Deck 17: Multiple Regression

Question 1

To use the Durbin-Watson test to test for positive first-order autocorrelation, the null hypothesis will be H₀: ____________________ (there is/there is no) first-order autocorrelation.

Answer 1

there is no

Question 2

If the value of the Durbin-Watson statistic, d, satisfies the inequality d_L $\le$ d $\le$ d_U, where d_L and d_U are the critical values for d, then the test for positive first-order autocorrelation is inconclusive.

Answer 2

True

Question 3

Large values of the Durbin-Watson statistic d (d > 2) indicate a positive first-order autocorrelation.

Answer 3

False

Question 4

If the value of the Durbin-Watson test statistic, d, satisfies the inequalities d < d_L or d > 4 - d_L, where d_L and d_U are the critical values of d, we conclude that positive first-order autocorrelation exists.

Question 5

The range of the values of the Durbin-Watson statistic d is ____________________.

Question 6

The Durbin-Watson d statistic is used to check the assumption of normality.

Question 7

If the Durbin-Watson statistic d has values smaller than 2, this indicates

A)a positive first-order autocorrelation
B)a negative first-order autocorrelation
C)no first-order autocorrelation at all
D)None of these choices.

Question 8

The range of the values of the Durbin-Watson statistic d is:

A)-4 $\le$ d $\le$ 4
B)-2 $\le$ d $\le$ 2
C)0 $\le$ d $\le$ 2
D)0 $\le$ d $\le$ 4

Question 9

Small values of the Durbin-Watson statistic d (d < 2) indicate a negative first-order autocorrelation.

Question 10

To use the Durbin-Watson test to test for negative first-order autocorrelation, the null hypothesis will be H₀: ____________________ (there is/there is no) first-order autocorrelation.

Question 11

The range of the values of the Durbin-Watson statistic, d, is 0 $\le$ d $\le$ 4.

Question 12

The Durbin-Watson test allows the statistics practitioner to determine whether there is evidence of first-order autocorrelation.

Question 13

If the Durbin-Watson statistic, d, has values greater than 2, this indicates

A)a positive first-order autocorrelation
B)a negative first-order autocorrelation
C)no first-order autocorrelation at all
D)None of these choices.

Question 14

If the Durbin-Watson statistic has a value close to 0, which assumption is violated?

A)Homoscedasticity.
B)Normality of the errors.
C)Independence of errors.
D)None of these choices.

Question 15

If the residuals in a regression analysis of time ordered data are not correlated, the value of the Durbin-Watson d statistic should be near ____________________.

Question 16

The Durbin-Watson statistic, d, is defined as $d = \sum _ { i = 2 } ^ { n } \left( e _ { i } - e _ { i - 1 } \right) ^ { 2 } / \sum _ { i = 1 } ^ { n } e _ { i }$ , where e_i is the residual at time period i.

Question 17

If the value of the Durbin-Watson statistic d is large (d > 2), this indicates a(n) ____________________ (positive/negative) first-order autocorrelation exists.

Question 18

If the value of the Durbin-Watson statistic d is small (d < 2), this indicates a(n) ____________________ (positive/negative) first-order autocorrelation exists.

Question 19

If the Durbin-Watson statistic has a value close to 4, which assumption is violated?

A)Homoscedasticity
B)Normality of the errors
C)Independence of errors
D)None of these choices.

Question 20

If the value of the Durbin-Watson test statistic, d, satisfies the inequality d > 4-d_L, we conclude that positive first-order autocorrelation exists.

Question 21

One of the consequences of multicollinearity in multiple regression is biased estimates on the slope coefficients.

Question 22

Test the hypotheses: H₀: There is no first-order autocorrelation vs. H₁: There is negative first-order autocorrelation, given that: Durbin-Watson Statistic d = 1.75, n = 20, k = 2, and $\alpha$ = 0.01.

Question 23

____________________ is a condition that exists when independent variables are correlated with one another.

Question 24

If a group of independent variables are not significant individually but are significant as a group at a specified level of significance, this is most likely due to:

A)heteroscedasticity.
B)an error in the analysis.
C)multicollinearity.
D)None of these choices.

Question 25

The parameter estimates are biased when multicollinearity is present in a multiple regression equation.

Question 26

If multicollinearity exists among the independent variables included in a multiple regression model, then:

A)the regression coefficients will be difficult to interpret.
B)the standard errors of the regression coefficients for the correlated independent variables will increase.
C)one or more of the coefficients may have the wrong sign.
D)All of these choices are true.

Question 27

Test the hypotheses H₀: no first-order autocorrelation vs. H₁: first-order autocorrelation, given that: Durbin-Watson Statistic d = 1.89, n = 28, k = 3, and $\alpha$ = 0.05.

Question 28

Multicollinearity is present when there is a high degree of correlation between the dependent variable and any of the independent variables.

Question 29

Multicollinearity is a situation in which two or more of the independent variables are highly correlated with each other.

Question 30

Multicollinearity will result in excessively low standard errors of the parameter estimates reported in the regression output.

Question 31

Multicollinearity is present if the dependent variable is linearly related to one of the explanatory variables.

Question 32

One of the consequences of multicollinearity in multiple regression is inflated standard errors in some or all of the estimated slope coefficients.

Question 33

Which of the following statements regarding multicollinearity is not true?

A)It exists in virtually all multiple regression models.
B)It is also called collinearity and intercorrelation.
C)It is a condition that exists when the independent variables are highly correlated with the dependent variable.
D)All of these choices are true.

Question 34

When the independent variables are correlated with one another in a multiple regression analysis, this condition is called:

A)heteroscedasticity.
B)homoscedasticity.
C)multicollinearity.
D)None of these choices.

Question 35

Given that the Durbin-Watson test is conducted to test for positive first-order autocorrelation with $\alpha$ = .05, n = 20, and there are two independent variables in the model, the critical values for the test are d_L = __________ and d_U = __________, respectively.

Question 36

Multicollinearity affects the t-tests of the individual coefficients as well as the F-test in the analysis of variance for regression because the F-test combines the t-tests into a single test.

Question 37

The problem of multicollinearity arises when the:

A)dependent variables are highly correlated with one another.
B)independent variables are highly correlated with one another.
C)independent variables are highly correlated with the dependent variable.
D)None of these choices.

Question 38

Because of multicollinearity, the t-tests of the individual coefficients may indicate that some independent variables are not linearly related to the dependent variable, when in fact they are.

Question 39

Test the hypotheses H₀: There is no first-order autocorrelation vs. H₁: There is positive first-order autocorrelation, given that: Durbin-Watson Statistic d = 1.12, n = 45, k = 5, and $\alpha$ = 0.05.

Question 40

Multicollinearity is present when there is a high degree of correlation between the independent variables included in the regression model.

Question 41

How do you go about checking for multicollinearity?

Question 42

A high correlation between two independent variables is an indication of ____________________.

Question 43

One clue to the presence of multicollinearity is an independent variable known to be an important predictor that ends up having a regression coefficient that is not ____________________.

Question 44

Three predictor variables are being considered for use in a linear regression model. Given the correlation matrix below, does it appear that multicollinearity could be a problem?

Question 45

In reference to the equation $\hat { y } = 1.86 - 0.51 x _ { 1 } + 0.60 x _ { 2 }$ , the value 0.60 is the average change in y per unit change in x₂, regardless of the value of x₁.

Question 46

In multiple regression analysis, the adjusted coefficient of determination is adjusted for the number of independent variables and the sample size.

Question 47

In a multiple regression analysis involving 50 observations and 5 independent variables, the total variation in y is 475 and SSE = 71.25. Then, the coefficient of determination is 0.85.

Question 48

A practical way to identify multicollinearity is through the examination of a correlation ____________________ that shows the correlations of each variable with each of the other variables.

Question 49

A multiple regression model involves 40 observations and 4 independent variables produces a total variation in y of 100,000 and SSR = 80,400. Then, the value of MSE is 560.

Question 50

In testing the significance of a multiple regression model with three independent variables, the null hypothesis is $H _ { 0 } : \beta _ { 1 } = \beta _ { 2 } = \beta _ { 3 }$ .

Question 51

In reference to the equation $\hat { y } = - 0.80 + 0.12 x _ { 1 } + 0.08 x _ { 2 }$ , the value -0.80 is the y-intercept.

Question 52

In reference to the equation $\hat { y } = - 0.80 + 0.12 x _ { 1 } + 0.08 x _ { 2 }$ , the value 0.12 is the average change in y per unit change in x₁, when x₂ is held constant.

Question 53

There are several clues to the presence of multicollinearity. One clue is when a regression coefficient exhibits the wrong ____________________.

Question 54

A multiple regression equation has a coefficient of determination of 0.81. Then, the percentage of the variation in y that is explained by the regression equation is 90%.

Question 55

In order to test the significance of a multiple regression model involving 4 independent variables and 25 observations, the numerator and denominator degrees of freedom for the critical value of F are 3 and 21, respectively.

Question 56

There are several clues to the presence of multicollinearity. One clue is when an independent variable is added or deleted, the regression coefficients for the other variables ____________________.

Question 57

Discuss two indicators that can be found in an analysis that suggest multicollinearity is present.

Question 58

An adverse effect of multicollinearity is that the estimated regression coefficients of the independent variables that are correlated tend to have large sampling ____________________.

Question 59

In a multiple regression analysis involving 4 independent variables and 30 data points, the number of degrees of freedom associated with the sum of squares for error, SSE, is 25.

Question 60

Most statistical software print a second R² statistic, called the coefficient of determination adjusted for degrees of freedom, which has been adjusted to take into account the sample size and the number of independent variables.

Question 61

When an additional explanatory variable is introduced into a multiple regression model, coefficient of determination adjusted for degrees of freedom can never decrease.

Question 62

When an additional explanatory variable is introduced into a multiple regression model, the coefficient of determination will never decrease.

Question 63

In a multiple regression analysis, if the model provides a poor fit, this indicates that:

A)the coefficient of determination will be close to zero.
B)the standard error of estimate will be large.
C)the sum of squares for error will be large.
D)All of these choices are true.

Question 64

The adjusted coefficient of determination is adjusted for the:

A)number of independent variables and the sample size.
B)number of dependent variables and the sample size.
C)coefficient of correlation and the significance level.
D)number of regression parameters including the y-intercept.

Question 65

In regression analysis, the total variation in the dependent variable y, measured by $\sum \left( y _ { i } - \bar { y } \right) ^ { 2 }$ , can be decomposed into two parts: the explained variation, measured by SSR, and the unexplained variation, measured by SSE.

Question 66

Suppose a multiple regression analysis involving 25 data points has $s _ { z } ^ { 2 } = 1.8$ and SSE = 36. Then, the number of the independent variables must be:

A)3
B)4
C)5
D)6

Question 67

A high value of the coefficient of determination significantly above 0 in multiple regression, accompanied by insignificant t-statistics on all parameter estimates, very often indicates a high correlation between independent variables in the model.

Question 68

A multiple regression model is assessed to be good if the error sum of squares SSE and the standard error of estimate s _{$\varepsilon$} are both small, the coefficient of determination R² is close to 1, and the value of the test statistic F is large.

Question 69

A multiple regression is called "multiple" because it has several explanatory variables.

Question 70

When an explanatory variable is dropped from a multiple regression model, the adjusted coefficient of determination can increase.

Question 71

From the coefficient of determination, we cannot detect the strength of the relationship between the dependent variable y and any individual independent variable.

Question 72

In multiple regression, the standard error of estimate is defined by $s _ { z } = \sqrt { \operatorname { SSE } / ( n - k ) }$ , where n is the sample size and k is the number of independent variables.

Question 73

A multiple regression model has the form $\hat { y } = b _ { 0 } + b _ { 1 } x _ { 1 } + b _ { 2 } x _ { 2 }$ . The coefficient b₁ is interpreted as the average change in y per unit change in x₁.

Question 74

When an explanatory variable is dropped from a multiple regression model, the coefficient of determination can increase.

Question 75

The total variation in y in a regression model will never exceed the regression sum of squares (SSR).

Question 76

A small value of F indicates that most of the variation in y is explained by the regression equation and that the model is useful.

Question 77

The coefficient of determination R² measures the proportion of variation in y that is explained by the explanatory variables included in the model.

Question 78

A multiple regression model is assessed to be poor if the error sum of squares SSE and the standard error of estimate s _{$\varepsilon$} are both large, the coefficient of determination R² is close to 0, and the value of the test statistic F is large.

Question 79

In calculating the standard error of the estimate, $s _ { z } = \sqrt { \mathrm { MSE } }$ , there are (n - k - 1) degrees of freedom, where n is the sample size and k is the number of independent variables in the model.

Question 80

In multiple regression analysis, when the response surface (the graphical depiction of the regression equation) hits every single point, the sum of squares for error SSE = 0, the standard error of estimate s _{$\varepsilon$} = 0, and the coefficient of determination R² = 1.