Deck 15: Model Building and Model Diagnostics

Question 1

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

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

Answer 1

C

Question 2

When the quadratic regression model y = ₀ + ₁x + ₂x² + $\varepsilon$ is used the term ₁ shows the rate of curvature of the parabola.

Answer 2

True

Question 3

The standard error decreases if and only if the adjusted multiple coefficient of determination decreases.

Answer 3

False

Question 4

If we increase the number of independent variables in a multiple regression model,the F statistic will always increase.

Question 5

In the quadratic regression model the ₁ term represents the:

A)Rate of curvature of the parabola.
B)Value of Y when X is zero.
C)Shift parameter of the parabola.
D)Y-intercept of the parabola.

Question 6

An independent variable dropped during an iteration of the backward elimination process may be added back to the regression model during a later iteration of the process.

Question 7

In multiple regression analysis,if the simple correlation coefficient between the dependent variable and one of the independent variables is .95,then this indicates that the problem of multicollinearity exists.

Question 8

As we increase the number of independent variables in a multiple regression model,the F statistic will _____ increase.

A)Always
B)Sometimes
C)Never

Question 9

The general form of the quadratic multiple regression models is:

A)y =
B)y =
C)y =
D)y =
E)y =

Question 10

In the quadratic regression model if the term ₂ is ______ zero,then the parabola opens __________.

A)Less than,upward
B)Greater than,upward
C)Greater than,either upward or downward
D)Less than,either upward or downward
E)Equal to,downward

Question 11

In comparing regression models,the regression model with the largest R² will also have the smallest standard error(s).

Question 12

One way to identify outliers with respect to their x values is to calculate their leverage values.

Question 13

When there are indications of autocorrelation,first an investigation should be conducted to determine whether one or more independent variables that might explain the autocorrelation have been omitted from the model.

Question 14

Multicollinearity hinders the regression model's ability to predict the dependent variable on the basis of a combination of values of the independent variable in the experimental region.

Question 15

If a particular multiple regression model has a small value of the C statistic and C for this model is less than k + 1,where k is the number of independent variables in the model,then the model should be considered biased and therefore undesirable.

Question 16

In a multiple regression mode if the largest VIF is 21.6,then it can be concluded that there are indications of multicollinearity.

Question 17

The variance inflation factor measures the relationship between the dependent variable and the rest of the independent variables in the regression model.

Question 18

Even when an unimportant variable is added to a regression model,the explained variation will increase.

Question 19

In the quadratic regression model ,the v₂ term represents the:

A)Rate of curvature of the parabola.
B)Value of Y when X is zero.
C)Shift parameter of the parabola.
D)Y-intercept of the parabola.

Question 20

Cook's distance is a way to determine whether an observation is influential.

Question 21

If the Durbin-Watson statistic is less than d_L,then it is concluded that

A)There is significant positive autocorrelation.
B)There is significant negative autocorrelation.
C)There is significant autocorrelation but it cannot be identified whether it is positive or negative.
D)The test results are inconclusive.

Question 22

As we increase the number of independent variables in a multiple regression model,the F statistic in the analysis of variance table for the multiple regression model will ________ increase.

A)Always
B)Sometimes
C)Never

Question 23

The Durbin-Watson test statistic ranges from:

A)-4 to 4
B)0 to 4
C)0 to 3
D)-1 to 1
E)0 to 1

Question 24

What value of Durbin-Watson statistic indicates there is no autocorrelation present in a time ordered data?

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

Question 25

As rough rule of thumb,if the absolute value of the studentized residual for an observation is greater than ______,then it is concluded that there is some evidence that the observation is an outlier.

A)1
B)2
C)2.5
D)4

Question 26

Multicollinearity between independent variables is serious if the mean variance inflation factor is

A)Substantially less than 1
B)Substantially greater than 1
C)Between - 1 and + 1
D)Less than .5
E)Substantially less than zero

Question 27

Dropping an independent variable from a multiple linear regression model will always result in

A)An increase in the MSE value
B)An increase in the R² value
C)A decrease in the R² value
D)A decrease in the MSE value

Question 28

A very insignificant independent variable (an independent variable that has a very weak relationship with the dependent variable)is added to a multiple regression equation.As a result of this change,the value of explained variation (SSR)will _________,the value of multiple coefficient of determination (R²)will _________,and the calculated value of the F statistic will most likely _________.

A)Decrease,increase,decrease
B)Increase,decrease,decrease
C)Increase,increase,increase
D)Increase,increase,decrease
E)Decrease,decrease,decrease

Question 29

Which one of the following procedures is not a variable selection method for multiple regression analysis?

A)Backward elimination
B)Stepwise regression
C)Durbin-Watson test
D)Maximum R² improvement
E)Best subset regression based on all possible combinations of multiple regression equations

Question 30

In a multiple regression analysis,the current model has three independent variables.The analyst decides to add another (fourth)independent variable while retaining the other three independent variables.As a result of this addition,the value of SSE will ____________ decrease.

A)Always
B)Sometimes
C)Never

Question 31

In a multiple regression analysis,the current model has three independent variables.The analyst decides to add another (fourth)independent variable while retaining the other three independent variables.As a result of this addition,the value of MSE will ____________ decrease.

A)Always
B)Sometimes
C)Never

Question 32

If a regression model with k independent variables has a C statistic less than _______,then the model is considered to be desirable.

A)k + 1
B)k
C)k-1
D)1/k
E)k-2

Question 33

If the Durbin-Watson statistic is greater than (4 - d_L),then it is concluded that

A)There is significant positive autocorrelation.
B)There is significant negative autocorrelation.
C)There is significant autocorrelation but it cannot be identified whether it is positive or negative.
D)The test result is inconclusive.

Question 34

In a multiple regression analysis,the current model has three independent variables.The analyst decides to add another (fourth)independent variable while retaining the other three independent variables.As a result of this addition,the value of adjusted R² will ____________ decrease.

A)Always
B)Sometimes
C)Never

Question 35

In using a regression model,if a new independent variable is added,the value of the R² (coefficient of multiple determination)will ___________ decrease.

A)Always
B)Sometimes
C)Never

Question 36

In a multiple regression analysis,the current model has three independent variables.The analyst decides to add another (fourth)independent variable while retaining the other three independent variables.As a result of this addition,the value of explained variation will ____________ decrease.

A)Always
B)Sometimes
C)Never

Question 37

A leverage value is considered to be large if it is substantially greater than

A).5 times the average leverage value
B)1.5 times the average leverage value
C)2.0 times the average leverage value
D)5.0 times the average leverage value
E)4.0 times the average leverage value

Question 38

Adding any independent variable to a regression model will increase

A)Adjusted R² or
B)s
C)MSE
D)R²
E)The length of all prediction intervals

Question 39

All of the following are desirable outcomes for a multiple regression model except

A)High R²
B)Small s
C)Small C statistic
D)Large Cook's distance measure
E)Large F statistic

Question 40

Cook's distance measure is used in:

A)Determining if there is significant first order auto-correlation.
B)Identifying influential observations in multiple regression analysis.
C)Determining the significance of an independent variable.
D)Determining if there is significant multicollinearity.
E)Determining if the overall regression model is significant.

Question 41

In multiple regression analysis an outlier observation is ____________ influential.

A)Always
B)Sometimes
C)Never

Question 42

In a multiple regression model we can conclude that multicollinearity exists if the average variance inflation factor is substantially greater than _____.

A)100
B)5
C)10
D)1

Question 43

When independent variables in a regression model are related to,or dependent on each other,then there exists _____ among the independent variables.

A)Multicollinearity
B)Autocorrelation
C)Independence
D)Probability

Question 44

_________ regression method is used when the response variable is a qualitative or a categorical variable.

A)Quadratic
B)Logistics
C)Multiple
D)Simple

Question 45

In residual analysis,as the value of the leverage _____________,the value of the studentized residual _____________.

A)Decreases,increases
B)Increases,decreases
C)Decreases,decreases
D)None of the above

Question 46

When the quadratic regression model y = $\beta$ ₀ + $\beta$ ₁x + $\beta$ ₂x² + $\varepsilon$ is used,the term _____ shows the rate of curvature of the parabola.

A) $\beta$ ₁
B) $\beta$ ₂
C) $\beta$ 0

Question 47

If the simple correlation coefficient between two independent variables is greater than .90,then ______________________ is considered to be severe.

A)autocorrelation
B)interaction
C)multicollinearity
D)coefficient of determination

Question 48

Given the regression model y = $\beta$ ₀ + $\beta$ ₁X₁ + $\beta$ ₂X₂ + $\beta$ ₃X₁² + $\beta$ ₄X₂² + $\varepsilon$ ,if we wish to test the significance of higher order terms, (X₁² and X₂²)we would use the following test.

A)Overall F test
B)Durbin-Watson test
C)Partial F test
D)t test
E)Cook's distance measure

Question 49

A(n)_____ observation is an observation that causes the least squares point estimates to be substantially different from what they would be if the observation were removed from the data.

A)Outlier
B)Dummy
C)Influential
D)Quadratic

Question 50

Given the regression model y = $\beta$ ₀ + $\beta$ ₁X₁ + $\beta$ ₂X₂ + $\beta$ ₃X₁² + $\beta$ ₄X₂² + $\varepsilon$ ,if we wish to test the significance of the independent variable X₂,the appropriate null hypothesis is:

A)H₀: X₂ = 0
B)H₀: $\beta$ ₂ $\neq$ 0
C)H₀: $\beta$ ₂ $\neq$ X₂
D)H₀: $\beta$ ₂ = 0
E)H₀: $\beta$ ₂ - X₂ = 0

Question 51

An overall measure of the difference between the least squares point estimates calculated using observation i,and the least squares point estimates calculated without using observation i is called the ____________ measure.

A)Durbin-Watson
B)Cook's distance
C)R²
D)C

Question 52

In the quadratic regression model y = $\beta$ ₀ + $\beta$ ₁x + $\beta$ ₂x² + $\varepsilon$ ,if the term $\beta$ ₂ is greater than zero,then the parabola opens __________.

A)Up
B)Down
C)To the left
D)To the right

Question 53

In the quadratic regression model y = $\beta$ ₀ + $\beta$ ₁x + $\beta$ ₂x² + $\varepsilon$ ,if the value of the term $\beta$ ₁ increases,then the parabola shifts _________.

A)Left
B)Right
C)Up
D)Down

Question 54

The _____ procedure works the same way as the stepwise regression procedure except that once an independent variable is eliminated from the model,it is never returned to the model.

A)logistic
B)stepwise
C)quadratic
D)backward

Question 55

In multiple regression analysis which of the following can be used to identify multicollinearity?

A)The VIF
B)The correlation matrix
C)The standard error of estimate
D)Both A and B
E)All of the above

Question 56

In regression analysis the _________ is used to identify outliers with respect to their x values and ________ is used to identify outliers with respect to their y values.

A)Leverage value,Durbin-Watson statistic
B)Leverage value,residuals
C)Residuals,standardized residuals
D)Durbin-Watson statistic,residuals
E)Variance Inflation Factor,Leverage value

Question 57

The primary use of stepwise regression is to identify the most important ___________ that should be included in the multiple regression model.

A)independent variables
B)dependent variables
C)dummy variables
D)quadratic variables

Question 58

Multicollinearity is severe if the largest variance inflation factor (VIF)is greater than _____.

A)100
B)5
C)10
D)1

Question 59

Which one of the following is not a tool used to identify multicollinearity?

A)Variance Inflation Factor
B)Correlation matrix
C)Studentized residuals
D)Scatter plots that show the scatter plots for all combinations of variables in the regression model

Question 60

In a multiple regression model,as a result of adding a new independent variable,as s ___________,the length of the prediction interval for y will _________.

A)Increases,always increase
B)Decreases,sometimes decrease
C)Increases,never increase
D)Decreases,always increase
E)Increases,always decrease

Question 61

Significant _________ may exist when the overall F-statistic is significant and the individual t statistics for all independent variables is insignificant.

A)autocorrelation
B)independence
C)Multicollinearity
D)outliers

Question 62

Inclusion of redundant independent variables in the regression model increases the problem of __________.

A)autocorrelation
B)independence
C)Multicollinearity
D)outliers

Question 63

In a regression model a(n)______ is an observation that is well separated from the rest of the data with respect to its y value and/or its x values.

A)Outlier
B)Influential
C)Independent
D)Dependent

Question 64

Below is a partial multiple regression computer output based on a quadratic regression model.
Test the overall usefulness of the model at $\alpha$ = .05.Calculate the F statistic and make your decision.

Question 65

Stepwise regression uses a series of _____ tests during each iteration in order to determine which independent variables should be brought into the regression model.

A)C
B)F
C)t
D)VIF

Question 66

Multicollinearity affects the ability of the ____ statistic in assessing the importance of an independent variable.

A)C
B)F
C)t
D)VIP

Question 67

If successive values of the residuals are close together,then there is a(n)___________ autocorrelation,and the value of the Durbin-Watson statistic is _________.

A)negative,large
B)positive,small
C)negative,small
D)positive,large

Question 68

When using a multiple linear regression model,data transformations on the dependent variable may be used in order to correct a violation of a(n)__________ of the multiple linear regression model.

A)assumption
B)independent variables
C)autocorrelation
D)normality

Question 69

Below is a partial multiple regression computer output based on a quadratic regression model to predict student enrollment at a local university.The dependent variable is the annual enrollment given in thousands of students,the independent variable X is the increase in tuition stated in thousands of dollars per year,and X² is the square of tuition increase given in squared thousands of dollars per year.
Interpret $\beta$ ₀ (the y intercept)and $\beta$ ₁ (the $\beta$ coefficient for the X variable).Does the parabola open upward or downward? Why?

Question 70

If a multiple regression model has a(n)_____ statistic substantially greater than k + 1,then it can be shown that this model has substantial bias and is undesirable.

A)C
B)F
C)Cook's distance
D)Durbin-Watson

Question 71

In general,a multiple regression model is considered to be desirable if the value of the C statistic is small and the value of C is less than _____.

A)k
B)k - 1
C)k + 1
D)n - k

Question 72

The _____________ statistic is used to test for autocorrelation among the residuals.

A)Cook's distance
B)C
C)Durbin-Watson
D)R²

Question 73

When the assumption of __________ - residuals (error terms)is violated,the Durbin-Watson statistic is used to test to determine if there is significant _____________ among the residuals.

A)normality,probability
B)independent,probability
C)independent,autocorrelation
D)normality,autocorrelation

Question 74

If the absolute value of the ______________ is greater than t_.005,then there is strong evidence that the observation is an outlier with respect to its y value.

A)Cook's distance
B)C statistic
C)F
D)studentized deleted residual

Question 75

Below is a partial multiple regression computer output based on a quadratic regression model. Test the usefulness of the variable X² in the model at = .05.

Question 76

Below is a partial multiple regression computer output based on a quadratic regression model. Calculate R².

Question 77

___________ is an iterative variable selection procedure that allows an independent variable to be added to a multiple regression model in one iteration and deleted during the next iteration?

A)Logistic regression
B)Stepwise regression
C)Quadratic regression
D)Backward regression

Question 78

Below is a partial multiple regression computer output based on a quadratic regression model. Determine the number of observations in the sample,explained variation and the MSE.

Question 79

In converting the residual to a studentized (standardized)residual for a given observation,the residual for the observation is divided by the residual's __________.

A)sample size
B)t value
C)standard error
D)square

Question 80

Below is a partial multiple regression computer output based on a quadratic regression model. Assuming a quadratic model was used,write the least squares prediction equation.