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oksian1 [2.3K]
3 years ago
5

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.
Mathematics
1 answer:
frutty [35]3 years ago
8 0

Answer:

\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.

Step-by-step 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.

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