Question 1

A term used to describe the case when the independent variables in a multiple regression model are correlated is
A) regression.
B) correlation.
C) multicollinearity.
D) leverage.

Accepted Answer

Multicollinearity refers to the situation where the independent variables in a multiple regression model are highly correlated with each other, which can lead to unreliable coefficient estimates and make it difficult to isolate the individual effects of each independent variable on the dependent variable.

Question 2

The mathematical equation that explains how the dependent variable y is related to several independent variables x₁, x₂, …, xp and the error term ε is a(n) A) simple nonlinear regression model. B) multiple regression model. C) estimated multiple regression equation. D) multiple regression equation.

Accepted Answer

Multiple regression involves multiple independent variables and the equation used to model their relationship to the dependent variable y is known as a multiple regression model.

Question 3

A multiple regression model has
A) only one independent variable.
B) more than one dependent variable.
C) more than one independent variable.
D) at least two dependent variables.

Accepted Answer

A multiple regression model has more than one independent variable. It is used to study the relationship between a dependent variable and multiple independent variables.

Question 4

A variable that takes on the values of 0 or 1 and is used to incorporate the effect of categorical independent variables in a regression model is called
A) an interaction.
B) a constant variable.
C) a dummy variable.
D) a logit variable.

Accepted Answer

A dummy variable is a variable that takes on the values of 0 or 1 to represent the presence or absence of a categorical independent variable in a regression model. This allows us to incorporate the effect of categorical variables in a regression model that only accepts continuous numerical inputs. Therefore, option C is the correct answer.

Question 5

In a multiple regression model, the variance of the error term ε is assumed to be
A) the same for all values of the dependent variable.
B) zero.
C) the same for all values of the independent variable.
D) one.

Accepted Answer

In a multiple regression model, the assumption of homoscedasticity implies that the variance of the error term (ε) is constant across all levels of the independent variables. This means that the spread of the residuals (errors) should be roughly the same across all values of the independent variables, ensuring that the model's predictions are equally reliable across the range of the independent variables.

Question 6

In regression analysis, the response variable is the
A) independent variable.
B) dependent variable.
C) slope of the regression function.
D) intercept.

Accepted Answer

The response variable is the variable being predicted or explained by the other variables (called predictor or explanatory variables). Hence, it is dependent on the predictor variables and is considered the dependent variable.

Question 7

In order to test for the significance of a regression model involving 3 independent variables and 47 observations, the numerator and denominator degrees of freedom (respectively) for the critical value of F are
A) 47 and 3.
B) 3 and 47.
C) 2 and 43.
D) 3 and 43.

Accepted Answer

The numerator degrees of freedom for the F-test in regression analysis are equal to the number of independent variables, which is 3 in this case. The denominator degrees of freedom are calculated as the total number of observations minus the number of independent variables minus 1 (for the intercept), which is 47 - 3 - 1 = 43.

Question 8

In regression analysis, an outlier is an observation whose
A) mean is larger than the standard deviation.
B) residual is zero.
C) mean is zero.
D) residual is much larger than the rest of the residual values.

Accepted Answer

An outlier in regression analysis is defined as an observation whose residual, or the difference between its actual response value and predicted response value, is much larger than the rest of the residual values. Therefore, option D is the correct answer. The mean and standard deviation of an observation have no bearing on whether it is an outlier or not, so options A and C can be eliminated. Option B is also incorrect as a residual of zero would indicate a perfectly fitted model.

Question 9

The equation which has the form of E(y) = = b₀ + b₁x₁ + b₂x₂ + ... + b_px_p is a(n) A) estimated multiple nonlinear regression equation. B) multiple nonlinear regression model. C) estimated multiple regression equation. D) multiple regression equation.

Accepted Answer

The answer of The equation which has the form of...

Question 10

The adjusted multiple coefficient of determination is adjusted for the
A) number of dependent variables.
B) number of independent variables.
C) number of equations.
D) sample size.

Accepted Answer

The adjusted multiple coefficient of determination is adjusted for the number of independent variables. This helps to prevent overestimation of the coefficient of determination when more independent variables are added to the model. The adjusted coefficient takes into account the number of independent variables and the sample size, giving a more accurate indication of the strength of the relationship between the independent and dependent variables.

Question 11

In a multiple regression model, the error term ε is assumed to be a random variable with a mean of
A) zero.
B) -1.
C) 1.
D) any value.

Accepted Answer

The error term ε is assumed to be a random variable with a mean of zero in a multiple regression model. This means that, on average, the errors made by the model will cancel each other out and not significantly impact the overall accuracy of the model.

Question 12

In multiple regression analysis, the correlation among the independent variables is termed
A) adjusted correlation.
B) linearity.
C) multicollinearity.
D) adjusted coefficient of determination.

Accepted Answer

Multicollinearity refers to the correlation among independent variables in multiple regression analysis. This can lead to unstable and unreliable estimates of the regression coefficients, as the variables are no longer independent from each other.

Question 13

In a multiple regression model, the error term ε is assumed to
A) have a mean of 1.
B) have a variance of zero.
C) have no distribution.
D) be normally distributed.

Accepted Answer

The error term ε is commonly assumed to be normally distributed with a mean of zero and constant variance. This assumption is necessary for conducting hypothesis testing, constructing confidence intervals, and making prediction intervals. Therefore, the best choice is D which states that the error term should be normally distributed.

Question 14

A regression model in which more than one independent variable is used to predict the dependent variable is called
A) a simple linear regression model.
B) a multiple regression model.
C) an independent model.
D) an adjusted prediction model.

Accepted Answer

In multiple regression, more than one independent variable is used to predict the dependent variable, making it the best choice. Option A, simple linear regression, only uses one independent variable. Neither option C nor D accurately reflect the nature of the regression model.

Question 15

A measure of goodness of fit for the estimated regression equation is the
A) multiple coefficient of determination.
B) multicollinearity.
C) mean square due to regression.
D) studentized residual.

Accepted Answer

The multiple coefficient of determination, also known as R-squared, is a measure of how well the estimated regression equation fits the data. It measures the proportion of the variation in the dependent variable that is explained by the independent variables in the model. A higher value of R-squared indicates a better fit. Therefore, it is the best choice for measuring the goodness of fit of the estimated regression equation.

Question 16

The mathematical equation which has the form of E(y) = β₀ + β₁x₁ + β₂x₂ + ... + β_pxp relating the expected value of the dependent variable to the value of the independent variables is a(n) A) estimated multiple nonlinear regression equation. B) multiple nonlinear regression model. C) estimated multiple regression equation. D) multiple regression equation.

Accepted Answer

The equation given is a multiple regression equation, which models the expected value of a dependent variable as a linear combination of multiple independent variables.

Question 17

The numerical value of the coefficient of determination.
A) is always larger than the coefficient of correlation.
B) is always smaller than the coefficient of correlation.
C) is negative if the coefficient of correlation is negative.
D) can be larger or smaller than the coefficient of correlation.

Accepted Answer

The coefficient of determination (R²) can be larger or smaller than the coefficient of correlation (r). R² is the square of the correlation coefficient (r), meaning that it takes into account the proportion of variance in the dependent variable that is explained by the independent variable(s). Therefore, R² is always equal to or less than r because it is less sensitive to outliers and reflects the effect of all independent variables.

Question 18

In a multiple regression model, the values of the error term ε are assumed to be
A) zero.
B) dependent on each other.
C) independent of each other.
D) always negative.

Accepted Answer

In a multiple regression model, the errors are assumed to be independent of each other, meaning that the value of an error term for a particular observation or data point is not dependent on the value of error terms for other observations. Additionally, error terms can be positive or negative and their values do not have to sum to zero, so choice A and D are incorrect. Finally, the correlation between error terms is not assumed, so choice B is also incorrect.

Question 19

In multiple regression analysis,
A) there can be any number of dependent variables, but only one independent variable.
B) the adjusted coefficient of determination can never be negative.
C) the multiple coefficient of determination must be larger than 1.
D) there can be several independent variables, but only one dependent variable.

Accepted Answer

Multiple regression analysis can have several independent variables and only one dependent variable. Option A is incorrect as there can be only one dependent variable. Option B is incorrect as the adjusted coefficient of determination can be negative. Option C is incorrect as the multiple coefficient of determination is always between 0 and 1.

Question 20

A measure of identifying the effect of an unusual x value on the regression results is called
A) Cook's D.
B) Leverage.
C) odd ratio.
D) unusual regression.

Accepted Answer

The answer of A measure of identifying the effect of...

Quiz 15: Multiple Regression

A term used to describe the case when the independent variables in a multiple regression model are correlated is

The mathematical equation that explains how the dependent variable y is related to several independent variables x1, x2, …, xp and the error term ε is a(n)

A multiple regression model has

A variable that takes on the values of 0 or 1 and is used to incorporate the effect of categorical independent variables in a regression model is called

In a multiple regression model, the variance of the error term ε is assumed to be

In regression analysis, the response variable is the

In order to test for the significance of a regression model involving 3 independent variables and 47 observations, the numerator and denominator degrees of freedom (respectively) for the critical value of F are

In regression analysis, an outlier is an observation whose

The equation which has the form of E(y) = = b0 + b1x1 + b2x2 + ... + bpxp is a(n)

The adjusted multiple coefficient of determination is adjusted for the

In a multiple regression model, the error term ε is assumed to be a random variable with a mean of

In multiple regression analysis, the correlation among the independent variables is termed

In a multiple regression model, the error term ε is assumed to

A regression model in which more than one independent variable is used to predict the dependent variable is called

A measure of goodness of fit for the estimated regression equation is the

The mathematical equation which has the form of E(y) = β0 + β1x1 + β2x2 + ... + βpxp relating the expected value of the dependent variable to the value of the independent variables is a(n)

The numerical value of the coefficient of determination.

In a multiple regression model, the values of the error term ε are assumed to be

In multiple regression analysis,

A measure of identifying the effect of an unusual x value on the regression results is called

The mathematical equation that explains how the dependent variable y is related to several independent variables x₁, x₂, …, xp and the error term ε is a(n)

The equation which has the form of E(y) = = b₀ + b₁x₁ + b₂x₂ + ... + b_px_p is a(n)

The mathematical equation which has the form of E(y) = β₀ + β₁x₁ + β₂x₂ + ... + β_pxp relating the expected value of the dependent variable to the value of the independent variables is a(n)