Deck 3: Multiple Regression Analysis Estimation

Question 1

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

Answer 1

B

Question 2

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

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

Answer 2

C

Question 3

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

Answer 3

C

Question 4

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

Question 5

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

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

Question 6

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

Question 7

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 8

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 9

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 10

In the equation, is a(n) _____.

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

Question 11

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 12

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 13

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 14

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 15

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

Question 16

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 17

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

Question 18

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 19

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 20

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 21

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

Question 22

Suppose that you are interested in estimating the average impact a job training program has on wages. However, you recognize that there are some observed factors that influence wage, participation on the training program, or both. You may still get the unbiased estimate for the program effectiveness by:

A)Excluding those observed factors from your model and running a simple linear regression
B)Including only the factors that predict wage but not participation as controls and running a multiple linear regression
C)Including only the factors that predict participation but not wage as controls and running a multiple linear regression
D)​ Including factors that predict both wage and participation as controls and running a multiple linear regression
​
​

Question 23

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

Question 24

Suppose the relationship between wage, years of education (educ), years of experience (exper), and participation in a job training program (train) is modeled as: log ( ) = + + + . Which of the following is the most accurate interpretation of the coefficient, ?

A)Holding education and experience constant, participating in the training program increases the wage by $ .
B)Holding education and experience constant, participating in the training program is predicted to increase the wage by
C)Participating in the training program is predicted to increase the wage by % .
D)Participating in the training program increases the wage by $ .

Question 25

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

Question 26

Which of the following often implies that a single variable acts as a 'sufficient statistic' for predicting the outcome variable, y?

A)Ceteris paribus
B)Conditional independence assumption
C)Efficient markets theories
D)Gauss-Markov theorem

Question 27

In a multiple linear regression model, , where is a binary variable and is the years of experience, is the difference in the average wage between males and non-males, after accounting for experience.

Question 28

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.​