In a multiple regression model, the error term e is assumed to be a random variable with a mean of

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Question restatement: In a multiple regression model, the error term e is assumed to be a random variable with a mean of what value?
Options: ["0", "-1", "1", "Any value"]

Option 1: 0. The standard assumption in classical linear regression is that the error term has an expected value of zero, i.e., E[e] = 0. This implies the errors are, on average, centered around zero, which supports unbiasedness of the OLS estimates and the interpretation that the model captures systematic variation, while remaining random noise with no systematic bias.

Option 2: -1. An expectation of -1 would imply a systematic downward bias in the errors across observations, which is not a standard assumption and would distort the interpretation of residuals and the properties of estimators. There is no theoretical basis in classical linear regression for the mean of the error term to be -1.

Option 3: 1. Similarly, an expectation of +1 would indicate a systematic upward bias in the errors, again contradicting the standard assumption of zero mean for the error term. This would affect unbiasedness and consistency properties of the estimators.

Option 4: Any value. If the mean of the error term could be any value, the model would capture a systematic bias that cannot be separated from the intercept or the other coefficients. This would violate key OLS assumptions and undermine inference, as predictions would be biased and standard errors misestimated.

Additional note: The assumption E[e] = 0 is part of the Gauss-Markov framework, alongside homoskedasticity and no perfect multicollinearity. When E[e] = 0 holds, the expected value of the error term conditional on the regressors is also zero, which underpins the unbiasedness of the OLS estimators. Deviations from E[e] = 0 would imply a misspecified model or omitted variable bias, leading to inconsistent or biased estimates.

MSIS 212 P 1 05 Mngrl Decision Makng Spring 2025 HW5.Reg.2

In a multiple regression model, the error term e is assumed to be a random variable with a mean of

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