The standard model for multiple lincar regression is where the ei are iid. norma

Question

The standard model for multiple lincar regression is where the ei are iid. normal random variables with mean 0 and variance 2. We write B , . . . , for the estimators of Bo,., k, respectively. Answer each the following questions with 'true' or 'false'. 1ything beyond your first word will not be graded. (a) The estimators Bo, , Bk are constructed by minimizing _(A) + A;" + + over o, (b) Bo and B are independent random variables (c) If we test statistically whether Bo 15, then the test statistic has a chi-squared distribution (d)Azil) + + kzik) h (e) All of the linear regression tools apply if the zil) only take the value 0 (r 1. as a normal distribution for every i

Explanation / Answer

a) True. Since these are the least square estimates obtained by minimising the sum of squares of errors.

b) false.B0 and B1 are not independent as there is effect of common y in both.

c) false. this test follows a t-distribution.

d) false. these are the parameters of the normal distributions.

e) false. x may take any value in real line

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