Deck 11: Regression Analysis: Statistical Inference

Question 1

In regression analysis,the ANOVA table analyzes:

A)the variation of the response variable Y
B)the variation of the explanatory variable X
C)the total variation of all variables
D)All of these options

Answer 1

A

Question 2

The t-value for testing is calculated using which of the following equations:

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

Answer 2

D

Question 3

Another term for constant error variance is:

A)homoscedasticity
B)heteroscedasticity
C)autocorrelation
D)multicollinearity

Answer 3

A

Question 4

A scatterplot that exhibits a "fan" shape (the variation of Y increases as X increases)is an example of:

A)homoscedasticity
B)heteroscedasticity
C)autocorrelation
D)multicollinearity

Question 5

Which of the following is not one of the assumptions of regression?

A)There is a population regression line
B)The response variable is normally distributed
C)The standard deviation of the response variable increases as the explanatory variables increase
D)The errors are probabilistically independent

Question 6

Which of the following definitions best describes parsimony?

A)Explaining the most with the least
B)Explaining the least with the most
C)Being able to explain all of the change in the response variable
D)Being able to predict the value of the response variable far into the future

Question 7

The test statistic in an ANOVA analysis is:

A)the t-statistic
B)the z-statistic
C)the F-statistic
D)the Chi-square statistic

Question 8

The value k in the number of degrees of freedom,n-k-1,for the sampling distribution of the regression coefficients represents:

A)the sample size
B)the population size
C)the number of coefficients in the regression equation,including the constant
D)the number of independent variables included in the equation

Question 9

The ANOVA table splits the total variation into two parts.They are the

A)acceptable and unacceptable variation
B)adequate and inadequate variation
C)resolved and unresolved variation
D)explained and unexplained variation

Question 10

Which of the following is the relevant sampling distribution for regression coefficients?

A)Normal distribution
B)t-distribution with n-1 degrees of freedom
C)t-distribution with n-1-k degrees of freedom
D)F-distribution with n-1-k degrees of freedom

Question 11

The appropriate hypothesis test for a regression coefficient is:

A)
B)
C)
D)None of these options

Question 12

Which of the following is true regarding regression error,e

A)it is the same as a residual
B)it can be calculated from the observed data
C)it cannot be calculated from the observed data
D)it is unbiased

Question 13

In regression analysis,multicollinearity refers to:

A)the response variables being highly correlated
B)the explanatory variables being highly correlated
C)the response variable(s)and the explanatory variable(s)are highly correlated with one another
D)the response variables are highly correlated over time.

Question 14

Time series data often exhibits which of the following characteristics?

A)homoscedasticity
B)heteroscedasticity
C)autocorrelation
D)multicollinearity

Question 15

The error term represents the vertical distance from any point to the

A)estimated regression line
B)population regression line
C)value of the Y's
D)mean value of the X's

Question 16

Suppose you run a regression of a person's height on his/her right and left foot sizes,and you suspect that there may be multicollinearity between the foot sizes.What types of problems might you see if your suspicions are true?

A)"Wrong" values for the coefficients for the left and right foot size
B)Large p-values for the coefficients for the left and right foot size
C)Small t-values for the coefficients for the left and right foot size
D)All of these options

Question 17

The appropriate hypothesis test for an ANOVA test is:

A)
B)
C)
D)

Question 18

Which of the following is not one of the guidelines for including/excluding variables in a regression equation?

A)Look at t-value and associated p-value
B)Check whether t-value is less than or greater than 1.0
C)Variables are logically related to one another
D)Use economic or physical theory to make decision
E)All of these options are guidelines

Question 19

The term autocorrelation refers to:

A)analyzed data refers to itself
B)sample is related too closely to the population
C)data are in a loop (values repeat themselves)
D)time series variables are usually related to their own past values

Question 20

In the standardized value ,the symbol represents the:

A)mean of
B)variance of
C)standard error of
D)degrees of freedom of

Question 21

Many statistical packages have three types of equation-building procedures.They are:

A)forward,linear and non-linear
B)forward,backward and stepwise
C)simple,complex and stepwise
D)inclusion,exclusion and linear

Question 22

Forward regression:

A)begins with all potential explanatory variables in the equation and deletes them one at a time until further deletion would do more harm than good.
B)adds and deletes variables until an optimal equation is achieved.
C)begins with no explanatory variables in the equation and successively adds one at a time until no remaining variables make a significant contribution.
D)randomly selects the optimal number of explanatory variables to be used

Question 23

When the error variance is nonconstant,it is common to see the variation increases as the explanatory variable increases (you will see a "fan shape" in the scatterplot).There are two ways you can deal with this phenomenon.These are:

A)the weighted least squares and a logarithmic transformation
B)the partial F and a logarithmic transformation
C)the weighted least squares and the partial F
D)stepwise regression and the partial F

Question 24

When determining whether to include or exclude a variable in regression analysis,if the p-value associated with the variable's t-value is above some accepted significance value,such as 0.05,then the variable:

A)is a candidate for inclusion
B)is a candidate for exclusion
C)is redundant
D)not fit the guidelines of parsimony

Question 25

Suppose you forecast the values of all of the independent variables and insert them into a multiple regression equation and obtain a point prediction for the dependent variable.You could then use the standard error of the estimate to obtain an approximate

A)confidence interval
B)prediction interval
C)hypothesis test
D)independence test

Question 26

In regression analysis,extrapolation is performed when you:

A)attempt to predict beyond the limits of the sample
B)have to estimate some of the explanatory variable values
C)have to use a lag variable as an explanatory variable in the model
D)don't have observations for every period in the sample

Question 27

A researcher can check whether the errors are normally distributed by using:

A)a t-test or an F-test
B)the Durbin-Watson statistic
C)a frequency distribution or the value of the regression coefficient
D)a histogram or a Q-Q plot

Question 28

Multiple regression represents an improvement over simple regression because it allows any number of response variables to be included in the analysis.

Question 29

There are situations where a set of explanatory variables forms a logical group.The test to determine whether the extra variables provide enough extra explanatory power to warrant inclusion in the equation is referred to as the:

A)complete F-test
B)reduced F-test
C)partial F-test
D)reduced t-test

Question 30

Which of the following would be considered a definition of an outlier?

A)An extreme value for one or more variables
B)A value whose residual is abnormally large in magnitude
C)Values for individual explanatory variables that fall outside the general pattern of the other observations
D)All of these options

Question 31

The assumptions of regression are: 1)there is a population regression line,2)the dependent variable is normally distributed,3)the standard deviation of the response variable remains constant as the explanatory variables increase,and 4)the errors are probabilistically independent.

Question 32

If you can determine that the outlier is not really a member of the relevant population,then it is appropriate and probably best to:

A)average it
B)reduce it
C)delete it
D)leave it

Question 33

The _____ can be used to test for autocorrelation.

A)regression coefficient
B)correlation coefficient
C)Durbin-Watson statistic
D)F-test or t-test

Question 34

In time series data,errors are often not probabilistically independent.

Question 35

The objective typically used in the tree types of equation-building procedures are to:

A)find the equation with a small s_e
B)find the equation with a large R²
C)find the equation with a small s_e and a large R²
D)find the equation with the largest F-statistic

Question 36

In regression analysis,homoscedasticity refers to constant error variance.

Question 37

If exact multicollinearlity exists,that means that there is redundancy in the data.

Question 38

If residuals separated by one period are autocorrelated,this is called:

A)simple autocorrelation
B)redundant autocorrelation
C)time 1 autocorrelation
D)lag 1 autocorrelation

Question 39

A point that "tilts" the regression line toward it,is referred to as a(n):

A)magnetic point
B)influential point
C)extreme point
D)explanatory point

Question 40

Determining which variables to include in regression analysis by estimating a series of regression equations by successively adding or deleting variables according to prescribed rules is referred to as:

A)elimination regression
B)forward regression
C)backward regression
D)stepwise regression

Question 41

A backward procedure is a type of equation building procedure that begins with all potential explanatory variables in the regression equation and deletes them two at a time until further deletion would reduce the percentage of variation explained to a value less than 0.50.

Question 42

In multiple regression,if there is multicollinearity between independent variables,the t-tests of the individual coefficients may indicate that some variables are not linearly related to the dependent variable,when in fact they are.

Question 43

In regression analysis,the unexplained part of the total variation in the response variable Y is referred to as sum of squares due to regression,SSR.

Question 44

In testing the overall fit of a multiple regression model in which there are three explanatory variables,the null hypothesis is .

Question 45

In multiple regressions,a large value of the test statistic F indicates that most of the variation in Y is unexplained by the regression equation and that the model is useless.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 46

In a multiple regression analysis involving 4 explanatory variables and 40 data points,the degrees of freedom associated with the sum of squared errors,SSE,is 35.

Question 47

Suppose that one equation has 3 explanatory variables and an F-ratio of 49.Another equation has 5 explanatory variables and an F-ratio of 38.The first equation will always be considered a better model.

Question 48

In regression analysis,the total variation in the dependent variable Y,measured by and referred to as SST,can be decomposed into two parts: the explained variation,measured by SSR,and the unexplained variation,measured by SSE.

Question 49

In order to test the significance of a multiple regression model involving 4 explanatory variables and 40 observations,the numerator and denominator degrees of freedom for the critical value of F are 4 and 35,respectively.

Question 50

In a simple linear regression model,testing whether the slope of the population regression line could be zero is the same as testing whether or not the linear relationship between the response variable Y and the explanatory variable X is significant.

Question 51

A multiple regression model involves 40 observations and 4 explanatory variables produces SST = 1000 and SSR = 804.The value of MSE is 5.6.

Question 52

In a multiple regression problem involving 30 observations and four explanatory variables,SST = 800 and SSE = 240.The value of the F-statistic for testing the significance of this model is 14.583.

Question 53

The residuals are observations of the error variable .Consequently,the minimized sum of squared deviations is called the sum of squared error,labeled SSE.

Question 54

In multiple regression,the problem of multicollinearity affects the t-tests of the individual coefficients as well as the F-test in the analysis of variance for regression,since the F-test combines these t-tests into a single test.

Question 55

In simple linear regression,if the error variable is normally distributed,the test statistic for testing is t-distributed with n - 2 degrees of freedom.

Question 56

In a simple linear regression problem,if the standard error of estimate = 15 and n = 8,then the sum of squares for error,SSE,is 1,350.

Question 57

When there is a group of explanatory variables that are in some sense logically related,all of them must be included in the regression equation.

Question 58

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

Question 59

In multiple regression with k explanatory variables,the t-tests of the individual coefficients allows us to determine whether (for i = 1,2,….,k),which tells us whether a linear relationship exists between and Y.

Question 60

The value of the sum of squares due to regression,SSR,can never be larger than the value of the sum of squares total,SST.

Question 61

In order to estimate with 90% confidence a particular value of Y for a given value of X in a simple linear regression problem,a random sample of 20 observations is taken.The appropriate t-value that would be used is 1.734.

Question 62

(A)Estimate a multiple regression model that includes the two given explanatory variables.Assess this set of explanatory variables with an F-test,and report a p-value.
(B)Conduct a partial F-test to decide whether it is worthwhile to add second-order terms (i.e., )to the multiple regression equation estimated in Question 114.Employ a 5% significance level in conducting this hypothesis test.
(C)Identify and interpret the percentage of variance explained for the model in (A).
(D)Identify and interpret the percentage of variance explained for the model in (B).
(E)Which regression equation is the most appropriate one for modeling the quality of the given product? Bear in mind that a good statistical model is usually parsimonious.

Question 63

(A)Determine the least-squares multiple regression equation.
(B)Interpret the Y- intercept of the regression equation.
(C)Interpret the partial regression coefficients.
(D)What is the estimated number of new visitors to a club if the size of the ad is 6 column-inches and a $100 discount is offered?
(E)Determine the approximate 95% prediction interval for the number of new visitors to a given club when the ad is 5 column-inches and the discount is $80.
(F)What is the value for the percentage of variation explained,and exactly what does it indicate?
(G)At the 0.05 level,is the overall regression equation in (A)significant?
(H)Use the 0.05 level in concluding whether each partial regression coefficient differs significantly from zero.
(I Interpret the results of the preceding tests in (H)and (I)in the context of the two explanatory variables described in the problem.
(J)Construct a 95% confidence interval for each partial regression coefficient in the population regression equation.

Question 64

(A)Estimate a multiple regression model for the data.
(B)Which of the variables in this model have regression coefficients that are statistically different from 0 at the 5% significance level?
(C)Given your findings in (B),which variables,if any,would you choose to remove from the model estimated in (A)? Explain your decision.

Question 65

The Durbin-Watson statistic can be used to measure of autocorrelation.

Question 66

(A)Summarize the findings of the stepwise regression method using this cutoff value.
(B)When the cutoff value was increased to 0.10,the output below was the result.The table at top left represents the change when the disposable income variable is added to the model and the table at top right represents the average price variable being added.The regression model with both added variables is shown in the bottom table.Summarize the results for this model.
(C)Which model would you recommend using? Why?

Question 67

(A)Estimate a simple linear regression model using the sample data.How well does the estimated model fit the sample data?
(B)Perform an F-test for the existence of a linear relationship between Y and X.Use a 5% level of significance.
(C)Plot the fitted values versus residuals associated with the model in Question 119.What does the plot indicate?
(D)How do you explain the results you have found in (A)through (C)?
(E)Suppose you learn that the 10^th employee in the sample has been fired for missing an excessive number of work-hours during the past year.In light of this information,how would you proceed to estimate the relationship between the number of work-hours an employee misses per year and the employee's annual wages,using the available information? If you decide to revise your estimate of this regression equation,repeat (A)and (B)

Question 68

(A)Use the information related to the multiple regression model to determine whether each of the regression coefficients are statistically different from 0 at a 5% significance level.Summarize your findings.
(B)Test at the 5% significance level the relationship between Y and X in each of the simple linear regression models.How does this compare to your answer in (A)? Explain.
(C)Is there evidence of multicollinearity in this situation? Explain why or why not.

Question 69

Below you will find a scatterplot of data gathered by a mail-order company.The company has been able to obtain the annual salaries of their customers and the amount that each of these customers spent with the company in 1998.Based on the scatterplot below,would you conclude that these data meet all four assumptions of regression? Explain your answer.

Question 70

A forward procedure is a type of equation building procedure that begins with only one explanatory variable in the regression equation and successively adds one variable at a time until no remaining variables make a significant contribution.

Question 71

(A)Estimate the regression model.How well does this model fit the data?
(B)Is there a linear relationship between the explanatory variables and the dependent variable? Explain how you arrived at your answer at the 5% significance level.
(C)Use the estimated regression model to predict the amount of money a customer will spend if their annual salary is $45,000,they have 1 child and they were a customer that purchased merchandise in the previous year (2004).
(D)Find a 95% prediction interval for the point prediction calculated in (C).Use a t-multiple = 2.02.
(E)Find a 95% confidence interval for the amount of money spent by all customers sharing the characteristics described in (C).Use a t-multiple = 2.02.
(F)How do you explain the differences between the widths of the intervals in (D)and (E)?

Question 72

One method of diagnosing heteroscedasticity is to plot the residuals against the predicted values of Y,then look for a change in the spread of the plotted values.

Question 73

If the partial F test indicates that a group of variables is significant,it also implies that each variable in the group is significant.

Question 74

(A)Estimate the regression model.How well does this model fit the given data?
(B)Yes,there is a linear relationship between the number of carpet installations and the number of building permits issued at a = 0.10; The p-value = 0.0866 for the F-statistic.You can conclude that there is a significant linear relationship between these two variables.
(C)The Durbin-Watson statistic for this data was 1.2183.Given this information what would you conclude about the data?
(D)Given your answer in (C),would you recommend modifying the original regression model? If so,how would you modify it?

Question 75

(A)Estimate the regression model.How well does this model fit the given data?
(B)Is there a linear relationship between X and Y at the 5% significance level? Explain how you arrived at your answer.
(C)Use the estimated regression model to predict the number of caps that will be sold during the next month if the average selling price is $10.
(D)Find a 95% prediction interval for the number of caps determined in Question 90.Use t- multiple = 2.
(E)Find a 95% confidence interval for the average number of caps sold given an average selling price of $10.Use a t-multiple = 2.
(F)How do you explain the differences between the widths of the intervals in (D)and (E)?

Question 76

The partial F test is a procedure to determine whether extra variables in a group provide any extra explanatory power in the regression equation

Question 77

One of the potential characteristics of an outlier is that the value of the dependent variable is much larger or smaller than predicted by the regression line.

Question 78

A confidence interval constructed around a point prediction from a regression model is called a prediction interval,because the actual point being estimated is not a population parameter

Question 79

(A)Estimate the regression model.How well does this model fit the given data?
(B)Is there a linear relationship between the two explanatory variables and the dependent variable at the 5% significance level? Explain how you arrived at your answer.
(C)Use the estimated regression model to predict the annual maintenance expense of a truck that is driven 14,000 miles per year and is 5 years old.
(D)Find a 95% prediction interval for the maintenance expense determined in (C).Use a t-multiple = 2.
(E)Find a 95% confidence interval for the maintenance expense for all trucks sharing the characteristics provided in Question 96.Use a t-multiple = 2.
(F)How do you explain the differences between the widths of the intervals in (D)and (E)?

Question 80

One method of dealing with heteroscedasticity is to try a logarithmic transformation of the data.