Answer:
![\epsilon = Y -X\beta](https://tex.z-dn.net/?f=%20%5Cepsilon%20%3D%20Y%20-X%5Cbeta)
And the expected value for
a vector of zeros and the covariance matrix is given by:
![Cov (\epsilon) = \sigma^2 I](https://tex.z-dn.net/?f=%20Cov%20%28%5Cepsilon%29%20%3D%20%5Csigma%5E2%20I)
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.
Step-by-step explanation:
Assuming that we have n observations from a dependent variable Y , given by ![Y_1, Y_2,....,Y_n](https://tex.z-dn.net/?f=%20Y_1%2C%20Y_2%2C....%2CY_n)
And for each observation of Y we have an independent variable X, given by ![X_1, X_2,...,X_n](https://tex.z-dn.net/?f=%20X_1%2C%20X_2%2C...%2CX_n)
We can write a linear model on this way:
![Y = X \beta +\epsilon](https://tex.z-dn.net/?f=%20Y%20%3D%20X%20%5Cbeta%20%2B%5Cepsilon%20)
Where
i a matrix for the error random variables, and for this case we can find the error ter like this:
![\epsilon = Y -X\beta](https://tex.z-dn.net/?f=%20%5Cepsilon%20%3D%20Y%20-X%5Cbeta)
And the expected value for
a vector of zeros and the covariance matrix is given by:
![Cov (\epsilon) = \sigma^2 I](https://tex.z-dn.net/?f=%20Cov%20%28%5Cepsilon%29%20%3D%20%5Csigma%5E2%20I)
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.