what is the major assumption I asked in class when I discussed the statistical properties of regression coefficients?

Question

BlackTom AI · Accepted Answer

Question restatement: What is the major assumption discussed in class about the statistical properties of regression coefficients, given the multiple-answer format?

Option 1: All randomness is coming from the residual and the factors are fixed. This aligns with a central textbook assumption for classical linear regression: the explanatory variables (factors) are fixed in repeated samples, and all randomness in the model comes from the error term (residual). This is precisely why the Gauss–Markov framework treats X as non-random and attributes variability to the residuals. Therefore, this option is correct.

Option 2: all factors are independent from one another. While independence of error terms is a part of the assumptions, and some models prefer orthogonality among predictors, the claim that all factors must be independent from each other is not the core or universal major assumption for the properties of regression coefficients. In practice, regressors can be correlated (leading to multicollinearity), so this is not the definitive foundational assumption.

Option 3: All factors are normal. The normality assumption in regression is about the error terms, not the predictors. The standard linear model does not require the predictor variables to be normally distributed; rather, the inference about coefficients relies on the distributional assumptions of the errors. Therefore, stating that all factors are normal is incorrect as the major assumption.

Option 4: NONE OF THE ABOVE. Since option 1 accurately captures a key classical assumption (fixed predictors, randomness only in residuals), claiming none of the above would be inaccurate.

In sum, the reasoning centers on identifying the fixed-X, random-error framework as the primary assumption for regression coefficient properties, while recognizing common misconceptions about predictor distribution, predictor independence, and normality of factors.

what is the major assumption I asked in class when I discussed the statistical properties of regression coefficients?Multiple choice

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