Question 1

One difference between simple regression and multiple regression is that,to avoid pitfalls in multiple regression,you must evaluate interaction terms.

Accepted Answer

A) True 
 B)False

Question 2

Instruction 16-6
Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y)and the independent variables are the age of the worker (XS1U1B11S1U1B0),the number of years of education received (XS1U1B12S1U1B0),the number of years at the previous job (XS1U1B13S1U1B0),a dummy variable for marital status (XS1U1B14S1U1B0: 1 = married,0 = otherwise),a dummy variable for head of household (XS1U1B15S1U1B0: 1 = yes,0 = no)and a dummy variable for management position (XS1U1B16S1U1B0: 1 = yes,0 = no).
The coefficient of multiple determination (RS1U1P12S1S1P0S1U1B1jS1U1B0)the regression model using each of the 6 variables XS1U1B1j S1U1B0as the dependent variable and all other X variables as independent variables are,respectively,0.2628,0.1240,0.2404,0.3510,0.3342 and 0.0993.
The partial results from best-subset regression are given below:
 $$\begin{array} { | l | l | l | l | } 
\hline \text { Model } & \text { R Square } & \text { Adj. R Square } & \text { Std. Error } \
\hline \text { X1X5Х6 } & 0.4568 & 0.4116 & 18.3534 \
\hline \times 1 \times 2 \times 5 \times 6 & 0.4697 & 0.4091 & 18.3919 \
\hline \times 1 \times 3 \times 5 \times 6 & 0.4691 & 0.4084 & 18.4023 \
\hline \times 1 \times 2 \times 3 \times 5 \times 6 & 0.4877 & 0.4123 & 18.3416 \
\hline \times 1 \times 2 \times 3 \times 4 \times 5 \times 6 & 0.4949 & 0.4030 & 18.4861 \
\hline
\end{array}$$
-Referring to Instruction 16-6,the model that includes X1,X3,X5 and X6 should be among the appropriate models using the Mallow's Cp statistic.

Accepted Answer

A) True 
 B)False

Question 3

Using the Cook's distance statistic Di to determine influential points in a multiple regression model with k independent variable and n observations and letting denote the critical value of an F distribution with v1 and v2 degrees of freedom at a 0.50 level of significance,Xi is an influential point if

Accepted Answer

A) Di n-k-1,k+1. 
B) Di k+1,n-k-1. 
C) Di > Fk+1,n-k-1. 
D) Di > Fn-k-1,k+1. 
A) Di n-k-1,k+1. 
B) Di k+1,n-k-1. 
C) Di > Fk+1,n-k-1. 
D) Di > Fn-k-1,k+1.

Question 4

Calculating Cook's Distance Statistic requires the use of matrix algebra.

Accepted Answer

A) True 
 B)False

Question 5

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

Accepted Answer

A) True 
 B)False

Question 6

Instruction 16-6
Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y)and the independent variables are the age of the worker (XS1U1B11S1U1B0),the number of years of education received (XS1U1B12S1U1B0),the number of years at the previous job (XS1U1B13S1U1B0),a dummy variable for marital status (XS1U1B14S1U1B0: 1 = married,0 = otherwise),a dummy variable for head of household (XS1U1B15S1U1B0: 1 = yes,0 = no)and a dummy variable for management position (XS1U1B16S1U1B0: 1 = yes,0 = no).
The coefficient of multiple determination (RS1U1P12S1S1P0S1U1B1jS1U1B0)the regression model using each of the 6 variables XS1U1B1j S1U1B0as the dependent variable and all other X variables as independent variables are,respectively,0.2628,0.1240,0.2404,0.3510,0.3342 and 0.0993.
The partial results from best-subset regression are given below:
 $$\begin{array} { | l | l | l | l | } 
\hline \text { Model } & \text { R Square } & \text { Adj. R Square } & \text { Std. Error } \
\hline \text { X1X5Х6 } & 0.4568 & 0.4116 & 18.3534 \
\hline \times 1 \times 2 \times 5 \times 6 & 0.4697 & 0.4091 & 18.3919 \
\hline \times 1 \times 3 \times 5 \times 6 & 0.4691 & 0.4084 & 18.4023 \
\hline \times 1 \times 2 \times 3 \times 5 \times 6 & 0.4877 & 0.4123 & 18.3416 \
\hline \times 1 \times 2 \times 3 \times 4 \times 5 \times 6 & 0.4949 & 0.4030 & 18.4861 \
\hline
\end{array}$$
-Referring to Instruction 16-6,the model that includes X1,X2,X5 and X6 should be among the appropriate models using the Mallow's Cp statistic.

Accepted Answer

A) True 
 B)False

Question 7

Applying a transformation to a data set,original values of Y of 1.6 and 4.2 become transformed values of 11.5 and 33.9.What transformation was used?

Accepted Answer

The answer of Applying a transformation to a data set,original...

Question 8

A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies.She proceeds to randomly select 26 large corporations and record information in millions of dollars.A statistical analyst discovers that capital spending by corporations has a significant inverse relationship with wage spending.What should the microeconomist who developed this multiple regression model be particularly concerned with?

Accepted Answer

A) Normality of residual. 
B) Randomness of error terms. 
C) Missing observations. 
D) Collinearity. 
A) Normality of residual. 
B) Randomness of error terms. 
C) Missing observations. 
D) Collinearity.

Question 9

Instruction 16-6
Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y)and the independent variables are the age of the worker (XS1U1B11S1U1B0),the number of years of education received (XS1U1B12S1U1B0),the number of years at the previous job (XS1U1B13S1U1B0),a dummy variable for marital status (XS1U1B14S1U1B0: 1 = married,0 = otherwise),a dummy variable for head of household (XS1U1B15S1U1B0: 1 = yes,0 = no)and a dummy variable for management position (XS1U1B16S1U1B0: 1 = yes,0 = no).
The coefficient of multiple determination (RS1U1P12S1S1P0S1U1B1jS1U1B0)the regression model using each of the 6 variables XS1U1B1j S1U1B0as the dependent variable and all other X variables as independent variables are,respectively,0.2628,0.1240,0.2404,0.3510,0.3342 and 0.0993.
The partial results from best-subset regression are given below:
 $$\begin{array} { | l | l | l | l | } 
\hline \text { Model } & \text { R Square } & \text { Adj. R Square } & \text { Std. Error } \
\hline \text { X1X5Х6 } & 0.4568 & 0.4116 & 18.3534 \
\hline \times 1 \times 2 \times 5 \times 6 & 0.4697 & 0.4091 & 18.3919 \
\hline \times 1 \times 3 \times 5 \times 6 & 0.4691 & 0.4084 & 18.4023 \
\hline \times 1 \times 2 \times 3 \times 5 \times 6 & 0.4877 & 0.4123 & 18.3416 \
\hline \times 1 \times 2 \times 3 \times 4 \times 5 \times 6 & 0.4949 & 0.4030 & 18.4861 \
\hline
\end{array}$$
-Referring to Instruction 16-6,the model that includes X1,X5 and X6 should be selected using the adjusted r2 statistic.

Accepted Answer

A) True 
 B)False

Question 10

Instruction 16-6
Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y)and the independent variables are the age of the worker (XS1U1B11S1U1B0),the number of years of education received (XS1U1B12S1U1B0),the number of years at the previous job (XS1U1B13S1U1B0),a dummy variable for marital status (XS1U1B14S1U1B0: 1 = married,0 = otherwise),a dummy variable for head of household (XS1U1B15S1U1B0: 1 = yes,0 = no)and a dummy variable for management position (XS1U1B16S1U1B0: 1 = yes,0 = no).
The coefficient of multiple determination (RS1U1P12S1S1P0S1U1B1jS1U1B0)the regression model using each of the 6 variables XS1U1B1j S1U1B0as the dependent variable and all other X variables as independent variables are,respectively,0.2628,0.1240,0.2404,0.3510,0.3342 and 0.0993.
The partial results from best-subset regression are given below:
 $$\begin{array} { | l | l | l | l | } 
\hline \text { Model } & \text { R Square } & \text { Adj. R Square } & \text { Std. Error } \
\hline \text { X1X5Х6 } & 0.4568 & 0.4116 & 18.3534 \
\hline \times 1 \times 2 \times 5 \times 6 & 0.4697 & 0.4091 & 18.3919 \
\hline \times 1 \times 3 \times 5 \times 6 & 0.4691 & 0.4084 & 18.4023 \
\hline \times 1 \times 2 \times 3 \times 5 \times 6 & 0.4877 & 0.4123 & 18.3416 \
\hline \times 1 \times 2 \times 3 \times 4 \times 5 \times 6 & 0.4949 & 0.4030 & 18.4861 \
\hline
\end{array}$$
-Referring to Instruction 16-6,what is the value of the variance inflationary factor of Manager?

Accepted Answer

The answer of Instruction 16-6
Given below are results from the...

Question 11

Cook's Distance Statistic can be used to analyze the influence of individual data points.

Accepted Answer

A) True 
 B)False

Question 12

One use of VIF in multiple regression is deciding which variable to include in a model.

Accepted Answer

A) True 
 B)False

Question 13

The Cp statistic is used

Accepted Answer

A) to determine if there is a problem of collinearity. 
B) to choose the best model. 
C) to determine if there is an irregular component in a time series. 
D) if the variances of the error terms are all the same in a regression model. 
A) to determine if there is a problem of collinearity. 
B) to choose the best model. 
C) to determine if there is an irregular component in a time series. 
D) if the variances of the error terms are all the same in a regression model.

Question 14

In multiple regression,the ________ procedure permits variables to enter and leave the model at different stages of its development.

Accepted Answer

A) stepwise regression 
B) forward selection 
C) backward elimination 
D) residual analysis 
A) stepwise regression 
B) forward selection 
C) backward elimination 
D) residual analysis

Question 15

Instruction 16-6
Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y)and the independent variables are the age of the worker (XS1U1B11S1U1B0),the number of years of education received (XS1U1B12S1U1B0),the number of years at the previous job (XS1U1B13S1U1B0),a dummy variable for marital status (XS1U1B14S1U1B0: 1 = married,0 = otherwise),a dummy variable for head of household (XS1U1B15S1U1B0: 1 = yes,0 = no)and a dummy variable for management position (XS1U1B16S1U1B0: 1 = yes,0 = no).
The coefficient of multiple determination (RS1U1P12S1S1P0S1U1B1jS1U1B0)the regression model using each of the 6 variables XS1U1B1j S1U1B0as the dependent variable and all other X variables as independent variables are,respectively,0.2628,0.1240,0.2404,0.3510,0.3342 and 0.0993.
The partial results from best-subset regression are given below:
 $$\begin{array} { | l | l | l | l | } 
\hline \text { Model } & \text { R Square } & \text { Adj. R Square } & \text { Std. Error } \
\hline \text { X1X5Х6 } & 0.4568 & 0.4116 & 18.3534 \
\hline \times 1 \times 2 \times 5 \times 6 & 0.4697 & 0.4091 & 18.3919 \
\hline \times 1 \times 3 \times 5 \times 6 & 0.4691 & 0.4084 & 18.4023 \
\hline \times 1 \times 2 \times 3 \times 5 \times 6 & 0.4877 & 0.4123 & 18.3416 \
\hline \times 1 \times 2 \times 3 \times 4 \times 5 \times 6 & 0.4949 & 0.4030 & 18.4861 \
\hline
\end{array}$$
-Referring to Instruction 16-6,the variable X5 should be dropped to remove collinearity.

Accepted Answer

A) True 
 B)False

Question 16

Which of the following is NOT used to determine observations that have influential effect on the fitted model?

Accepted Answer

A) The Cp statistic. 
B) The studentised deleted residuals ti. 
C) The hat matrix elements hi. 
D) Cook's distance statistic. 
A) The Cp statistic. 
B) The studentised deleted residuals ti. 
C) The hat matrix elements hi. 
D) Cook's distance statistic.

Question 17

Instruction 16-6
Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y)and the independent variables are the age of the worker (XS1U1B11S1U1B0),the number of years of education received (XS1U1B12S1U1B0),the number of years at the previous job (XS1U1B13S1U1B0),a dummy variable for marital status (XS1U1B14S1U1B0: 1 = married,0 = otherwise),a dummy variable for head of household (XS1U1B15S1U1B0: 1 = yes,0 = no)and a dummy variable for management position (XS1U1B16S1U1B0: 1 = yes,0 = no).
The coefficient of multiple determination (RS1U1P12S1S1P0S1U1B1jS1U1B0)the regression model using each of the 6 variables XS1U1B1j S1U1B0as the dependent variable and all other X variables as independent variables are,respectively,0.2628,0.1240,0.2404,0.3510,0.3342 and 0.0993.
The partial results from best-subset regression are given below:
 $$\begin{array} { | l | l | l | l | } 
\hline \text { Model } & \text { R Square } & \text { Adj. R Square } & \text { Std. Error } \
\hline \text { X1X5Х6 } & 0.4568 & 0.4116 & 18.3534 \
\hline \times 1 \times 2 \times 5 \times 6 & 0.4697 & 0.4091 & 18.3919 \
\hline \times 1 \times 3 \times 5 \times 6 & 0.4691 & 0.4084 & 18.4023 \
\hline \times 1 \times 2 \times 3 \times 5 \times 6 & 0.4877 & 0.4123 & 18.3416 \
\hline \times 1 \times 2 \times 3 \times 4 \times 5 \times 6 & 0.4949 & 0.4030 & 18.4861 \
\hline
\end{array}$$
-Referring to Instruction 16-6,what is the value of the Mallow's Cp statistic for the model that includes X1,X3,X5 and X6?

Accepted Answer

Question 18

Instruction 16-5
A chemist employed by a pharmaceutical firm has developed a muscle relaxant.She took a sample of 14 people suffering from extreme muscle constriction.She gave each a vial containing a dose (X)of the drug and recorded the time to relief (Y)measured in seconds for each.She fit a quadratic model to this data.The results obtained by Microsoft Excel follow.
 $\begin{array}{l|l|l|l|l|l|}
\text { SUMMARY } & output& \
\hline \text { Regression } & \text { Statistics } & \
\hline \text { Multiple R } & & 0.747 \
\hline \text { R Square } & & 0.558 \
\hline \text { Adj. R Square } & & 0.478 \
\hline \text { Std. Error } & 363.1 \
\hline \text { Observations } & 14 \\hline\
\hline \text { ANOVA } & & & & & \
\hline & \text { df } & \text { SS } & \text { MS } & F & \text { Signưf } F \
\hline \text { Regression } & 2 & 10344797 & 5172399 & 6.94 & 0.0110 \
\hline \text { Residual } & 11 & 8193929 & 744903 & & \
\hline \text { Total } & 13 & 18538726 & & & \\hline\
\hline & \text { Coeff } & \text { StdErior } & \text { Stat } & P \text {-value } \
\hline \text { Intercept } & 1283.0 & 352.0 & 3.65 & 0.0040 \
\hline \text { CenDose } & 25.228 & 3.631 & 2.92 & 0.0140 \
\hline \text { CenDoseSq } & 0.8604 & 0.3722 & 2.31 & 0.0410\
\hline
\end{array}$ Note: Adj.R Square = Adjusted R Square;Std.Error = Standard Error
-Referring to Instruction 16-5,suppose the chemist decides to use a t test to determine if there is a significant difference between a linear model and a quadratic model that includes a linear term.If she used a level of significance of 0.05,she would decide that the linear model is sufficient.

Accepted Answer

A) True 
 B)False

Question 19

Using the Cp statistic in model building,all models with Cp ≤ (k + 1)are equally good.

Accepted Answer

A) True 
 B)False

Question 20

Instruction 16-6
Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y)and the independent variables are the age of the worker (XS1U1B11S1U1B0),the number of years of education received (XS1U1B12S1U1B0),the number of years at the previous job (XS1U1B13S1U1B0),a dummy variable for marital status (XS1U1B14S1U1B0: 1 = married,0 = otherwise),a dummy variable for head of household (XS1U1B15S1U1B0: 1 = yes,0 = no)and a dummy variable for management position (XS1U1B16S1U1B0: 1 = yes,0 = no).
The coefficient of multiple determination (RS1U1P12S1S1P0S1U1B1jS1U1B0)the regression model using each of the 6 variables XS1U1B1j S1U1B0as the dependent variable and all other X variables as independent variables are,respectively,0.2628,0.1240,0.2404,0.3510,0.3342 and 0.0993.
The partial results from best-subset regression are given below:
 $$\begin{array} { | l | l | l | l | } 
\hline \text { Model } & \text { R Square } & \text { Adj. R Square } & \text { Std. Error } \
\hline \text { X1X5Х6 } & 0.4568 & 0.4116 & 18.3534 \
\hline \times 1 \times 2 \times 5 \times 6 & 0.4697 & 0.4091 & 18.3919 \
\hline \times 1 \times 3 \times 5 \times 6 & 0.4691 & 0.4084 & 18.4023 \
\hline \times 1 \times 2 \times 3 \times 5 \times 6 & 0.4877 & 0.4123 & 18.3416 \
\hline \times 1 \times 2 \times 3 \times 4 \times 5 \times 6 & 0.4949 & 0.4030 & 18.4861 \
\hline
\end{array}$$
-Referring to Instruction 16-6,there is reason to suspect collinearity between some pairs of predictors based on the values of the variance inflationary factor.

Accepted Answer

A) True 
 B)False

One difference between simple regression and multiple regression is that,to avoid pitfalls in multiple regression,you must evaluate interaction terms.

Calculating Cook's Distance Statistic requires the use of matrix algebra.

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

Applying a transformation to a data set,original values of Y of 1.6 and 4.2 become transformed values of 11.5 and 33.9.What transformation was used?

Cook's Distance Statistic can be used to analyze the influence of individual data points.

One use of VIF in multiple regression is deciding which variable to include in a model.

The C_p statistic is used

In multiple regression,the ________ procedure permits variables to enter and leave the model at different stages of its development.

Which of the following is NOT used to determine observations that have influential effect on the fitted model?

Using the C_p statistic in model building,all models with C_p ≤ (k + 1)are equally good.

Introduction and Data Collection

Presenting Data in Tables and Charts

Numerical Descriptive Measures

Basic Probability

Some Important Discrete Probability Distributions

The Normal Distribution and Other Continuous Distributions

Sampling Distributions

Confidence Interval Estimation

Fundamentals of Hypothesis Testing: One-Sample Tests

Hypothesis Testing: Two Sample Tests

Analysis of Variance

Simple Linear Regression

Introduction to Multiple Regression

Time-Series Forecasting and Index Numbers

Chi-Square Tests

Decision Making

Statistical Applications in Quality and Productivity Management

Further Non-Parametric Tests

Filters

Exam 16: Multiple Regression Model Building

One difference between simple regression and multiple regression is that,to avoid pitfalls in multiple regression,you must evaluate interaction terms.

Calculating Cook's Distance Statistic requires the use of matrix algebra.

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

Applying a transformation to a data set,original values of Y of 1.6 and 4.2 become transformed values of 11.5 and 33.9.What transformation was used?

Cook's Distance Statistic can be used to analyze the influence of individual data points.

One use of VIF in multiple regression is deciding which variable to include in a model.

The Cp statistic is used

In multiple regression,the ________ procedure permits variables to enter and leave the model at different stages of its development.

Which of the following is NOT used to determine observations that have influential effect on the fitted model?

Using the Cp statistic in model building,all models with Cp ≤ (k + 1)are equally good.

Introduction and Data Collection

Presenting Data in Tables and Charts

Numerical Descriptive Measures

Basic Probability

Some Important Discrete Probability Distributions

The Normal Distribution and Other Continuous Distributions

Sampling Distributions

Confidence Interval Estimation

Fundamentals of Hypothesis Testing: One-Sample Tests

Hypothesis Testing: Two Sample Tests

Analysis of Variance

Simple Linear Regression

Introduction to Multiple Regression

Time-Series Forecasting and Index Numbers

Chi-Square Tests

Decision Making

Statistical Applications in Quality and Productivity Management

Further Non-Parametric Tests

Filters

The C_p statistic is used

Using the C_p statistic in model building,all models with C_p ≤ (k + 1)are equally good.