Question 1

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 binary variable that takes on the value of 0 or 1 and is used to represent a categorical independent variable in a regression model. This variable is also known as an indicator variable or a binary variable.

Question 2

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 adjusts for the number of independent variables in the regression model. This is important because as the number of independent variables increases, the standard multiple coefficient of determination tends to increase, even if the added variables do not actually contribute to the prediction of the dependent variable. The adjusted multiple coefficient of determination addresses this issue and gives a more accurate measure of the model's overall fit. The other options (number of dependent variables, number of equations, sample size) do not affect the calculation of the adjusted multiple coefficient of determination.

Question 3

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 should be roughly the same across all values of the independent variables, ensuring that the model's predictions are equally reliable across the entire range of the independent variables.

Question 4

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 in a multiple regression model is assumed to have a mean of zero. This implies that, on average, the errors associated with the model are equal to zero. If the mean of the errors was not zero, then the model would be biased and would not accurately reflect reality.

Question 5

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

In a multiple regression model, there are more than one independent variable. The model attempts to predict a dependent variable using the relationship with multiple independent variables. Therefore, the best choice is C.

Question 6

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

In multiple regression, the error term ε is assumed to be normally distributed with a mean of zero and a variance greater than zero. Therefore, the correct choice is D, as it states that the error term is normally distributed. Choices A, B, and C are incorrect as they do not reflect the assumptions of the error term in multiple regression.

Question 7

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 that is being predicted or explained by the independent variables in the regression analysis. It is the dependent variable, as its value depends on the values of the independent variables. Therefore, option B is the correct answer.

Question 8

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...

Question 9

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 the independent variables in a multiple regression analysis. This can create problems for the analysis, including making it difficult to determine the unique contribution of each variable to the dependent variable and producing unstable estimates of the regression coefficients. Therefore, it is important to check for multicollinearity and address it if present.

Question 10

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 11

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

For a regression model with k independent variables and n observations, the numerator degrees of freedom for the critical value of F is k and the denominator degrees of freedom is n-k-1. Therefore, for this model, the numerator degrees of freedom is 3 and the denominator degrees of freedom is 47-3-1 = 43. Thus, the best choice is D.

Question 12

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 models explain how a dependent variable (y) is related to several independent variables (x1, x2, ..., xp) and an error term (ε).

Question 13

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 (R-squared) is a measure of how well the regression equation fits the data, specifically how much of the variation in the dependent variable can be explained by the independent variables. A value of R-squared closer to 1 indicates a better fit.

Question 14

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 correlation between independent variables in a multiple regression model. This can cause problems such as unstable and unreliable coefficients, as well as reduced predictive power of the model. Regression and correlation are related concepts but do not specifically address the issue of multicollinearity. Leverage refers to the degree to which an observation in a dataset affects the regression line.

Question 15

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

In multiple regression analysis, there can be several independent variables (predictor variables) and one dependent variable (outcome variable). Option A is incorrect because there can be only one dependent variable. Option B is incorrect because the adjusted coefficient of determination can be negative if the model is a poor fit. Option C is incorrect because the multiple coefficient of determination can never be larger than 1 as it represents the proportion of variance in the dependent variable that is explained by the independent variables.

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

Question 17

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

A multiple regression model uses more than one independent variable to predict the dependent variable. Options A, C, and D are not correct definitions for this type of model.

Question 18

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 is equal to the square of the coefficient of correlation. Therefore, it can be larger or smaller than the coefficient of correlation, depending on the value of the coefficient of correlation. It is not necessarily negative if the coefficient of correlation is negative, as it is the squared value of the correlation coefficient.

Question 19

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 a data point that has a residual value that is much larger or smaller than the rest of the residual values. Residuals are the differences between the predicted value and the actual value. An outlier can have a significant impact on the regression line and can distort the results of the analysis.

Question 20

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

The error term ε represents the variability in the dependent variable (Y) that cannot be explained by the independent variables (Xs) in the model. It is assumed that the error term values are independent of each other, meaning that the value of an error term for one observation should not be influenced by the value of the error term for any other observation. Therefore, option C is the correct choice. Option A is incorrect because if the error term values were zero, it would mean that the model perfectly predicts the dependent variable, which is unlikely. Option B is incorrect because the assumption of independence of error term values is violated if they are dependent on each other. Option D is incorrect because the error term values can be positive, negative or zero.

Quiz 15: Multiple Regression

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

The adjusted multiple coefficient of determination is adjusted for the

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

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

A multiple regression model has

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

In regression analysis, the response variable is the

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

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

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

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

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

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

In multiple regression analysis,

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)

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

The numerical value of the coefficient of determination.

In regression analysis, an outlier is an observation whose

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

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

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 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)