Deck 4: Multiple Regression Analysis: Inference

Question 1

Which of the following statements is true?

A)When the standard error of an estimate increases,the confidence interval for the estimate narrows down.
B)Standard error of an estimate does not affect the confidence interval for the estimate.
C)The lower bound of the confidence interval for a regression coefficient,say β_j,is given by _J - [standard error × (
_J)]
D)The upper bound of the confidence interval for a regression coefficient,say β_j,is given by _J + [Critical value × standard error (
_J)]

Answer 1

D

Question 2

Which of the following statements is true of hypothesis testing?

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

Answer 2

C

Question 3

Which of the following correctly identifies a reason why some authors prefer to report the standard errors rather than the t statistic?

A)Having standard errors makes it easier to compute confidence intervals.
B)Standard errors are always positive.
C)The F statistic can be reported just by looking at the standard errors.
D)Standard errors can be used directly to test multiple linear regressions.

Answer 3

A

Question 4

Which of the following statements is true?

A)Taking a log of a nonnormal distribution yields a distribution that is closer to normal.
B)The mean of a nonnormal distribution is 0 and the variance is σ².
C)The CLT assumes that the dependent variable is unaffected by unobserved factors.
D)OLS estimators have the highest variance among unbiased estimators.

Question 5

If ₁ and ₂are estimated values of regression coefficients associated with two explanatory variables in a regression equation,then the standard error ( ₁ - ₂)= standard error ( ₁)- standard error ( ₂).

Question 6

Whenever the dependent variable takes on just a few values it is close to a normal distribution.

Question 7

Which of the following tools is used to test multiple linear restrictions?

A)t test
B)z test
C)F test
D)Unit root test

Question 8

Which of the following statements is true?

A)If the calculated value of F statistic is higher than the critical value,we reject the alternative hypothesis in favor of the null hypothesis.
B)The F statistic is always nonnegative as SSR_ris never smaller than SSR_ur.
C)Degrees of freedom of a restricted model is always less than the degrees of freedom of an unrestricted model.
D)The F statistic is more flexible than the t statistic to test a hypothesis with a single restriction.

Question 9

The significance level of a test is:

A)the probability of rejecting the null hypothesiswhen it is false.
B)one minus the probability of rejecting the null hypothesis when it is false.
C)the probability of rejecting the null hypothesiswhen it is true.
D)one minus the probability of rejecting the null hypothesiswhen it is true.

Question 10

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 σ².
B)the population error u is independent of the explanatory variables and is normally distributed with mean equal to one and variance σ.
C)the population error u is dependent on the explanatory variables and is normally distributed with mean zero and variance σ.
D)the population error u is independent of the explanatory variables and is normally distributed with mean zero and variance σ².

Question 11

Which of the following correctly defines F statistic if SSR_r represents sum of squared residuals from the restricted model of hypothesis testing,SSR_urrepresents sum of squared residuals of the unrestricted model,and q is the number of restrictions placed?

A)F =
B)F =
C)F =
D)F =

Question 12

Which of the following statements is true of confidence intervals?

A)Confidence intervals in a CLM are also referred to as point estimates.
B)Confidence intervals in a CLM provide a range of likely values for the population parameter.
C)Confidence intervals in a CLM do not depend on the degrees of freedom of a distribution.
D)Confidence intervals in a CLM can be truly estimated when heteroskedasticity is present.

Question 13

Consider the equation,Y = β₁ + β₂X₂+ u.A null hypothesis,H₀: β₂= 0 states that:

A)X₂ has no effect on the expected value of β₂.
B)X₂ has no effect on the expected value of Y.
C)β₂has no effect on the expected value of Y.
D)Y has no effect on the expected value of X_2.

Question 14

H₁: β_j ≠ 0,where β_jis a regression coefficient associated with an explanatory variable,represents a one-sided alternative hypothesis.

Question 15

Which of the following is a statistic that can be used to test hypotheses about a single population parameter?

A)F statistic
B)t statistic
C)χ² statistic
D)Durbin Watson statistic

Question 16

If R²_ur = 0.6873,R²_r = 0.5377,number of restrictions = 3,and n - k - 1 = 229,F statistic equals:

A)21.2
B)28.6
C)36.5
D)42.1

Question 17

The general t statistic can be written as:

A)t =
B)t = )
C)t =
D)t =

Question 18

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.

Question 19

If the calculated value of the t statistic is greater than the critical value,the null hypothesis,H₀ is rejected in favor of the alternative hypothesis,H₁.

Question 20

Standard errors must always be positive.