Which of the following is not a requirement for regression analysis?

• A. The errors should be $normally$ distributed.
• B. The relationship between variables must be $linear$.
• C. The independent variable must be measured on a $nominal$ scale.
• D. The residuals should have constant variance ($homoscedasticity$).

Answer: (C)

Verified step by step guidance

1. Understand that regression analysis relies on several key assumptions to produce valid results. These assumptions ensure the model fits the data appropriately and that inference is reliable.
2. Recall the common assumptions for linear regression: (1) The relationship between the independent and dependent variables is linear, (2) The errors (residuals) are normally distributed, (3) The residuals have constant variance, known as homoscedasticity, and (4) The observations are independent.
3. Recognize that the independent variable should be measured on at least an interval or ratio scale to meaningfully assess linear relationships. Nominal scale variables represent categories without inherent order, which do not satisfy the linearity assumption.
4. Therefore, the statement 'The independent variable must be measured on a nominal scale' contradicts the requirement for regression analysis, as nominal variables cannot be used directly in linear regression without appropriate coding (e.g., dummy variables).
5. Conclude that among the given options, the requirement that the independent variable must be measured on a nominal scale is NOT a valid assumption for regression analysis.