Question

1.

Consider regression through the origin, y=β₁x₁+β₂x₂+u, which of the following statements is wrong?

	a.	The degree of freedom for estimating the variance of error term is n−2.
	b.	The sum of residuals equals to 0.
	c.	If the true intercept parameter doesn’t equal to 0, all slope estimators are biased.
	d.	The residual is uncorrelated with the independent variable.

2.

Which of the following statements is true of hypothesis testing?

	a.	OLS estimates maximize the sum of squared residuals.
	b.	The t test can be used to test multiple linear restrictions.
	c.	A test of single restriction is also referred to as a joint hypotheses test.
	d.	A restricted model will always have fewer parameters than its unrestricted model.

Answer 1

1. a) The degree of freedom for estimating the variance of the error term is n−1. Thus the statement is False

b) The sum of residuals equals 0. Thus true

c) If the true intercept parameter doesn’t equal to 0, all slope estimators are biased. Thus this true

d) The residual is uncorrelated with the independent variable. Hence true

Thus the answer is: (a)

2. a) Ols estimates minimizes the sum of squared residuals. Thus false

b) The t-test is used to test single linear restrictions. Thus the statement is false.

c) A test of multiple restrictions is also referred to as a joint hypotheses test. Hence False.

d) A restricted model will always have fewer parameters than its unrestricted model. Thus the statement is true.

Hence answer is (d).