Question

1. A random sample of 15 weeks of sales (measured in $) and 15 weeks of advertising expenses (measured in $) was taken and the sample correlation coefficient was found to be r = 0.80. Based on this sample correlation coefficient we could state

1. That the percentage of the variation in sales that is shared with the variation in advertising is about 80%.
2. That the percentage of the variation in sales that is shared with the variation in advertising is about 64%.
3. That the percentage of variation that is shared by the two variables cannot be determined from the information given.
4. That the percentage of variation that is shared between the two variables is 100% because the two variables are positively correlated.

2. A scatterplot of two variables is constructed. “Stretching” the scatterplot horizontally or vertically would

1. Change the perceived slope but not the correlation.
2. Change the correlation but not the perceived slope
3. Leave the correlation and the perceived slope unchanged.
4. Change both the correlation and the perceived slope.

5. Suppose that a random sample of 25 automobiles yields a sample correlation coefficient for the linear relationship between the automobile’s weight (in pounds) and its miles per gallon of 0.64. How is the sample correlation coefficient affected if the same sample data automobile weight is measured in kilograms, rather than pounds, and kilometers per liter is used, rather than miles per gallon? (Hint: a kilogram is approximately equal to 2.204 pounds, one gallon is approximately equal to 3.785 liters and 1 mile is approximately 1.61 kilometers).

1. The sample correlation coefficient remains unchanged at 0.64.
2. The sample correlation coefficient will increase because a kilogram is more than a pound.
3. The sample correlation coefficient will decrease because one gallon is more than one liter.
4. No one knows the answer without first putting all the transformed data into a computer.

6. Which of the following conditions must be verified before conducting a correlation analysis?

1. Quantitative Variables Condition—correlation applies only to quantitative variables so make certain the variables are quantitative.
2. Straight Enough Condition—if the relationship is not linear the correlation will be misleading so look a linear relationship.
3. Outlier Condition—outliers can distort the correlation dramatically. Make certain there are no outliers.
4. All of the above.

Answer 1

(1)

Correct option:

b.   That the percentage of the variation in sales that is shared with the variation in advertising is about 64%.

Explanation:
Coefficient of Determination = R² = 0.80² = 0.64 = 64%

(2)

Correct option:

a.   Change the perceived slope and not the correlation.

Explanation:

If the points are stretched out horizontally or vertically, the slope changes but the correlation does not change.

(3)

Correct option:

a. The sample correlation coefficient remains unchanged at 0.64.

Explanation:

Correlation coefficient is independent of change of origin and scale.

(4)

Correct option:

d.   All of above