1. The normality assumption implies that: a. the population error u is dependent on the explanatory...

1. The normality assumption implies that:

	a.	the population error u is dependent on the explanatory variables and is normally distributed with mean equal to one and variance ².
	b.	the population error u is independent of the explanatory variables and is normally distributed with mean equal to one and variance .
	c.	the population error u is dependent on the explanatory variables and is normally distributed with mean zero and variance .
	d.	the population error u is independent of the explanatory variables and is normally distributed with mean zero and variance ².

2. A normal variable is standardized by:

	a.	subtracting off its mean from it and multiplying by its standard deviation.
	b.	adding its mean to it and multiplying by its standard deviation.
	c.	subtracting off its mean from it and dividing by its standard deviation.
	d.	adding its mean to it and dividing by its standard deviation.

3. In the multiple regression model , if x₁ is correlated with u but the other independent variables are uncorrelated with u, then all of the OLS estimators are generally consistent.

	a.	True
	b.	False

Solutions

Expert Solution

1) option "d" is correct i.e the population error u is independent of the explanatory variables and is normally distributed with mean zero and variance

The assumption of Normality states that the distribution of sample means (across the independent samples) is normally distributed. In static terms, the Assumption of Normality suugests that the sampling distribution of the mean is normal or that the distribution of means across samples is also normal.

2) option "c" is correct i.e subtracting off its mean from it and dividing by its standard deviation

a normal variable means who follows the normal distribution, so where there mean is equal to zero and variance is σ2

3) True

in the presence of multicollinearity ( i.e if x1 is correlated with u), the OLS estimator will still be consistent, unbiased and efficient, This is the only case since none of the four (Gauss-Markov) assumptions of the CLRM have been violated.

For any query please comment and please upvote

Rahul Sunny answered 1 month ago

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