Question

Which of these statements is best? The errors in a regression model are assumed to have an increasing mean. The regression model assumes the error terms are dependent. The errors in a regression model are assumed to have zero variance. The regression model assumes the errors are normally distributed.

Answer 1

`\epsilon = Y -X\beta`

And the expected value for
`E(\epsilon) = 0` a vector of zeros and the covariance matrix is given by:

`Cov (\epsilon) = \sigma^2 I`

So we can see that the error terms not have a variance of 0. We can't assume that the errors are assumed to have an increasing mean, and we other property is that the errors are assumed independent and following a normal distribution so then the best option for this case would be:

The regression model assumes the errors are normally distributed.

Explanation:

Assuming that we have n observations from a dependent variable Y , given by
`Y_1, Y_2,....,Y_n`

And for each observation of Y we have an independent variable X, given by
`X_1, X_2,...,X_n`

We can write a linear model on this way:

`Y = X \beta +\epsilon`

Where
`\epsilon_(nx1)` i a matrix for the error random variables, and for this case we can find the error ter like this:

`\epsilon = Y -X\beta`

And the expected value for
`E(\epsilon) = 0` a vector of zeros and the covariance matrix is given by:

`Cov (\epsilon) = \sigma^2 I`

So we can see that the error terms not have a variance of 0. We can't assume that the errors are assumed to have an increasing mean, and we other property is that the errors are assumed independent and following a normal distribution so then the best option for this case would be:

The regression model assumes the errors are normally distributed.