Deck 4: Multiple Regression Analysis: Inference

Question 1

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)
statistic
D) Durbin Watson statistic

Answer 1

B
Explanation: The t statistic can be used to test hypotheses about a single population parameter.

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
Explanation: A restricted model will always have fewer parameters than its unrestricted model.

Question 3

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

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

D) F =

Answer 3

B
Explanation: The F statistic is given by, F = .

Question 4

Which of the following is true of standard error?

A)It can take negative values.
B)​It is an estimate of the standard deviation.
C) ​It is the square root of the variance.
D) It complicates the computation of confidence intervals.

Question 5

Which of the following is true of confidence intervals?

A)​Two quantities and c are required to construct the confidence intervals.
B)To obtain the value c in the confidence interval, only the degrees of freedom need to be known.
C) Confidence intervals are also called interval estimates.
D) ​A constructed confidence intervals will always contain the population parameter
.

Question 6

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 âj, is given by
- [standard error × (
)].
D) The upper bound of the confidence interval for a regression coefficient, say âj, is given by
+ [Critical value × standard error (
)].

Question 7

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 ².
C) The CLT assumes that the dependent variable is unaffected by unobserved factors.
D) OLS estimators have the highest variance among unbiased estimators.

Question 8

If R²ur = 0.6873, R²r = 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 9

The ordinary least square estimators have the smallest variance among all the unbiased estimators.​

Question 10

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 11

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 12

Consider the equation, y = + ₁x_{1 +
2}x₂ + u. A null hypothesis, H₀: ₂ = 0 states that:

A)x₂ has no effect on the expected value of 2.
B)x₂ has no effect on the expected value of y.
C)
₂ has no effect on the expected value of y.
D) y has no effect on the expected value of x_2.

Question 13

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 SSRr is never smaller than SSRur.
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 14

The significance level of a test is:

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

Question 15

The population parameter in the null hypothesis _____.​

A)​is always greater than zero
B)​is always equal to zero
C) ​is always less than zero
D) ​is not always equal to zero

Question 16

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.

Question 17

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

Question 18

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.

Question 19

The general t statistic can be written as:

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

D) t =

Question 20

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 21

Standard errors must always be positive.

Question 22

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 23

H₁: âj 0, where â_j is a regression coefficient associated with an explanatory variable, represents a one-sided alternative hypothesis.

Question 24

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

Question 25

In regression analysis, the standard errors should not always be included along with the estimated coefficients.
​