Q21. What does the R² of a simple regression of two variables measure and what calculation is used to equate the correlation coefficient to the coefficient of determination?

         R2 measures:                                        Correlation coefficient

A) percent of variability of the independent variable that

is explained by the variability of the dependent variable         R2 = r2

B) percent of variability of the independent variable that

is explained by the variability of the dependent variable         R2 = r × 2

C) percent of variability of the dependent variable that

is explained by the variability of the independent variable        R2 = r2

Q22. The R² of a simple regression of two factors, A and B, measures the:

A)   impact on B of a one-unit change in A.

B)   percent of variability of one factor explained by the variability of the second factor.

C)   statistical significance of the coefficient in the regression equation.

答案和详解如下：

Q21. What does the R² of a simple regression of two variables measure and what calculation is used to equate the correlation coefficient to the coefficient of determination?

         R2 measures:                                        Correlation coefficient

A) percent of variability of the independent variable that

is explained by the variability of the dependent variable         R2 = r2

B) percent of variability of the independent variable that

is explained by the variability of the dependent variable         R2 = r × 2

C) percent of variability of the dependent variable that

is explained by the variability of the independent variable        R2 = r2

Correct answer is C)

R², or the Coefficient of Determination, is the square of the coefficient of correlation (r). The coefficient of correlation describes the strength of the relationship between the X and Y variables. The standard error of the residuals is the standard deviation of the dispersion about the regression line. The t-statistic measures the statistical significance of the coefficients of the regression equation. In the response: "percent of variability of the independent variable that is explained by the variability of the dependent variable," the definitions of the variables are reversed.

Q22. The R² of a simple regression of two factors, A and B, measures the:

A)   impact on B of a one-unit change in A.

B)   percent of variability of one factor explained by the variability of the second factor.

C)   statistical significance of the coefficient in the regression equation.

Correct answer is B)

The coefficient of determination measures the percentage of variation in the dependent variable explained by the variation in the independent variable.