Which condition is required for an ordinary least-squares regression slope to be uniquely defined?
Correct answer: D. The independent variable has nonzero variance
- A. The dependent variable has zero variance
- B. The independent variable has zero variance
- C. The correlation must equal exactly one
- D. The independent variable has nonzero variance
Explanation
The slope uses the variation in the independent variable in its denominator. If X has no variation, its slope cannot be estimated from the data.
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About Correlation and Regression
Correlation describes the direction and strength of association between two variables using scatter diagrams and correlation coefficients. Regression covers fitted lines, regression equations, prediction and least squares, with a clear distinction between association and causation and between estimating a response value and reversing the roles of the variables.
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