Deck 14: Multiple Regression and Correlation Analysis

Question 1

The values of b₁,b₂ and b₃ in a multiple regression equation are called the sample regression coefficients.

Answer 1

True

Question 2

In a multiple regression analysis with two independent variables,the multiple standard error of estimate measures the variation of the dependent variable about a regression plane.

Answer 2

True

Question 3

In multiple regression analysis,a and b₁ are sample statistics that estimate the population parameters, $\alpha$ and $\beta$ ₁.

Answer 3

True

Question 4

If the hypothesis,H_o: $\beta$ ₁= 0 is rejected,then the sample regression coefficeint b₁,indicates the change in the predicted value for a unit change in X₁ when all other X_i variables are held constant.

Question 5

Multiple R² measures the proportion of explained variation relative to total variation.

Question 6

The values of $\beta$ ₁, $\beta$ ₂ and $\beta$ ₃ in a multiple regression equation are called the sample regression coefficients.

Question 7

A correlation matrix shows individual correlation coefficients for all pairs of variables.

Question 8

To test the global hypothesis in multiple regression analysis,a t-statistic is used.

Question 9

To test the global hypothesis in multiple regression analysis,an F-statistic is used.

Question 10

A correlation matrix can be used to assess multicollinearity between independent variables.

Question 11

If a dummy variable for gender is included in a multiple regression analysis,"male" would be coded as 1 and "female" would be coded as 2.

Question 12

The multiple coefficient of determination, ,reports the proportion of the variation in Y that is not explained by the variation in the set of independent variables.

Question 13

A coefficient of multiple determination could be equal to -0.76.

Question 14

The coefficient of multiple determination reports the strength of the association between a dependent variable and a set of independent variables.

Question 15

Multiple regression analysis is used when two or more independent variables are used to predict a value of a single dependent variable.

Question 16

A multiple regression equation defines the relationship between a dependent variable and a set of independent variables in the form of an equation.

Question 17

A dummy variable is added to the regression equation to control for error.

Question 18

A coefficient of multiple determination equaling -0.99 shows that the dependent variable is inversely related to a set of independent variables.

Question 19

A correlation matrix can be used to assess homoscedasticity between independent variables.

Question 20

Multiple regression analysis is used when one independent variable is used to predict values of two or more dependent variables.

Question 21

In multiple regression analysis,a residual is the difference between the value of an independent variable and its corresponding dependent variable value.

Question 22

A dummy variable is limited to two values.

Question 23

Homoscedasticity occurs when the variance of the residuals (Y - )is different for different values of .

Question 24

In multiple regression analysis,a residual is the difference between the value of a dependent variable,Y,and its predicted value, .

Question 25

Autocorrelation often happens when data has been collected over periods of time.

Question 26

For a global test of a multiple regression equation,the F-statistic is based on the regression and residual degrees of freedom.

Question 27

A variance inflation factor cannot be computed for a dummy variable.

Question 28

An example of a dummy variable is three different "brands of MP3 player".

Question 29

An ANOVA table for multiple regression has the required information to compute the coefficient of multiple determination.

Question 30

In a multiple regression analysis,if the regression coefficient of a dummy variable is significant and has a sample value of 100,then the dummy variable's effect on the dependent variable is: no effect,or an increase of 100.

Question 31

For a global test of a multiple regression equation,the F-statistic is based on the residual degrees of freedom.

Question 32

If a dummy variable for gender is included in a multiple regression analysis,"male" would be coded as 0 and "female" would be coded as 1.

Question 33

To evaluate homoscedasticity,we plot the values of for all values of X.

Question 34

An example of a dummy variable is "time to product's first repair" in years.

Question 35

To evaluate the assumption of linearity,a multiple regression analysis should include

A)calculation of variance inflation factors.
B)hypothesis tests of individual regression coefficients.
C)scatter diagrams of the dependent variable plotted as a function of each independent variable.
D)an ANOVA table.

Question 36

The variance inflation factor is used to select or remove independent variables to reduce the effects of multicollinearity in a multiple regression equation.

Question 37

For a global test of a multiple regression equation,the F- statistic is the mean square error from the ANOVA table.

Question 38

In multiple regression analysis,residual analysis is used to test the requirement that

A)the variation in the residuals is the same for all fitted values of
B)the independent variables are the direct cause of the dependent variable
C)the number of independent variables included in the analysis is correct
D)prediction error is minimized

Question 39

Homoscedasticity occurs when the variance of the residuals (Y - )is the same for all values of X.

Question 40

In a multiple regression analysis,if the regression coefficient of a dummy variable is significant and has a sample value of 100,then the dummy variable's effect on the dependent variable is: no effect,an increase of 100,or a decrease of 100.

Question 41

When does multicollinearity occur in a multiple regression analysis?

A)The dependent variables are highly correlated
B)The independent variables are minimally correlated
C)The independent variables are highly correlated
D)The independent variables have no correlation

Question 42

What are the degrees of freedom associated with the regression sum of squares?

A)Number of independent variables
B)1
C)F-ratio
D)(n - 2)

Question 43

If there are four independent variables in a multiple regression equation,there are also four

A)Y-intercepts.
B)regression coefficients.
C)dependent variables.
D)constant terms.

Question 44

If the coefficient of multiple determination is 0.81,what percent of variation is not explained?

A)19%
B)90%
C)66%
D)81%

Question 45

In multiple regression analysis,when the independent variables are highly correlated,this situation is called ____________________.

A)Autocorrelation
B)Multicollinearity
C)Homoscedasticity
D)Curvilinearity

Question 46

A valid multiple regression analysis assumes or requires that

A)the dependent variable is measured using an ordinal,interval,or ratio scale
B)the residuals follow an F-distribution
C)the independent variables and the dependent variable have a linear relationship
D)the observations are autocorrelated

Question 47

What can we conclude if the global test of regression rejects the null hypothesis?

A)Strong correlations exist among the variables.
B)No relationship exists between the dependent variable and any of the independent variables.
C)At least one of the net regression coefficients is not equal to zero.
D)Good predictions are not possible.

Question 48

What is the range of values for multiple R?

A)-100% to -100% inclusive
B)-100% to 0% inclusive
C)0% to +100% inclusive
D)Unlimited range

Question 49

What does the correlation matrix for a multiple regression analysis contain?

A)Multiple correlation coefficients
B)Simple correlation coefficients
C)Multiple coefficients of determination
D)Multiple standard errors of estimate

Question 50

Which of the following is a characteristic of the F-distribution?

A)Normally distributed
B)Positively skewed
C)Negatively skewed
D)Equal to the t-distribution

Question 51

If the correlation between the two independent variables of a regression analysis is 0.11 and each independent variable is highly correlated to the dependent variable,what does this indicate?

A)Only one of the independent variables should be used in the regression equation.
B)The independent variables are strongly related.
C)Two separate regression equations are required.
D)Both independent variables should be used to predict the dependent variable.

Question 52

If a multiple regression analysis is based on ten independent variables collected from a sample of 125 observations,what will be the value of the denominator in the calculation of the multiple standard error of estimate?

A)125
B)10
C)114
D)115

Question 53

In multiple regression analysis,testing the global null hypothesis that the multiple regression coefficients are all zero is based on

A)a z statistic
B)a t statistic
C)a F statistic
D)binomial distribution

Question 54

In the general multiple regression equation which of the following variables represents the Y intercept?

A)b1
B)x1
C)
D)a

Question 55

If the correlation between the two independent variables of a regression analysis is 0.11 and each independent variable is highly correlated to the dependent variable,what does this indicate?

A)Multicollinearity between these two independent variables
B)A negative relationship is not possible
C)Only one of the two independent variables will explain a high percent of the variation
D)An effective regression equation

Question 56

In a regression analysis,three independent variables are used in the equation based on a sample of forty observations.What are the degrees of freedom associated with the F-statistic?

A)3 and 39
B)4 and 40
C)3 and 36
D)2 and 39

Question 57

What can we conclude if the global test of regression does not reject the null hypothesis?

A)A strong relationship exists among the variables
B)No relationship exists between the dependent variable and any of the independent variables
C)The independent variables are good predictors
D)Good forecasts are possible

Question 58

How is the degree of association between a set of independent variables and a dependent variable measured?

A)Confidence intervals.
B)Autocorrelation.
C)Coefficient of multiple determination.
D)Standard error of estimate.

Question 59

What does the multiple standard error of estimate measure?

A)Change in for a change in X₁
B)The "error" or variability in predicting Y
C)The regression mean square error in the ANOVA table
D)Amount of explained variation

Question 60

In a multiple regression ANOVA table,explained variation is represented by

A)the regression sum of squares
B)the total sum of squares
C)the regression coefficients
D)the correlation matrix

Question 61

Which statistic is used to test a hypothesis a regression equation?

A)t-statistic
B)z-statistic
C) (chi-square statistic)
D)F

Question 62

In multiple regression analysis,a dummy variable is

A)An additional quantitative variable
B)A nominal variable with three or more values
C)A nominal variable with only two values
D)A new regression coefficient

Question 63

The following correlations were computed as part of a multiple regression analysis that used education,job,and age to predict income. Which independent variable has the weakest association with the dependent variable?

A)Income
B)Age
C)Education
D)Job

Question 64

The following correlations were computed as part of a multiple regression analysis that used education,job,and age to predict income. Which independent variable has the strongest association with the dependent variable?

A)Income
B)Age
C)Education
D)Job

Question 65

The coefficient of determination measures the proportion of

A)explained variation relative to total variation.
B)variation due to the relationship among variables.
C)error variation relative to total variation.
D)variation due to regression.

Question 66

In an ANOVA table for a multiple regression analysis,the global test of significance is based on the

A)treatment mean square divided by the error variation
B)block and error variation
C)treatment mean square and block mean square
D)regression mean square divided by the mean square error

Question 67

The best example of a null hypothesis for testing an individual regression coefficient is:

A)Option A
B)Option B
C)Option C
D)Option D

Question 68

For a unit change in the first independent variable with other things being held constant,what change can be expected in the dependent variable in the multiple regression equation ?

A)-7.1
B)+6.3
C)+5.2
D)+4.4

Question 69

The following correlations were computed as part of a multiple regression analysis that used education,job,and age to predict income. Which is the dependent variable?

A)Income
B)Age
C)Education
D)Job

Question 70

Multiple regression analysis is applied when analyzing the relationship between

A)An independent variable and several dependent variables
B)A dependent variable and several independent variables
C)Several dependent variables and several independent variables
D)Several regression equations and a single sample

Question 71

In multiple regression analysis,residuals (Y - Ŷ )are used to:

A)Provide a global test of a multiple regression model.
B)Evaluate multicollinearity.
C)Evaluate homoscedasticity.
D)Compare two regression coefficients.

Question 72

In an ANOVA table for a multiple regression analysis,the mean square of error is

A)the treatment sum of squares divided by the regression degrees of freedom.
B)n - (k - 1 ).
C)the regression sum of squares divided by the regression degrees of freedom.
D)total sum of squares divided by the regression degrees of freedom.

Question 73

In an ANOVA table for a multiple regression analysis,total variation is separated into

A)treatment and error variation
B)regression and residual variation
C)treatment and block variation
D)block and error variation

Question 74

In multiple regression analysis,residuals (Y - Ŷ )are used to:

A)Provide a global test of a multiple regression model.
B)Evaluate the assumption of linearity.
C)Calculate the variance inflation factor.
D)Compare two regression coefficients.

Question 75

What happens as the scatter of data values about the regression plane increases?

A)Standard error of estimate increases
B)R² increases
C)(1 - R²)decreases
D)Error sum of squares decreases

Question 76

The best example of an alternate hypothesis for a global test of a multiple regression model is:

A)Option A
B)Option B
C)Option C
D)Option D

Question 77

Which statistic is used to test hypotheses about individual regression coefficients?

A)t-statistic
B)z-statistic
C) (chi-square statistic)
D)F

Question 78

In multiple regression,a dummy variable is significantly related to the dependent variable when

A)the global test of the regression equation is rejected.
B)the test of the dummy variable's regression coefficient is rejected.
C)the dummy variable is correlated with other independent variables.
D)the dummy variable is coded as 2 or 3.

Question 79

The following correlations were computed as part of a multiple regression analysis that used education,job,and age to predict income. What is this table called?

A)Net regression coefficients
B)Coefficients of nondetermination
C)Analysis of variance
D)Correlation matrix

Question 80

The best example of a null hypothesis for a global test of a multiple regression model is:

A)Option A
B)Option B
C)Option C
D)Option D