute for Global Ethics has data which relates its Country Corruption Index (CCI)...

Question 1.
The Institute for Global Ethics has data which relates its Country Corruption Index (CCI) to the percentage growth of GDP in 118 countries. The regression line (best-fit line) obtained is:

GDP growth = 0.74 - 3.46*CCI

Which of the following statements is true:

a. the correlation between GDP growth and CCI on the data set is positive but cannot be determined precisely from the information given

b: the correlation between GDP growth and CCI on the data set is negative but cannot be determined precisely from the information given

c: the correlation between GDP growth and CCI on the data set is 0.74

d: the correlation between GDP growth and CCI is 0.74/-3.46= -0.21387

Question 2

Indicate which one of the following two statements is true:

a: In a simple regression model, the slope coefficient represents the average change in the independent variable for a one unit change in the dependent variable.

b: In a simple regression model, the slope coefficient represents the average change in the dependent variable for a one unit change in the independent variable.

Question 3

The regression equation (best fit line) obtained from the data set described in Chapter 3 of K/S/M/S textbook is

Price = 5787.9 + 0.2275*Income

where income is the annual income of each applicant and price is the price of the car each is buying, both measured in dollars. According to this equation, how much on average would a person with an income of $100,000 spend on a car?

a: $22,750

b: $28,537.9

c: $57,879

d: none of the above

Solutions

Expert Solution

Question 1

b: the correlation between GDP growth and CCI on the data set is negative but cannot be determined precisely from the information given.

Explanation:

We know that if the slope of the regression equation is negative, then a correlation between given variables would be negative. For the calculation of the correlation coefficient, we need different sums or sum of squares which are not given. So, we cannot calculate the correlation coefficient based on the given information.

Question 2

b: In a simple regression model, the slope coefficient represents the average change in the dependent variable for a one unit change in the independent variable.

Explanation:

We know that the slope of the regression model interpreted as the average change in the dependent variable per unit change in the independent variable.

Question 3

b: $28,537.9

Explanation:

We are given a regression equation as

Price = 5787.9 + 0.2275*Income

We are given Income = $100,000

Price = 5787.9 + 0.2275*100000

Price = 28537.9

Price = $28,537.9

orchestra answered 2 years ago
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