Deck 12: Multiple Regression

Question 1

The mean square in an Analysis of Variance (ANOVA) for multiple regression is the explained sum of squares (MSR) divided by the unexplained sum of squares (MSE).

Answer 1

False

Question 2

The standard error of the estimate (s_y.x) in multiple linear regression is the square of the Mean Square Error (MSE).

Answer 2

False

Question 3

In regression analysis, a set of binary (0-1) variables can be used to introduce qualitative (categorical) variables into the model.

Answer 3

True

Question 4

The square root of the Mean Square Error (MSE) gives the standard error of estimate in regression analysis.

Question 5

Introducing a series of highly correlated independent variables into a regression analysis will make it difficult to interpret the estimated regression coefficients because they may tend to fluctuate widely in response to small changes in the model or data set.

Question 6

In multiple regression, one's goal should be to effectively explain the variation in the dependent variable by using as many independent variables as possible.

Question 7

Residual analysis may make use of a plot showing the residuals or errors to evaluate the assumptions about the error term.

Question 8

In simple linear regression analysis, when testing for significance, the F test and the t test will always yield consistent results.

Question 9

In simple linear regression analysis, when testing for significance, the F test and the t test will always result in the same conclusion.

Question 10

The Mean Square Regression (MSR) in an Analysis of Variance (ANOVA) for multiple regression is the sum of squares divided by (sample size -1) degrees of freedom.

Question 11

In regression analysis, a data point that does not fall along the least squares line (or plane) is called a residual.

Question 12

The mean square (MS) values in an Analysis of Variance (ANOVA) for multiple regression are the sum of squares (SS) values divided by their corresponding degrees of freedom.

Question 13

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 dummy variable.

Question 14

In multiple regression, adding more independent variables to the model will never decrease the value of r².

Question 15

In regression analysis, a residual plot that shows a clear pattern rather than random behavior can be generally considered an indication that at least one assumption regarding the error terms is being violated.

Question 16

In multiple regression analysis, multicollinearity (or simply collinearity) refers to the correlation among the independent variables.

Question 17

In multiple regression, an adjusted r² value can be used to help avoid adding more and more potentially collinear independent variables to the model.

Question 18

In multiple linear regression, the correlation coefficient is reported as a non-negative value.

Question 19

The coefficient of determination r², a measure of the goodness of fit of the estimated regression equation, is the ratio of the explained variation in y (SSR) to the total variation in y (SST), and takes on values between 0 and 1.

Question 20

In multiple linear regression analysis, rejecting the "all $\beta$ s are 0" null hypothesis means that you have found no useful relationship between the variables.

Question 21

Which of the following relationships in linear regression is correct?

A)SSE = SSR + SST
B)SSR = SSE + SST
C)SST = (SSR)²
D)SST = SSR + SSE
E)none of the above

Question 22

In residual analysis for multiple regression, if the assumptions about the error term are valid and the model is an adequate representation of the relationships between the variables, then the plot of the residuals versus the predicted y values

A)shows a horizontal band of points
B)has a funnel shape
C)has a curved shape
D)is upward sloping
E)none of the above

Question 23

A regression analysis linking demand (y in 1000 units) to price (x₁ in dollars) and advertising (x₂ in $1000s) resulted in the following equation: estimated Y = 9 - 5x₁ + 2x₂.This equation implies that a $1 increase in price can be associated with a ____ in demand.

A)9000 - 5000 = 4000 unit increase
B)9000 unit decrease
C)9000 + 5000 = 14,000 unit decrease
D)5,000 unit decrease
E)none of the above

Question 24

Adding independent variables to a regression model will typically_______ the value of r².

A)decrease
B)increase
C)not affect
D)nullify
E)reduce by half or more

Question 25

In regression analysis, which of the following is NOT a required assumption about the error term, $\varepsilon$ ?

A)the expected value of the error term is zero
B)the error term has a normal distribution
C)the standard deviation of the error term is constant
D)the values of the error term are independent
E)none of the above, all are required assumptions

Question 26

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

A)auto-regression
B)multi-collinearity
C)correlation
D)coefficient of determination
E)none of the above

Question 27

Which of the following is true regarding the F distribution?

A)it is the ratio of two variances from two normal populations
B)it is not symmetric
C)values can never be negative
D)it has numerator degrees of freedom from sample 1 and denominator degrees of freedom from sample 2
E)all of the above

Question 28

In regression analysis, if r² = 1, then

A)SSE = SST
B)SSR = SST
C)SSR = SSE
D)SSE = 1
E)none of the above

Question 29

In simple linear regression analysis, which of the following is NOT true?

A)the F test and the t test yield the same results
B)the F test and the t test have different p-values
C)the relationship between x and y is represented by means of a straight line
D)the value of F = t²
E)none of the above

Question 30

Larger values of r² imply that the observations are more closely grouped about the

A)average value of the independent variables
B)average value of the dependent variable
C)least squares line or plane
D)origin
E)none of the above

Question 31

Which of the following is NOT true regarding the coefficient of determination, r²?

A)it is the sum of squares error (SSE) divided by the sum of squares total (SST)
B)it is a measure of the goodness of fit of the estimated regression equation
C)it takes on values between 0 and 1
D)it explains the amount of variation in y associated with variation in x
E)none of the above: all are true

Question 32

The adjusted r² value is adjusted for

A)the number of dependent variables
B)the number of independent variables
C)the number of equations
D)the number of numbers
E)none of the above

Question 33

In simple linear regression, if the correlation coefficient is a positive value, then the slope of the estimated regression line

A)must also be positive
B)can be either negative or positive
C)can be zero
D)must be negative
E)none of the above

Question 34

In simple linear regression, a least squares regression line

A)assumes a relationship between the slope of x and the intercept of y
B)may be used to predict a value of y if the corresponding x value is given
C)must be linear, upward-sloping and have a positive y-intercept
D)minimizes the sum of the deviations between the observed value of y and the estimated value of y
E)all of the above

Question 35

In a simple linear regression model, the variance of the error term $\varepsilon$ is assumed to be

A)the same for all values of x
B)zero
C)increasing as x values increase
D)-1
E)none of the above

Question 36

In multiple linear regression, which of the following is NOT true about the hypothesis tests:

A)the F test measures the overall significance of the regression equation
B)the t test measures the significance of an individual regression coefficient
C)F = t² just as in simple linear regression
D)the null hypothesis for the F test is that all the slopes are equal to 0
E)the null hypothesis for the t test is that the particular slope is equal to 0

Question 37

In the ANOVA table for simple linear regression, the mean square regression (MSR) is the

A)sum of squares regression (SSR) divided by degrees of freedom = 1
B)sum of squares regression (SSR) divided by degrees of freedom = n-2
C)mean square total minus mean square error
D)mean square error divided by mean square total
E)none of the above

Question 38

In multiple regression, the adjusted r² value is generally

A)greater than r²
B)used to discourage adding more independent variables.
C)used to encourage adding more independent variables.
D)test for the significance of y
E)a and d

Question 39

Adding independent variables to a regression model will ______ decrease the value of r².

A)sometimes
B)never
C)always
D)rarely
E)often

Question 40

In regression analysis, which of the following is not a required assumption about the error term $\varepsilon$ :

A)the expected value of the error term is zero
B)the variance of the error term is constant
C)the values of the error term must be positive.
D)the error term is normally distributed
E)all of the above

Question 41

A simple regression analysis linking a dependent variable y to an independent variable x is conducted with 20 observations.The p-value value for t_stat in the  = 0 hypothesis test turns out to be .0162.The p-value value for F_stat in the same test must be

A)1 - .0162 = .9838.
B)2 times .0162 = .0324
C).0162.
D)statistically significant at the 1% significance level.
E)none of the above

Question 42

1% of the values in an F distribution with numerator degrees of freedom= 5 and denominator degrees of freedom = 22 are greater than ___.

A)3.988
B)2.661
C)4.102
D)3.939
E)2.699

Question 43

A regression analysis involved 4 independent variables and 20 observations.In using the F table to find the critical value of F for testing the 'all s are 0' null hypothesis, the numerator degrees of freedom should be

A)15
B)4
C)2
D)16
E)none of the above

Question 44

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
E)none of the above

Question 45

A simple regression analysis linking dependent variable y to independent variable x is conducted with 25 observations.The value of F_stat used to test the $\beta$ = 0 null hypothesis turns out to be 12.7.The value of t_stat for the x coefficient is

A)15
B)3.56
C)12.7
D)161.29
E)cannot be determined from the information given

Question 46

A simple regression analysis linking dependent variable y to independent variable x is conducted with 20 observations.The F ratio used to test the  = 0 null hypothesis indicates that the slope coefficient is statistically significant at the 5% significance level.The value of t_stat for the x coefficient will also show that the slope coefficient is

A)statistically significant at the 2.5% significance level.
B)greater than F
C)statistically significant at the 5% significance level.
D)statistically significant at the 1% significance level.
E)none of the above

Question 47

A regression analysis involved 5 independent variables and 15 observations..In using the F table to find the critical value of F for testing the 'all s are 0' null hypothesis, the denominator degrees of freedom should be

A)9
B)10
C)14
D)4
E)none of the above

Question 48

5% of the values in an F distribution with numerator degrees of freedom = 3 and denominator degrees of freedom = 12 are greater than ___.

A)3.634
B)4.451
C)6.112
D)6.226
E)3.490

Question 49

A regression analysis involved 6 independent variables and 20 observations.In using the F table to find the critical value of F for testing the 'all s are 0' null hypothesis, the denominator degrees of freedom should be

A)26
B)13
C)14
D)25
E)none of the above

Question 50

A multiple regression analysis uses 5 independent variables and 15 observations.The F ratio for testing the 'all s are 0' null hypothesis turns out to be statistically significant at the 5% significance level.It must be true that ____ of the regression coefficients are (is) statistically significant at the 5% level.

A)all
B)at least one
C)most
D)none
E)none of the above

Question 51

A regression analysis involved 6 independent variables and 27 observations.The t distribution in which we will find the critical value of t for testing the significance of each of the independent variable coefficients will have

A)20 degrees of freedom
B)21 degrees of freedom
C)26 degrees of freedom
D)27 degrees of freedom
E)none of the above

Question 52

In an F distribution with numerator degrees of freedom of 4 and denominator degrees of freedom of 8, 99% of the values are less than ______ .

A)3.838
B)6.041
C)7.006
D)14.799

Question 53

5% of the values in an F distribution with numerator degrees of freedom = 3 and denominator degrees of freedom = 17 are greater than ___.

A)3.758
B)2.576
C)2.549
D)3.812
E)3.197