Exam 2

When an analysis of variance is performed on samples drawn from k populations, the mean square between treatments (MSTR) is _____. a. SSTR/nT b. SSTR/k c. SSTR/(k - 1) d. SSTR/(nT - 1)

SSTR/(k - 1)

An ANOVA procedure is used for data obtained from five populations. Five samples, each comprised of 20 observations, were taken from the five populations. The numerator and denominator (respectively) degrees of freedom for the critical value of F are _____. a. 4 and 95 b. 4 and 20 c. 4 and 99 d. 5 and 20

a. 4 and 95

In a regression analysis, if r2 = 1, then _____. a. SSE must be equal to 0 b. SSE must also be equal to 1 c. SSE can be any positive value d. SSE must be negative

a. SSE must be equal to 0

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

a. dependent variable

Exhibit 15-4 a. y = β0 + β1x1 + β2x2 + ε b. E(y) = β0 + β1x1 c. ŷ = b0 + b1 x1 + b2 x2 d. E(y) = β0 + β1x1 + β2x2 Which equation describes the multiple regression model? a. equation a b. equation d c. equation c d. equation b

a. equation a

A term that means the same as the term "variable" in an ANOVA procedure is _____. a. factor b. replication c. variance within d. treatment

a. factor

An experimental design that permits statistical conclusions about two or more factors is a _____. a. factorial design b. completely randomized design c. randomized block design d. randomized design

a. factorial design

If a qualitative variable has k levels, the number of dummy variables required is _____. a. k − 1 b. 2k c. k d. k + 1

a. k − 1

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

a. multiple coefficient of determination

In a multiple regression model, the variance of the error term ε is assumed to be _____. a. the same for all values of the independent variable b. −1 c. the same for all values of the dependent variable d. 0

a. the same for all values of the independent variable

In a simple regression analysis (where y is a dependent and x an independent variable), if the slope is positive, then it must be true that _____. a. there is a positive correlation between x and y b. the y-intercept is 0 c. there is no correlation between x and y d. there is a negative correlation between x and y

a. there is a positive correlation between x and y

The ANOVA procedure is a statistical approach for determining whether the means of _____. a. two or more populations are equal b. two samples are equal c. more than two samples are equal d. two or more samples are equal

a. two or more populations are equal

To test for the significance of a regression model involving 8 independent variables and 121 observations, the numerator and denominator degrees of freedom (respectively) for the critical value of F are _____. a. 7 and 120 b. 8 and 112 c. 8 and 121 d. 7 and 112

b. 8 and 112 (Observations-variables(n))-1

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

b. SSR/SST

In regression analysis, if the dependent variable is measured in dollars, the independent variable _____. a. must be in some unit of currency b. can be any units c. must also be in dollars d. cannot be in dollars

b. can be any units

The interval estimate of the mean value of y for a given value of x is the _____. a. prediction interval b. confidence interval c. correlation interval d. residual interval

b. confidence interval

In factorial designs, the response produced when the treatments of one factor interact with the treatments of another in influencing the response variable is known as _____. a. the main effect b. interaction c. a factor d. replication

b. interaction

In a regression analysis, the variable that is used to predict the dependent variable ______. a. usually is denoted by y b. is the independent variable c. is the dependent variable d. must have the same units as the variable doing the predicting

b. is the independent variable

Larger values of r2 imply that the observations are more closely grouped about the _____. a. origin b. least squares line c. average value of the dependent variable d. average value of the independent variables

b. least squares line

The equation that describes how the dependent variable (y) is related to the independent variable (x) is called _____. a. the correlation model b. the regression model c. the least squares criterion d. correlation analysis

b. the regression model

If two variables, x and y, have a strong linear relationship, then _____. a. the slope of the regression equation must be negative b. there may or may not be any causal relationship between x and y c. x causes y to happen d. y causes x to happen

b. there may or may not be any causal relationship between x and y

In ANOVA, which of the following is NOT affected by whether or not the population means are equal? a. x̄ b. within-samples estimate of σ2 c. between-samples estimate of σ2 d. Population means must be equal in ANOVA.

b. within-samples estimate of σ2

In simple linear regression analysis, which of the following is NOT true? a. The relationship between x and y is represented by means of a straight line. b. The F test and the t test yield the same results. c. The F test and the t test may or may not yield the same results. d. The value of F = t2.

c. The F test and the t test may or may not yield the same results.

A regression model in which more than one independent variable is used to predict the dependent variable is called _____. a. a dependent model b. a simple linear regression model c. a multiple regression model d. an independent model

c. a multiple regression model

In a multiple regression model, the error term ε is assumed to _____. a. have a variance of 0 b. have a mean of 1 c. be normally distributed d. have a standard deviation of 1

c. be normally distributed

The mean square is the sum of squares divided by _____. a. the sample size b. its corresponding degrees of freedom minus1 c. its corresponding degrees of freedom d. the total number of observations

c. its corresponding degrees of freedom

A least squares regression line ______. a. can only be determined if a good linear relationship exists between x and y b. is only used for positively correlated data c. may be used to predict a value of y if the corresponding x value is given d. implies a cause-effect relationship between x and y

c. may be used to predict a value of y if the corresponding x value is given

As the goodness of fit for the estimated regression equation increases, the _____. a. value of the correlation coefficient increases b. absolute value of the regression equation's slope increases c. value of the coefficient of determination increases d. value of the regression equation's y-intercept decreases

c. value of the coefficient of determination increases

An ANOVA procedure is used for data that were obtained from six sample groups each comprised of seven observations. The degrees of freedom for the critical value of F are _____. a. 5 and 42 b. 6 and 37 c. 5 and 41 d. 5 and 36

d. 5 and 36

Which of the following is correct? a. SSR = SSE + SST b. SSE = SSR + SST c. SST = (SSR)2 d. SST = SSR + SSE

d. SST = SSR + SSE

Exhibit 15-4 a. y = β0 + β1x1 + β2x2 + ε b. E(y) = β0 + β1x1 c. ŷ = b0 + b1 x1 + b2 x2 d. E(y) = β0 + β1x1 + β2x2 Which equation describes the multiple regression equation? a. equation b b. equation a c. equation c d. equation d

d. equation d

Application of the least squares method results in values of the y-intercept and the slope that minimizes the sum of the squared deviations between the _____. a. predicted values of the independent variable and the actual values of the dependent variable b. actual values of the independent variable and the predicted values of the dependent variable c. observed values of the independent variable and the predicted values of the independent variable d. observed values of the dependent variable and the predicted values of the dependent variable

d. observed values of the dependent variable and the predicted values of the dependent variable

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

If there is a very strong negative correlation between two variables, then the correlation coefficient must be _____. a. very close to 1 b. very close to -0.5 c. exactly 0 d. very close to -1

d. very close to -1

In regression analysis, the independent variable is typically plotted on the _____. a. y-axis of a scatter diagram b. x-axis of a histogram c. y-axis of a histogram d. x-axis of a scatter diagram

d. x-axis of a scatter diagram