Deck 11: Regression Analysis: Statistical Inference

Question 1

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.

Answer 1

False

Question 2

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

Answer 2

False

Question 3

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.

Answer 3

True

Question 4

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 5

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 6

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

Question 7

In multiple regression,if the F-ratio is large,the explained variation is large relative to the unexplained variation.

Question 8

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

Question 9

In regression analysis,homoscedasticity refers to constant error variance.

Question 10

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 11

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 12

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 13

In multiple regression,if the F-ratio is small,the explained variation is small relative to the unexplained variation.

Question 14

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 15

If exact multicollinearity exists,redundancy exists in the data.

Question 16

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

Question 17

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 18

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 19

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 20

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

Question 21

Heteroscedasticity means that the variability of Y values is larger for some X values than for others.

Question 22

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

Question 23

The Durbin-Watson statistic can be used to test for autocorrelation.

Question 24

Another term for constant error variance is

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

Question 25

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

Question 26

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 27

An 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 28

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 29

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,because the F-test combines these t-tests into a single test.

Question 30

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 31

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 32

In regression analysis,multicollinearity refers to the

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

Question 33

The term autocorrelation refers to the observation that

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 34

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 35

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 36

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

A)There is a population regression line that joins the means of the dependent variable for all values of the explanatory variables.
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 37

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 38

Homoscedasticity means that the variability of Y values is the same for all X values.

Question 39

Which statement is true regarding regression error,ε?

A)It is the same as a residual.
B)It can be calculated from the predicted observations.
C)It cannot be calculated from the observed data.
D)It is unbiased.

Question 40

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 41

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

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

Question 42

There is evidence that the regression equation provides little explanatory power when the F-ratio

A)is large.
B)equals the regression coefficient.
C)is small.
D)is the constant.

Question 43

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 44

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

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

Question 45

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 46

In the standardized value ,the symbol represents the

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

Question 47

The appropriate hypothesis test for an ANOVA test is

A) .
B) .
C) .
D) .

Question 48

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)does not fit the guidelines of parsimony.

Question 49

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 _____ regression.

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

Question 50

Time series data often exhibits which of the following characteristics?

A)Homoscedasticity
B)Heteroscedasticity
C)Autocorrelation
D)Multicollinearity

Question 51

The appropriate hypothesis test for a regression coefficient is

A) .
B) .
C) .
D)none of these choices.

Question 52

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

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

Question 53

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 54

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)Large t-values for the coefficients for the left and right foot size

Question 55

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 choices

Question 56

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)some of the variation in the explanatory variable and some of the variation in the response variable.

Question 57

Which definition 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 58

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 59

The objective typically used in the tree types of equation-building procedures is to find the equation with

A)a small s_e.
B)a large R².
C)a small s_e and a large R².
D)the smallest F-ratio.

Question 60

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

A)Look at the t-value and associated p-value.
B)Check whether the t-value is less than or greater than 1.0.
C)The variables are logically related to one another.
D)Use economic or physical theory to make the decision.

Question 61

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

A)There is a population regression line.
B)The explanatory variable is normally distributed.
C)The response variable is normally distributed.
D)The errors are probabilistically independent.

Question 62

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

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

Question 63

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 64

Which approach can be used to test for autocorrelation?

A)Regression coefficient
B)Correlation coefficient
C)Durbin-Watson statistic
D)F-test or t-test

Question 65

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

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

Question 66

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 67

Residuals separated by one period that are autocorrelated indicate _____ autocorrelation.

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

Question 68

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 69

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)do not have observations for every period in the sample.