If two variables taken together account for 65% of the variability in Y , and a third variable has a simple squared correlation with Y of .10, then adding that variable to the equation will allow us to account for
A) 65% of the variability in Y .
B) 75% of the variability in Y .
C) 10% of the variability in Y .
D) at least 65% of the variability in Y .

Question

Quizplus · Accepted Answer

Adding a third variable with a simple squared correlation of .10 with Y to the equation does not guarantee that the total explained variability will increase to 75% due to potential overlap in the explained variance between variables. However, it does ensure that the explained variability will be at least 65%, as the addition of a variable cannot decrease the already explained variability.

If Two Variables Taken Together Account for 65% of the Variability