Q1. Determine and interpret the correlation coefficient for the two variables X and Y. The standard deviation of X is 0.05, the standard deviation of Y is 0.08, and their covariance is −0.003.

A)   +0.75 and the two variables are positively associated.

B)   −0.75 and the two variables are negatively associated.

C)   −1.33 and the two variables are negatively associated.

Q2. Unlike the coefficient of determination, the coefficient of correlation:

A)   indicates the percentage of variation explained by a regression model.

B)   measures the strength of association between the two variables more exactly.

C)   indicates whether the slope of the regression line is positive or negative.

Q3. In order to have a negative correlation between two variables, which of the following is most accurate?

A)   Either the covariance or one of the standard deviations must be negative.

B)   The covariance must be negative.

C)   The covariance can never be negative.

Q4. Which of the following statements regarding a correlation coefficient of 0.60 for two variables Y and X is least accurate? This correlation:

A)   is significantly different from zero.

B)   indicates a positive covariance between the two variables.

C)   indicates a positive linear relation between the two variables.

Q5. Which model does not lend itself to correlation coefficient analysis?

A)   Y = X³.

B)   Y = X + 2.

C)   X = Y × 2.

答案和详解如下：

Q1. Determine and interpret the correlation coefficient for the two variables X and Y. The standard deviation of X is 0.05, the standard deviation of Y is 0.08, and their covariance is −0.003.

A)   +0.75 and the two variables are positively associated.

B)   −0.75 and the two variables are negatively associated.

C)   −1.33 and the two variables are negatively associated.

Correct answer is B)

The correlation coefficient is the covariance divided by the product of the two standard deviations, i.e. −0.003 / (0.08 × 0.05).

Q2. Unlike the coefficient of determination, the coefficient of correlation:

A)   indicates the percentage of variation explained by a regression model.

B)   measures the strength of association between the two variables more exactly.

C)   indicates whether the slope of the regression line is positive or negative.

Correct answer is C)

In a simple linear regression the coefficient of determination (R²) is the squared correlation coefficient, so it is positive even when the correlation is negative.

Q3. In order to have a negative correlation between two variables, which of the following is most accurate?

A)   Either the covariance or one of the standard deviations must be negative.

B)   The covariance must be negative.

C)   The covariance can never be negative.

Correct answer is B)

In order for the correlation between two variables to be negative, the covariance must be negative. (Standard deviations are always positive.)

Q4. Which of the following statements regarding a correlation coefficient of 0.60 for two variables Y and X is least accurate? This correlation:

A)   is significantly different from zero.

B)   indicates a positive covariance between the two variables.

C)   indicates a positive linear relation between the two variables.

Correct answer is A)

A test of significance requires the sample size. So this statement may or may not be true. The others are certainly true.

Q5. Which model does not lend itself to correlation coefficient analysis?

A)   Y = X³.

B)   Y = X + 2.

C)   X = Y × 2.

Correct answer is A)

The correlation coefficient is a measure of linear association. All of the functions except for Y = X³ are linear functions. Notice that Y – X = 2 is the same as Y = X + 2.

答案和详解如下：

A)   +0.75 and the two variables are positively associated.

B)   −0.75 and the two variables are negatively associated.

C)   −1.33 and the two variables are negatively associated.

Correct answer is B)

The correlation coefficient is the covariance divided by the product of the two standard deviations, i.e. −0.003 / (0.08 × 0.05).

Q2. Unlike the coefficient of determination, the coefficient of correlation:

A)   indicates the percentage of variation explained by a regression model.

B)   measures the strength of association between the two variables more exactly.

C)   indicates whether the slope of the regression line is positive or negative.

Correct answer is C)

In a simple linear regression the coefficient of determination (R²) is the squared correlation coefficient, so it is positive even when the correlation is negative.

Q3. In order to have a negative correlation between two variables, which of the following is most accurate?

A)   Either the covariance or one of the standard deviations must be negative.

B)   The covariance must be negative.

C)   The covariance can never be negative.

Correct answer is B)

In order for the correlation between two variables to be negative, the covariance must be negative. (Standard deviations are always positive.)

Q4. Which of the following statements regarding a correlation coefficient of 0.60 for two variables Y and X is least accurate? This correlation:

A)   is significantly different from zero.

B)   indicates a positive covariance between the two variables.

C)   indicates a positive linear relation between the two variables.

Correct answer is A)

A test of significance requires the sample size. So this statement may or may not be true. The others are certainly true.

Q5. Which model does not lend itself to correlation coefficient analysis?

A)   Y = X³.

B)   Y = X + 2.

C)   X = Y × 2.

Correct answer is A)

The correlation coefficient is a measure of linear association. All of the functions except for Y = X³ are linear functions. Notice that Y – X = 2 is the same as Y = X + 2.

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