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True or False? State with reason. Based on the normality assumption of ? ?? ? =...

True or False? State with reason.

Based on the normality assumption of ? ?? ? = ? ∗ ? + ? , ? has a Chi-Square distribution.

For a model such as ? = ? + ? ? + ? , because the mean and individual predictions are all ? = ? + ? ? , the mean and individual predictions are the same.

If the assumptions in Classical Normal Linear Regression Model are true, for a model such as ? = ? + ? ? + ? , we use chi-squre test to test hypothesis related to the parameters (?1, ?2), and t test to test hypothesis related to the variance of error (?2).

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Answer #1

1) FALSE. Based on the normality assumption of u, Beta has a Normal Distribution and not Chi Square Distribution.

2) TRUE. The expressions for the mean and individual predictions are the same and hence, the predicted values are same for both in all the cases. However, the variance of the two is different.

3) FALSE. If the assumptions are true, then we use t test to test hypothesis related to (beta1, beta2), and chi square to test hypothesis related to the variance of error.

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