Deck 11: Regression Analysis: Statistical Inference

Question 1

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

Answer 1

True

Question 2

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.

Answer 2

True

Question 3

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.

Answer 3

True

Question 4

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 5

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

Question 6

In multiple regression with k explanatory variables,the t-tests of the individual coefficients allows us to determine whether $B _ { i } \neq 0$
(for i = 1,2,…. ,k),which tells us whether a linear relationship exists between $x$
and Y.

Question 7

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

Question 8

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

Question 9

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 10

In simple linear regression,if the error variable $\varepsilon$
is normally distributed,the test statistic for testing $H _ { 0 } : B _ { 1 } = 0$
is t-distributed with n - 2 degrees of freedom.

Question 11

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 12

In regression analysis,the total variation in the dependent variable Y,measured by $\sum \left( y _ { i } - \bar { y } \right) ^ { 2 }$
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 13

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 14

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 15

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 16

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

Question 17

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 18

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

Question 19

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

Question 20

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 21

In a simple linear regression model,testing whether the slope $\beta _ { 1 }$
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 22

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 23

In regression analysis,homoscedasticity refers to constant error variance.

Question 24

In testing the overall fit of a multiple regression model in which there are three explanatory variables,the null hypothesis is $H _ { 0 } : B _ { 1 } = B _ { 2 } = B _ { 3 }$
.

Question 25

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

Question 26

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

Question 27

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 28

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

Question 29

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 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

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 32

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 33

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 34

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 35

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 36

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 37

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 38

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 39

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 40

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 41

Another term for constant error variance is:

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

Question 42

The t-value for testing $H _ { 0 } : B _ { i } = 0$
Is calculated using which of the following equations:

A) n - k - 1
B)
$\sum \left( X _ { i } / Y _ { i } \right)$
C)
$B _ { j } / s _ { i }$
D)
$$b _ { i } / s _ { b _ { i } }$$

Question 43

The appropriate hypothesis test for a regression coefficient is:

A)
$H _ { 0 } : B \neq 0 , H _ { \alpha } : B = 0$
B)
$H _ { 0 } : B = 0 , H _ { \alpha } : B \neq 0$
C)
$H _ { 0 } : B = 1 , H _ { \alpha } : B \neq 1$
D) None of these options

Question 44

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 45

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 46

In the standardized value $\left( b _ { i } - B _ { i } \right) / s _ { b _ { j } }$
,the symbol $s _ { b _ { 1 } }$
Represents the:

A) mean of
$b _ { j }$
B) variance of
$b _ { j }$
C) standard error of
$b _ { j }$
D) degrees of freedom of
$b _ { j }$

Question 47

The appropriate hypothesis test for an ANOVA test is:

A)
$H _ { 0 } : \text { all } B \neq 0 , H _ { \alpha } : \text { at least one } B = 0$
B)
$H _ { 0 } \text { : all } B = 0 , H _ { \alpha } \text { : at least one } B \neq 0$
C)
$H _ { 0 } \text { : at least on } B \neq 0 , H _ { a } : \text { all } B = 0$
D)
$H _ { 0 } \text { : at least one } B = 0 , H _ { \alpha } \text { : all } B \neq 0$

Question 48

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 49

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 50

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 51

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 52

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 53

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 54

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 55

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 56

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 57

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 58

Time series data often exhibits which of the following characteristics?

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

Question 59

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 60

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 61

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 62

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

Question 63

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 64

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 65

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 66

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 67

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

A) There is a population regression line
B) The response variable is not normally distributed
C) The response variable is normally distributed
D) The errors are probabilistically independent
The manager of a commuter rail transportation system was recently asked by his governing board to predict the demand for rides in the large city served by the transportation network.The system manager has collected data on variables thought to be related to the number of weekly riders on the city's rail system.The table shown below contains these data.
$\begin{array}{cccccc}\text { Year } & \text { Weekly Riders } & \text { Price perRide } & \text { Population } & \text { Income } & \text { Parking Rate } \\1 & 1200 & \$ 0.15 & 1800 & \$ 2,900 & \$ 0.50 \\2 & 1190 & \$ 0.15 & 1790 & \$ 3,100 & \$ 0.50 \\3 & 1195 & \$ 0.15 & 1780 & \$ 3,200 & \$ 0.60 \\4 & 1100 & \$ 0.25 & 1778 & \$ 3,250 & \$ 0.60 \\5 & 1105 & \$ 0.25 & 1750 & \$ 3,275 & \$ 0.60 \\6 & 1115 & \$ 0.25 & 1740 & \$ 3,290 & \$ 0.70 \\7 & 1130 & \$ 0.25 & 1725 & \$ 4,100 & \$ 0.75 \\8 & 1095 & \$ 0.30 & 1725 & \$ 4,300 & \$ 0.75 \\9 & 1090 & \$ 0.30 & 1720 & \$ 4,400 & \$ 0.75 \\10 & 1087 & \$ 0.30 & 1705 & \$ 4,600 & \$ 0.80\\11 & 1080 & \$ 0.30 & 1710 & \$ 4,815 & \$ 0.80 \\12 & 1020 & \$ 0.40 & 1700 & \$ 5,285 & \$ 0.80 \\13 & 1010 & \$ 0.40 & 1695 & \$ 5,665 & \$ 0.85 \\14 & 1010 & \$ 0.40 & 1695 & \$ 5,800 & \$ 1.00 \\15 & 1005 & \$ 0.40 & 1690 & \$ 5,900 & \$ 1.05 \\16 & 995 & \$ 0.40 & 1630 & \$ 5,915 & \$ 1.05 \\17 & 930 & \$ 0.75 & 1640 & \$ 6,325 & \$ 1.05 \\18 & 915 & \$ 0.75 & 1635 & \$ 6,500 & \$ 1.10 \\19 & 920 & \$ 0.75 & 1630 & \$ 6,612 & \$ 1.25 \\20 & 940 & \$ 0.75 & 1620 & \$ 6,883 & \$ 1.30\\21 & 950 & \$ 0.75 & 1615 & \$ 7,005 & \$ 1.50 \\22 & 910 & \$ 1.00 & 1605 & \$ 7,234 & \$ 1.55 \\23 & 930 & \$ 1.00 & 1590 & \$ 7,500 & \$ 1.65 \\24 & 933 & \$ 1.00 & 1595 & \$ 7,600 & \$ 1.75 \\25 & 940 & \$ 1.00 & 1590 & \$ 7,800 & \$ 1.75 \\26 & 948 & \$ 1.00 & 1600 & \$ 8,000 & \$ 1.90 \\27 & 955 & \$ 1,00 & 1610 & \$ 8,100 & \$ 2.00\\\end{array}$
The variables "weekly riders" and "population" are measured in thousands,and the variables "price per ride","income",and "parking rate" are measured in dollars.

Question 68

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 69

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