Deck 14: Multiple Regression

Question 1

Testing the contribution of individual independent variables with t-tests is performed prior to the F-test for the model in multiple regression analysis.

Answer 1

False

Question 2

The normal plot is a residual plot that checks the normality assumption.

Answer 2

True

Question 3

An application of the multiple regression model generated the following results involving the F test of the overall regression model: p - value = .0012,R² = .67 and s = .076.Thus,the null hypothesis,which states that none of the independent variables are significantly related to the dependent variable,should be rejected at the .05 level of significance.

Answer 3

True

Question 4

If we are predicting y when the values of the independent variables are x01,x02,...... ,x0k,the farther the values of x01,x02,..... ,x0kare from the center of the experimental region,the smaller the distance value and the more precise the associated confidence and prediction intervals.

Question 5

A t-test is used in testing the significance of an individual independent variable.

Question 6

In a regression model,a value of the error term depends upon other values of the error term.

Question 7

The multiple correlation coefficient can assume any value between zero and 1,inclusive.

Question 8

For the same point estimate of the dependent variable and the same level of significance,the confidence interval is always wider than the corresponding prediction interval.

Question 9

Due to the fact that multiple regression models consist of multiple independent variables,residual analysis cannot be performed.

Question 10

The assumption of independent error terms in regression analysis is often violated when using time series data.

Question 11

Completely randomized analysis of variance models (one-way ANOVA)can always be converted to a multiple regression models with dummy independent variables.

Question 12

In a multiple regression analysis,if the normal probability plot exhibits approximately a straight line,then it can be concluded that the assumption of normality is not violated.

Question 13

The error term in the regression model describes the effects of all factors other than the independent variables on y (response variable).

Question 14

Regression models that employ more than one independent variable are referred to as multiple regression models.

Question 15

In a regression model,at any given combination of values of the independent variables,the population of potential error terms is assumed to have an F-distribution.

Question 16

The range of feasible values for the multiple coefficient of determination is from:

A)0 to
B)-1 to 0
C)-1 to 1
D)0 to 1
E)-

Question 17

When the F test is used to test the overall significance of a multiple regression model,if the null hypothesis is rejected,it can be concluded that all of the independent variables x₁,x₂,.....x_k are significantly related to the dependent variable y.

Question 18

Which is not an assumption of a multiple regression model?

A)Positive autocorrelation of error terms
B)Normality of error terms
C)Independence of error terms
D)Constant variation of error terms

Question 19

The multiple coefficient of determination is the _______ divided by the total variation

A)Unexplained variation
B)SSE
C)Explained variation
D)Distance value
E)Leverage value

Question 20

When using a multiple regression model,we assume that error terms (residuals)are distributed according to a(n)________________ distribution.

A)Binomial
B)Normal
C)Exponential
D)Poisson

Question 21

Which of the following is not an assumption of the multiple linear regression model?

A)Independent error terms
B)Population of error terms has a normal distribution.
C)Populations of error terms observed at different combinations of values of the independent variable (x₁,x₂,x_k)have equal variances.
D)The level of measurement of the data for the dependent variable is at least ordinal.
E)At any combination of values of x₁,x₂,x_k,the population of potential error term values has a mean equal to zero.

Question 22

Consider the following partial computer output for a multiple regression model. What is R²?

A)31.308%
B)76.95%
C)87.72%
D)72.63%
E)23.1%

Question 23

For a given multiple regression model with three independent variables,the value of the adjusted multiple coefficient of determination is _________ less than R².

A)Always
B)Sometimes
C)Never

Question 24

In multiple regression analysis,a desirable residual plot has what type of appearance?

A)Curved
B)Cyclical
C)Fanning out
D)Funneling in
E)Horizontal band

Question 25

In multiple regression analysis,the mean square regression divided by mean square error yields the:

A)Standard error
B)F statistic
C)R²
D)Adjusted R² or
E)t statistic

Question 26

In multiple regression analysis,the explained sum of squares divided by the total sum of squares yields the:

A)Standard error
B)F statistic
C)R²
D)Adjusted R² or
E)t statistic

Question 27

In regression analysis,the standard error (s)is _________ greater than the standard deviation of y (the dependent variable).

A)Always
B)Sometimes
C)Never

Question 28

In multiple regression analysis,which one of the following is the appropriate notation for error (residual)?

A)
B)
C)
D)
E)None of the above

Question 29

Consider the following partial computer output for a multiple regression model. What is the adjusted R²?

A)31.308%
B)76.95%
C)87.72%
D)72.63%
E)23.1%

Question 30

An investigator hired by a client suing for sex discrimination has developed a multiple regression model for employee salaries for the company in question.In this multiple regression model,the salaries are in thousands of dollars.For example,a data entry of 35 for the dependent variable indicates a salary of $35,000.The indicator (dummy)variable for gender is coded as X₁ = 0 if male and X₁ = 1 if female.The computer output of this multiple regression model shows that the coefficient for this variable (X₁)is - 4.2.The t test showed that X₁ was significant at $\alpha$ = 0.1.This result implies that for male and female workers of the company,

A)On the average,females earn $4200 less.
B)On the average,males earn $4200 less.
C)On the average,salaries do not differ.
D)On the average,males have 4.2 more years of experience.
E)On the average,females have 4.2 more years of experience.

Question 31

An acceptable residual plot exhibits:

A)Increasing error variance
B)Decreasing error variance
C)Constant error variance
D)A curved pattern
E)A mixture of increasing and decreasing error variance

Question 32

R² is defined as:

A)Total variation/explained variation
B)Explained variation/total variation
C)Unexplained variation/explained variation
D)Total variation/unexplained variation
E)Unexplained variation/total variation

Question 33

A multiple regression analysis with 20 observations on each of three independent variables and the dependent variable would yield ______ and _______ degrees of freedom respectively for regression (explained)and error.

A)3,17
B)3,16
C)4,16
D)3,19
E)3,20

Question 34

If it is desired to include marital status in a multiple regression model by using the categories: single,married,separated,divorced,widowed,what will be the effect on the model?

A)One more independent variable will be included.
B)Two more independent variables will be included.
C)Three more independent variables will be included.
D)Four more independent variables will be included.
E)Five more independent variables will be included.

Question 35

Which of the following residual plots is not used in regression analysis?

A)Residuals vs.parameter estimates
B)Residuals vs.values of an independent variable
C)Residuals vs.time order
D)Residuals vs.predicted values of the dependent variable
E)Standardized residuals vs.predicted values of the dependent variable

Question 36

Consider the following partial computer output for a multiple regression model. How many observations were taken?

A)3
B)16
C)19
D)20
E)13

Question 37

The graph of the prediction equation obtained from the model is a(n)

A)Line
B)Plane
C)Parabola
D)Exponential curve

Question 38

Which one of the following is not an assumption about the residuals in a regression model?

A)Constant variance
B)Independence
C)Normality
D)Variance of zero
E)Mean of zero

Question 39

The range of feasible values for the multiple coefficient of correlation is from:

A)0 to
B)-1 to 0
C)-1 to 1
D)0 to 1
E)-

Question 40

The mean square error of a multiple regression model with k independent variables and n observations is

A)SSE / (n)
B)SSE / [(n)+ (k + 1)]
C)SSE / [(n)- (k + 1)]
D)SSE / (k + 1)

Question 41

_____ variation is the sum of explained variation plus the sum of unexplained variation.

A)Explained
B)Unexplained
C)Error
D)Total

Question 42

The _____ term describes the effects on y of all factors other than the independent variables in a multiple regression model.

A)Dependent
B)t-test
C)Error
D)Dummy

Question 43

The difference between the observed values of y and the predicted value of y is referred to as a/an _____.

A)Dependent variable
B)Predicted value
C)Residual
D)Explained variation

Question 44

Consider the following partial computer output for a multiple regression model. The calculated value of the t statistic for X₁ is ________.

A)2.325
B)-2.325
C)0.4301
D)-0.4301

Question 45

Plotting the residuals in a time-ordered sequence will reveal possible violations of the __________ of error terms assumption.

A)Normality
B)Independence
C)Constant variation
D)Residual sum

Question 46

Dummy or indicator variables typically are values of zero or one,and are used to model the effects of different levels of _____ variables.

A)Qualitative
B)Quantitative
C)Ratio
D)Measured

Question 47

In using the multiple regression method,we can model the effects of the different levels of a qualitative independent variable by using a(n):

A)Interaction variable
B)Cross-product term
C)Quadratic term
D)Dummy (indicator)variable
E)Variance equalizing transformation

Question 48

In a multiple regression model,a point estimate of $\sigma$ ² is called the ________________ error.

A)standard
B)regression
C)mean square
D)multiple regression

Question 49

The effects of different levels of qualitative independent variables are described using _____ variables.

A)Dependent
B)Response
C)Dummy
D)Quantitative

Question 50

The range of the previously observed combinations of values of the independent variables is referred to as the _____.

A)Area under the normal curve
B)Residual
C)Experimental region
D)Correlation coefficient

Question 51

If we are testing the significance of the independent variable X₁ and we reject the null hypothesis H₀: $\beta$ ₁ = 0,we conclude that:

A)X₁ is significantly related to y.
B)X₁ is not significantly related to y.
C)X₁ is an unimportant independent variable.
D) $\beta$ ₁ is significantly related to the dependent variable y.

Question 52

A particular multiple regression model has 3 independent variables,the sum of the squared error is 7680,and the total number of observations is 34.What is the value of the standard error of estimate?

A)256
B)232.72
C)225.89
D)16
E)15.03

Question 53

The y intercept ( $\beta$ ₀)in a multiple regression model represents the estimated value of the ________ variable,when the value of all independent variables is/are _______.

A)Response,one
B)Dummy,zero
C)Response,zero
D)Dummy,one

Question 54

Which one of the following tools is not used to check the normality of residuals assumption for a multiple regression model?

A)Histogram
B)Stem-and-leaf display
C)Scatter diagram
D)Normal plot

Question 55

The multiple _________ measures the proportion of the variation in y (response variable)explained by the multiple regression model or the set of independent variables included in the multiple regression equation.

A)Correlation coefficient
B)Coefficient of determination
C)Total variation
D)Standard error
E)F test

Question 56

In a multiple regression model the residuals were plotted against the values of one of the independent variables.The plot exhibited a funneling out pattern of residuals.This means that as the value of the independent variable increases,the error terms tend to ________ and the model assumption of ________ is violated.

A)increase,constant variance
B)increase,independence
C)decrease,constant variance
D)decrease,normality

Question 57

In a multiple regression analysis,if the normal probability plot ____________,then it can be concluded that the assumption of normality is not violated.

A)Is a straight line
B)Has the shape of a symmetric bell shaped curve
C)Is greatly curved
D)Is left skewed
E)Has the shape of a parabola that opens upward

Question 58

In a multiple regression analysis,if the normal probability plot is a ____________,then it can be concluded that the assumption of normality is not violated.

A)Normal curve
B)Straight line
C)Parabola
D)Curved line

Question 59

In a multiple regression model,the explained sum of squares divided by the total sum of squares yields the ___________.

A)F model
B)t statistic
C)R
D)R²

Question 60

Dummy variables take on the values of ______ and are used to model the effects of different levels of qualitative variables.

A)1 or -1
B)1 or 2
C)0 or 2
D)0 or 1

Question 61

Below is a partial multiple regression ANOVA table.
Test the overall usefulness of the model at $\alpha$ = .05.Calculate the F statistic and make your decision.

Question 62

Below is a partially completed multiple regression analysis of variance (ANOVA)table. Calculate R².

Question 63

Below is a partial multiple regression ANOVA table.

Test the overall usefulness of the model at $\alpha$ = .01.Calculate F and make your decision about whether the model is useful for prediction purposes.

Question 64

Assumptions of a regression model can be evaluated by plotting and analyzing the _________.

A)independent variables
B)dependent variables
C)error terms
D)beta values

Question 65

Consider the following partial computer output for a multiple regression model.
Test the overall usefulness of the model at $\alpha$ = .01.Calculate F and make your decision.

Question 66

Consider the following partial computer output for a multiple regression model. What is the total sum of squares,explained variation,and mean square error?

Question 67

Below is a partial multiple regression ANOVA table. What is the total sum of squares,explained variation,mean square error and the number of observations in the sample?

Question 68

Below is a partial multiple regression computer output. Write the least squares prediction equation.

Question 69

Below is a partial multiple regression computer output. Test the overall usefulness of the model at = .01.Calculate the F statistic and make your decision.

Question 70

Below is a partial multiple regression ANOVA table. Calculate R².

Question 71

Below is a partial multiple regression ANOVA table. Calculate the explained variation.

Question 72

Below is a partial multiple regression ANOVA table. Calculate the adjusted R².

Question 73

Below is a partial multiple regression ANOVA table. How many observations were in the sample?

A)8
B)10
C)12
D)11

Question 74

A(n)________ plot is a residual plot that is used for the purpose of checking the normality assumption of the multiple regression model.

A)Straight line
B)Normal
C)Scatter
D)Quadratic

Question 75

Below is a partial multiple regression ANOVA table. Calculate the proportion of the variation explained by the multiple regression model.

Question 76

Consider the following partial computer output for a multiple regression model. Calculate R².

Question 77

Consider the following analysis of variance table from a multiple regression model.Test the model for overall usefulness at = .01 and carefully make a managerial conclusion.

Question 78

Below is a partial multiple regression ANOVA table. What is the mean square error?

Question 79

Below is a partial multiple regression ANOVA table. What is the total sum of squares and the degrees of freedom for total sum of squares?

Question 80

Below is a partial multiple regression computer output. Determine the number of observations in the sample,the number of independent variables in the model and the mean squared error.