Deck 3: Multiple Regression Analysis: Estimation

Question 1

Find the degrees of freedom in a regression model that has 10 observations and 7 independent variables.

A)17
B)2
C) 3
D) 4

Answer 1

B
Explanation: The degrees of freedom in a regression model is computed by subtracting the number of parameters from the number of observations in a regression model. Since, the number of parameters is one more than the number of independent variables, the degrees of freedom in this case is 10-(7 + 1) = 2.

Question 2

If the explained sum of squares is 35 and the total sum of squares is 49, what is the residual sum of squares?

A)10
B)12
C) 18
D) 14

Answer 2

D
Explanation: The residual sum of squares is obtained by subtracting the explained sum of squares from the total sum of squares, or 49-35=14.

Question 3

The coefficient of determination (R²) decreases when an independent variable is added to a multiple regression model.

Answer 3

False
Explanation: The coefficient of determination (R²) never decreases when an independent variable is added to a multiple regression model.

Question 4

Which of the following is true of BLUE?​

A)​It is a rule that can be applied to any one value of the data to produce an estimate.
B)​An estimator is an unbiased estimator of if for any .
C) ​An estimator is linear if and only if it can be expressed as a linear function of the data on the dependent variable.
D) ​It is the best linear uniform estimator.

Question 5

Exclusion of a relevant variable from a multiple linear regression model leads to the problem of _____.

A)misspecification of the model
B)multicollinearity
C) perfect collinearity
D) homoskedasticity

Question 6

The Gauss-Markov theorem will not hold if _____.

A)the error term has the same variance given any values of the explanatory variables
B)the error term has an expected value of zero given any values of the independent variables
C) the independent variables have exact linear relationships among them
D) the regression model relies on the method of random sampling for collection of data

Question 7

Consider the following regression equation: . What does imply?

A) measures the ceteris paribus effect of on .
B) measures the ceteris paribus effect of on .
C)
measures the ceteris paribus effect of
on
.
D)
measures the ceteris paribus effect of
on
.

Question 8

The term "linear" in a multiple linear regression model means that the equation is linear in parameters.

Question 9

Which of the following is true of R²?

A)R² is also called the standard error of regression.
B)A low R² indicates that the Ordinary Least Squares line fits the data well.
C) R² usually decreases with an increase in the number of independent variables in a regression.
D) R² shows what percentage of the total variation in the dependent variable, Y, is explained by the explanatory variables.

Question 10

High (but not perfect) correlation between two or more independent variables is called _____.

A)heteroskedasticty
B)homoskedasticty
C) multicollinearity
D) micronumerosity

Question 11

If an independent variable in a multiple linear regression model is an exact linear combination of other independent variables, the model suffers from the problem of _____.

A)perfect collinearity
B)homoskedasticity
C) heteroskedasticty
D) omitted variable bias

Question 12

The assumption that there are no exact linear relationships among the independent variables in a multiple linear regression model fails if _____, where n is the sample size and k is the number of parameters.

A)n > 2
B)n = k + 1
C) n > k
D) n < k + 1

Question 13

In econometrics, the general partialling out result is usually called the _____.​

A)​Gauss-Markov assumption
B)​Best linear unbiased estimator
C) ​Frisch-Waugh theorem
D) ​Gauss-Markov theorem

Question 14

Suppose the variable x2 has been omitted from the following regression equation, is the estimator obtained when is omitted from the equation. The bias in is positive if _____.

A) >0 and and are positively correlated
B) <0 and and are positively correlated
C)
>0 and
and
are negatively correlated
D)
= 0 and
and
are negatively correlated

Question 15

In the equation, is a(n) _____.

A)independent variable
B)dependent variable
C) slope parameter
D) intercept parameter

Question 16

Suppose the variable has been omitted from the following regression equation, is the estimator obtained when is omitted from the equation. The bias in is negative if _____.

A) >0 and and are positively correlated
B) <0 and and are positively correlated
C)
=0 and
and
are negatively correlated
D)
=0 and
and
are negatively correlated

Question 17

The term _____ refers to the problem of small sample size.

A)micronumerosity
B)multicollinearity
C) homoskedasticity
D) heteroskedasticity

Question 18

The key assumption for the general multiple regression model is that all factors in the unobserved error term be correlated with the explanatory variables.

Question 19

Suppose the variable has been omitted from the following regression equation, is the estimator obtained when is omitted from the equation. If is said to _____.

A)have an upward bias
B)have a downward bias
C) be unbiased
D) be biased toward zero

Question 20

The value of R² always _____.

A)lies below 0
B)lies above 1
C) lies between 0 and 1
D) lies between 1 and 1.5

Question 21

An explanatory variable is said to be exogenous if it is correlated with the error term.

Question 22

If two regressions use different sets of observations, then we can tell how the R-squareds will compare, even if one regression uses a subset of regressors.​

Question 23

​When one randomly samples from a population, the total sample variation in x_j decreases without bound as the sample size increases.

Question 24

A larger error variance makes it difficult to estimate the partial effect of any of the independent variables on the dependent variable.