Question 1

Which is NOT true about the coefficient of determination? A) Its computation is r² B) It is Pearson r C) It is used to interpret values of the Pearson r D) It is used to explain variance

Accepted Answer

The coefficient of determination is not Pearson r itself; rather, it is the square of Pearson's r (r^2), which is used to explain the proportion of variance in the dependent variable that can be predicted from the independent variable.

Question 2

If r = .50, what is the coefficient of determination? _______________

Accepted Answer

25%

Question 3

For the above question, explain what this coefficient of determination means?

Accepted Answer

25% of variance in one variable is accounted for by the variance in the other variable.

Question 4

If a r² is .81, what percent of the variance in a variable is unexplained? A) 1.19% B) 21% C) 19% D) 119%

Accepted Answer

19%The given r² appears to be a typographical representation of a squared Pearson correlation coefficient (r^2), which in this case is .81. This value represents the proportion of variance in a dependent variable that is predictable from the independent variable. To find the percent of variance unexplained, we subtract this value from 1 (or 100%) and then convert the result into a percentage. Thus, 1 - .81 = .19, or 19% of the variance is unexplained.

Question 5

In interpreting values of r in the .20 to .40 range this means that 84% to 96% of the variance on one variable is not accounted for by the other.

Accepted Answer

The correlation coefficient (r) measures the strength and direction of a linear relationship between two variables. A value of r in the .20 to .40 range indicates a weak to moderate correlation. To determine the percentage of variance not accounted for by the other variable, you square the correlation coefficient (r^2) to get the coefficient of determination. For r values of .20 to .40, squaring these values gives you .04 to .16, indicating that 4% to 16% of the variance in one variable is explained by the other, leaving 96% to 84% of the variance unexplained.

Deck 31: Coefficient of Determination