In a multiple regression model, the error term ɛ is assumed to Have a mean of 1 Have a variance of 0 Have a standard deviation of 1 Be normally distributed

In a multiple regression model, the error term ɛ is assumed to:

1. Have a mean of 0: This assumption means that the expected value of the error term is zero. This is because we assume that our model is correctly specified, i.e., it includes all relevant variables and correctly models the relationship between the independent and dependent variables. Therefore, any deviation from the predicted value is considered random error with an expected value of zero.

2. Have a constant variance: This assumption, also known as homoscedasticity, means that the variance of the errors is constant across all levels of the independent variables. If the variance of the errors changes across the levels of the independent variables, it is known as heteroscedasticity.

3. Not have a standard deviation of 1: The standard deviation of the error term is not assumed to be 1 in multiple regression. The standard deviation can be any positive number.

4. Be normally distributed: This assumption means that the errors are assumed to follow a normal distribution. This is important for hypothesis testing and for creating confidence intervals around the regression coefficients. However, this assumption is not necessary for estimating the coefficients themselves.