Statistics Chapter 15 MC Questions

A measure of goodness of fit for the estimated regression equation is the a. multiple coefficient of determination b. mean square due to error c. mean square due to regression d. sample size

a. multiple coefficient of determination

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

a. zero

In a regression model involving more than one independent variable, which of the following tests must be used in order to determine if the relationship between the dependent variable and the set of independent variables is significant? a. t test b. F test c. Either a t test or a chi-square test can be used. d. chi-square test

b. F test

A measure of 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

b. Leverage

The correct relationship between SST, SSR, and SSE is given by a. SSR = SST + SSE b. SSR = SST - SSE c. SSE = SSR - SST d. None of these alternatives is correct.

b. SSR = SST - SSE

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. None of these alternatives is correct.

b. a multiple regression model

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. a simple nonlinear regression model b. a multiple regression model c. an estimated multiple regression equation d. a multiple regression equation

b. a multiple regression model

In regression analysis, the response variable is the a. independent variable b. dependent variable c. slope of the regression function d. intercept

b. dependent variable

The adjusted multiple coefficient of determination is adjusted for a. the number of dependent variables b. the number of independent variables c. the number of equations d. detrimental situations

b. the number of independent variables

In a multiple regression analysis involving 12 independent variables and 166 observations, SSR = 878 and SSE = 122. The coefficient of determination is a. 0.1389 b. 0.1220 c. 0.878 d. 0.7317

c. 0.878

A regression model involved 5 independent variables and 136 observations. The critical value of t for testing the significance of each of the independent variable's coefficients will have a. 121 degrees of freedom b. 135 degrees of freedom c. 130 degrees of freedom d. 4 degrees of freedom

c. 130 degrees of freedom

A regression analysis involved 8 independent variables and 99 observations. The critical value of t for testing the significance of each of the independent variable's coefficients will have a. 98 degrees of freedom b. 97 degrees of freedom c. 90 degrees of freedom d. 7 degrees of freedom

c. 90 degrees of freedom

The multiple coefficient of determination is a. MSR/MST b. MSR/MSE c. SSR/SST d. SSE/SSR

c. SSR/SST

A variable that takes on the values of 0 or 1 and is used to incorporate the effect of qualitative variables in a regression model is called a. an interaction b. a constant variable c. a dummy variable d. None of these alternatives is correct.

c. a dummy variable

The estimate of the multiple regression equation based on the sample data, which has the form of E(y) = B0 + B1x1 + B2x2 +...+BpXp is a. a simple linear regression model b. a multiple nonlinear regression model c. an estimated multiple regression equation d. a multiple regression equation

c. an estimated multiple regression equation

A multiple regression model has the form ŷ = 7 + 2x1 + 9x2 As x1 increases by 1 unit (holding x2 constant), y is expected to a. increase by 9 units b. decrease by 9 units c. increase by 2 units d. decrease by 2 units

c. increase by 2 units

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

c. independent of each other

In a situation where the dependent variable can assume only one of the two possible discrete values, a. we must use multiple regression b. there can only be two independent variables c. logistic regression should be applied d. all the independent variables must have values of either zero or one

c. logistic regression should be applied

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 2 dependent variables

c. more than one independent variable

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. None of the above answers is correct.

c. multicollinearity

In multiple regression analysis, the correlation among the independent variables is termed a. homoscedasticity b. linearity c. multicollinearity d. adjusted coefficient of determination

c. multicollinearity

In logistic regression, a. there can only be two independent variables b. there are two dependent variables c. the dependent variable only assumes two discrete values d. the dependent variable only assumes two continuous values

c. the dependent variable only assumes two discrete values

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. -1

c. the same for all values of the independent variable

In a multiple regression analysis involving 15 independent variables and 200 observations, SST = 800 and SSE = 240. The coefficient of determination is a. 0.300 b. 0.192 c. 0.500 d. 0.700

d. 0.700

For a multiple regression model, SSR = 600 and SSE = 200. The multiple coefficient of determination is a. 0.333 b. 0.275 c. 0.300 d. 0.75

d. 0.75

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

d. 3 and 43

The ratio of MSE/MSR yields a. SST b. the F statistic c. SSR d. None of these alternatives is correct.

d. None of these alternatives is correct.

In a multiple regression analysis SSR = 1,000 and SSE = 200. The F statistic for this model is a. 5.0 b. 1,200 c. 800 d. Not enough information is provided to answer this question.

d. Not enough information is provided to answer this question.

The mathematical equation relating the expected value of the dependent variable to the value of the independent variables, which has the form of E(y) = B0 + B1x1 + B2x2 +...+BpXp is a. a simple linear regression model b. a multiple nonlinear regression model c. an estimated multiple regression equation d. a multiple regression equation

d. a multiple regression equation

A variable that cannot be measured in numerical terms is called a. a non-measurable random variable b. a constant variable c. a dependent variable d. a qualitative variable

d. a qualitative variable

A variable that cannot be measured in terms of how much or how many but instead is assigned values to represent categories is called a. an interaction b. a constant variable c. a category variable d. a qualitative variable

d. a qualitative variable

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 a standard deviation of 1 d. be normally distributed

d. be normally distributed

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 determination is negative d. can be larger or smaller than the coefficient of correlation

d. can be larger or smaller than the coefficient of correlation

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

d. residual is much larger than the rest of the residual values

In multiple regression analysis, a. there can be any number of dependent variables but only one independent variable b. there must be only one independent variable c. the coefficient of determination must be larger than 1 d. there can be several independent variables, but only one dependent variable

d. there can be several independent variables, but only one dependent variable