Question 1

The term &#34;linear&#34; in a multiple linear regression model means that the equation is linear in parameters.

Accepted Answer

The term "linear" in a multiple linear regression model refers to the equation being linear in parameters, but not necessarily in the predictor variables themselves. It means that the parameters being estimated have a linear relationship with the outcome variable, and can be expressed as a linear combination of the predictor variables.

Question 2

Which of the following is true of R²? A)R² is also called the standard error of regression. B)A low R²indicates 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.

Accepted Answer

D

Question 3

High (but not perfect)correlation between two or more independent variables is called _____.&#10;A)heteroskedasticty&#10;B)homoskedasticty&#10;C)multicollinearity&#10;D)micronumerosity

Accepted Answer

Multicollinearity refers to the high correlation between independent variables in a regression model, which can lead to issues such as unstable and unreliable coefficient estimates. The other options (A, B, D) are not relevant to this concept.

Question 4

Suppose the variable x₂ has been omitted from the following regression equation, . is the estimator obtained when x₂ is omitted from the equation.If E( )>β₁, is said to _____. A)have an upward bias B)have a downward bias C)be unbiased D)be biased toward zero

Accepted Answer

If the omitted variable is positively correlated with the dependent variable and not included in the model, the estimated coefficient of the included variables will be biased upwards, resulting in an upward bias.

Question 5

Consider the following regression equation: .What does β₁ 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 .

Accepted Answer

The answer of Consider the following regression equation:  ...

Question 6

The Gauss-Markov theorem will not hold if _____.&#10;A)the error term has the same variance given any values of the explanatory variables&#10;B)the error term has an expected value of zero given any values of the independent variables&#10;C)the independent variables have exact linear relationships among them&#10;D)the regression model relies on the method of random sampling for collection of data

Accepted Answer

The Gauss-Markov theorem assumes that the independent variables are not exact linear combinations of each other, which is violated if they have exact linear relationships among them.

Question 7

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

Accepted Answer

A larger error variance means that the data points are more spread out and less precise, which makes it harder to identify the true relationships between the independent variables and the dependent variable. This can result in less accurate estimates of the partial effects of individual independent variables.

Question 8

The term _____ refers to the problem of small sample size.&#10;A)micronumerosity&#10;B)multicollinearity&#10;C)homoskedasticity&#10;D)heteroskedasticity

Accepted Answer

Micronumerosity specifically refers to the issue of small sample size. Multicollinearity refers to when predictor variables in a regression model are highly correlated, while homoskedasticity and heteroskedasticity refer to issues with the variance of the errors in a regression model.

Question 9

Exclusion of a relevant variable from a multiple linear regression model leads to the problem of _____.&#10;A)misspecification of the model&#10;B)multicollinearity&#10;C)perfect collinearity&#10;D)homoskedasticity

Accepted Answer

Exclusion of a relevant variable from a multiple linear regression model leads to misspecification of the model, as it does not take into account the influence of the excluded variable on the response variable. This can lead to biased and inaccurate results. Multicollinearity refers to the presence of strong correlations among the predictor variables, while perfect collinearity refers to a situation where one variable can be perfectly predicted from a combination of other variables. Homoskedasticity refers to the condition where the variance of the errors is constant across all levels of the predictor variables.

Question 10

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

Accepted Answer

R² is a value for a statistical metric or probability, and it represents a percentage value between 0 and 1. Therefore, the correct choice is C - it always lies between 0 and 1.

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 _____.&#10;A)perfect collinearity&#10;B)homoskedasticity&#10;C)heteroskedasticty&#10;D)omitted variable bias

Accepted Answer

The answer of If an independent variable in a multiple...

Question 12

In the equation,   ,   is a(n)_____.&#10;A)independent variable&#10;B)dependent variable&#10;C)slope parameter&#10;D)intercept parameter

Accepted Answer

The answer of In the equation,   , ...

Question 13

Suppose the variable x₂ has been omitted from the following regression equation, . is the estimator obtained when x₂ is omitted from the equation.The bias in is positive if _____. A) >0 and x₁ and x₂are positively correlated B) <0 and x₁ and x₂are positively correlated C) >0 and x₁ and x₂are negatively correlated D) = 0 and x₁ and x₂are negatively correlated

Accepted Answer

The answer of Suppose the variable x₂ has been omitted...

Question 14

Find the degrees of freedom in a regression model that has 10 observations and 7 independent variables.&#10;A)17&#10;B)2&#10;C)3&#10;D)4

Accepted Answer

The answer of Find the degrees of freedom in a...

Question 15

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

Accepted Answer

The answer of The coefficient of determination (R²)decreases when an...

Question 16

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

Accepted Answer

The answer of The assumption that there are no exact...

Question 17

Suppose the variable x₂ has been omitted from the following regression equation, . is the estimator obtained when x₂ is omitted from the equation.The bias in is negative if _____. A) >0 and x₁ and x₂are positively correlated B) <0 and x₁ and x₂are positively correlated C) =0 and x₁ and x₂are negatively correlated D) =0 and x₁ and x₂are negatively correlated

Accepted Answer

The answer of Suppose the variable x₂ has been omitted...

Question 18

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

Accepted Answer

The answer of An explanatory variable is said to be...

Question 19

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

Accepted Answer

The answer of The key assumption for the general multiple...

Question 20

If the explained sum of squares is 35 and the total sum of squares is 49,what is the residual sum of squares?&#10;A)10&#10;B)12&#10;C)18&#10;D)14

Accepted Answer

The answer of If the explained sum of squares is...

Deck 3: Multiple Regression Analysis: Estimation