If all the values of an independent variable x are equal, then performing a simple linear regression on a dependent variable y will result in a coefficient of determination that is equal to:
A) infinity.
B) 1.0.
C) 0.5.
D) 0.

Question

Quizplus · Accepted Answer

When all values of the independent variable x are equal, there is no variability in x to explain the variability in y. This situation leads to a division by zero in the calculation of the coefficient of determination (R^2), which is undefined. However, in practical terms, software or statistical calculations will typically result in an R^2 of 0, indicating that the model explains none of the variability of the response data around its mean.

If All the Values of an Independent Variable X Are