Which assumption is associated with linearity in regression analysis?

Which assumption is associated with linearity in regression analysis?

• A. Normal distribution of the outcome
• B. Independence of observations
• C. Linearity of the relationship between the predictor and the outcome
• D. Homoscedasticity of residuals

Answer: (C)

Linearity in regression means the outcome changes in a constant, proportional way as the predictor changes. In simple terms, the relationship is a straight line: y = β0 + β1x + ε, where the expected value of y given x lies on a straight line and a one-unit change in x produces a constant change in y across all x. This is why the key assumption is that the relationship between predictor and outcome is linear. If this linear form holds, the residuals should look random around zero with no systematic pattern, and predictions should follow the straight line. When the relationship isn’t linear, you’ll see patterns in the residuals (for example, a curve), and you’d need to transform the predictor, add polynomial or spline terms, or switch to a nonlinear model. The other statements relate to different aspects: normality concerns the distribution of outcomes or residuals for inference, independence relates to study design and whether observations influence each other, and homoscedasticity concerns whether the residual spread is constant across fitted values. None of these define the linearity of the predictor–outcome relationship.

Linearity in regression means the outcome changes in a constant, proportional way as the predictor changes. In simple terms, the relationship is a straight line: y = β0 + β1x + ε, where the expected value of y given x lies on a straight line and a one-unit change in x produces a constant change in y across all x. This is why the key assumption is that the relationship between predictor and outcome is linear.

If this linear form holds, the residuals should look random around zero with no systematic pattern, and predictions should follow the straight line. When the relationship isn’t linear, you’ll see patterns in the residuals (for example, a curve), and you’d need to transform the predictor, add polynomial or spline terms, or switch to a nonlinear model.

The other statements relate to different aspects: normality concerns the distribution of outcomes or residuals for inference, independence relates to study design and whether observations influence each other, and homoscedasticity concerns whether the residual spread is constant across fitted values. None of these define the linearity of the predictor–outcome relationship.