Question 1

Collinearity will result in excessively low standard errors of the parameter estimates reported in the regression output.

Accepted Answer

A) True 
 B)False

Question 2

The parameter estimates are biased when collinearity is present in a multiple regression equation.

Accepted Answer

A) True 
 B)False

Question 3

The stepwise regression approach takes into consideration all possible models.

Accepted Answer

A) True 
 B)False

Question 4

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 curvilinear model that includes a linear term.The p-value of the test statistic for the contribution of the quadratic curvilinear term is ________.

Accepted Answer

The answer of Instruction 16-5
A chemist employed by a pharmaceutical...

Question 5

Instruction 16-3
In Hawaii,condemnation proceedings are under way to enable private citizens to own the property upon which their homes are built.Until recently,only estates were permitted to own land,and homeowners leased the land from the estate.In order to comply with the new law,a large Hawaiian estate wants to use regression analysis to estimate the fair market value of the land.The following model was fit to data collected for n = 20 properties,10 of which are located near a
cove.Model 1: Y = β 0 + β 1X1 + β 2X2 + β 3X1X2 + β 4+ β 5X2 + ε where
Y = Sale price of property in thousands of dollars
X1 = Size of property in thousands of square metres
X2 = 1 if property located near cove,0 if not
Using the data collected for the 20 properties,the following partial output obtained from Microsoft Excel is shown:
 $\begin{array}{|l|l|l|l|l|l|}
\hline \text { SUMMARY } & \text { OUTPUT } & \
\hline \text { Regression } & \text { Statistics } & \
\hline \text { Multiple R } & & 0.985 \
\hline \text { R Square } & & 0.970 \
\hline \text { Std. Error } & & 9.5 \
\hline \text { Observations } & & 20 \
\hline\
\hline\text { ANOVA }\
\hline & d f & \text { SS } & \text { MS } & F & \text { Signif F } \
\hline \text { Regression } & 5 & 28324 & 5664 & 62.2 & 0.0001 \
\hline \text { Residual } & 14 & 1279 & 91 & & \
\hline \text { Total } & 19 & 29603 & & & \\hline\
\hline&\text {Coeff }&\text {StdError }&\text {t stat }&\text { P-Value}\
\hline \text { Intercept } & -32.1 & 35.7 & -0.90 & 0.3834 \
\hline \text { Size } & 12.2 & 5.9 & 2.05 & 0.0594 \
\hline \text { Cove } & -104.3 & 53.5 & -1.95 & 0.0715 \
\hline \text { Size }{ }^{*} \text { Cove } & 17.0 & 8.5 & 1.99 & 0.0661 \
\hline \text { SizeSq } & -0.3 & 0.2 & -1.28 & 0.2204 \
\hline \text { SizeSq } & -0.3 & 0.3 & -1.13 & 0.2749 \\hline 
\end{array}$ Note: Std.Error = Standard Error
-Referring to Instruction 16-3,is the overall model statistically adequate at a 0.05 level of significance for predicting sale price (Y)?

Accepted Answer

A) Yes,since the p-value for the test is smaller than 0.05. 
B) No,since some of the t tests for the individual variables are not significant. 
C) No,since the standard deviation of the model is fairly large. 
D) Yes,since none of the ?-estimates are equal to 0. 
A) Yes,since the p-value for the test is smaller than 0.05. 
B) No,since some of the t tests for the individual variables are not significant. 
C) No,since the standard deviation of the model is fairly large. 
D) Yes,since none of the ?-estimates are equal to 0.

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 variable X6 should be dropped to remove collinearity.

Accepted Answer

A) True 
 B)False

Question 7

Instruction 16-2
A certain type of rare gem serves as a status symbol for many of its owners.In theory,for low prices,the demand decreases as the price of the gem increases.However,experts hypothesise that when the gem is valued at very high prices,the demand increases with price due to the status owners believe they gain in obtaining the gem.Thus,the model proposed to best explain the demand for the gem by its price is the quadratic model:
Y = βS1U1B10S1U1B0 + βS1U1B11S1U1B0X + βS1U1B12S1U1B0XS1U1P12S1S1P0S1U1P1 S1S1P0+S1U1P1 S1S1P0S1U1P1εS1S1P0
where Y = demand (in thousands)and X = retail price per carat.
This model was fit to data collected for a sample of 12 rare gems of this type.A portion of the computer analysis obtained from Microsoft Excel is shown below:
 $\begin{array}{|l|l|l|l|l|l|}
\text { SUMMARY } &output & \
\hline \text { Regression } & \text { Statistics } & \
\hline \text { Multiple R } & & 0.994 \
\hline \text { R Square } & & 0.988 \
\hline \text { Std. Error } & & 12.42 \
\hline \text { Observations } & & 12\\hline\
\hline\text { ANOVA }\
\hline & \text { dff } & \text { SS } & \text { MS } & F & \text { Siguif } F \
\hline \text { Regression } & 2 & 115145 & 57573 & 373 & 0.0001 \
\hline \text { Residual } & 9 & 1388 & 154 & & \
\hline \text { Total } & 11 & 116533 & & &\\hline\
\hline & \text { Coeff } & \text { StdError } & \text { t Stat } & \text { P-Value } \
\hline \text { Intercept } & 286.42 & 9.66 & 29.64 & 0.0001 \
\hline \text { Price } & -0.31 & 0.06 & -5.14 & 0.0006 \
\hline\text { Price Sq } & p .000067 & p .00007 & p .95 & p .3647\\hline
\end{array}$ Note: Std.Error = Standard Error
-Referring to Instruction 16-2,a more parsimonious simple linear model is likely to be statistically superior to the fitted curvilinear for predicting sale price (Y).

Accepted Answer

A) True 
 B)False

Question 8

The goals of model building are to find a good model with the fewest independent variables that is easier to interpret and has lower probability of collinearity.

Accepted Answer

A) True 
 B)False

Question 9

Which of the following is used to determine observations that have influential effect on the fitted model?

Accepted Answer

A) Variance inflationary factor. 
B) The Cp statistic. 
C) Cook's distance statistic. 
D) Durbin Watson statistic. 
A) Variance inflationary factor. 
B) The Cp statistic. 
C) Cook's distance statistic. 
D) Durbin Watson statistic.

Question 10

Which of the following is used to find a "best" model?

Accepted Answer

A) Standard error of the estimate. 
B) Adjusted r2. 
C) Odds ratio. 
D) Mallow's Cp. 
A) Standard error of the estimate. 
B) Adjusted r2. 
C) Odds ratio. 
D) Mallow's Cp.

Question 11

A regression diagnostic tool used to study the possible effects of collinearity is

Accepted Answer

A) the VIF. 
B) the Y-intercept. 
C) the standard error of the estimate. 
D) the slope. 
A) the VIF. 
B) the Y-intercept. 
C) the standard error of the estimate. 
D) the slope.

Question 12

The Variance Inflationary Factor (VIF)measures the

Accepted Answer

A) standard deviation of the slope. 
B) contribution of each X variable with the Y variable after all other X variables are included in the model. 
C) correlation of the X variables with the Y variable. 
D) correlation of the X variables with each other. 
A) standard deviation of the slope. 
B) contribution of each X variable with the Y variable after all other X variables are included in the model. 
C) correlation of the X variables with the Y variable. 
D) correlation of the X variables with each other.

Question 13

Instruction 16-2
A certain type of rare gem serves as a status symbol for many of its owners.In theory,for low prices,the demand decreases as the price of the gem increases.However,experts hypothesise that when the gem is valued at very high prices,the demand increases with price due to the status owners believe they gain in obtaining the gem.Thus,the model proposed to best explain the demand for the gem by its price is the quadratic model:
Y = βS1U1B10S1U1B0 + βS1U1B11S1U1B0X + βS1U1B12S1U1B0XS1U1P12S1S1P0S1U1P1 S1S1P0+S1U1P1 S1S1P0S1U1P1εS1S1P0
where Y = demand (in thousands)and X = retail price per carat.
This model was fit to data collected for a sample of 12 rare gems of this type.A portion of the computer analysis obtained from Microsoft Excel is shown below:
 $\begin{array}{|l|l|l|l|l|l|}
\text { SUMMARY } &output & \
\hline \text { Regression } & \text { Statistics } & \
\hline \text { Multiple R } & & 0.994 \
\hline \text { R Square } & & 0.988 \
\hline \text { Std. Error } & & 12.42 \
\hline \text { Observations } & & 12\\hline\
\hline\text { ANOVA }\
\hline & \text { dff } & \text { SS } & \text { MS } & F & \text { Siguif } F \
\hline \text { Regression } & 2 & 115145 & 57573 & 373 & 0.0001 \
\hline \text { Residual } & 9 & 1388 & 154 & & \
\hline \text { Total } & 11 & 116533 & & &\\hline\
\hline & \text { Coeff } & \text { StdError } & \text { t Stat } & \text { P-Value } \
\hline \text { Intercept } & 286.42 & 9.66 & 29.64 & 0.0001 \
\hline \text { Price } & -0.31 & 0.06 & -5.14 & 0.0006 \
\hline\text { Price Sq } & p .000067 & p .00007 & p .95 & p .3647\\hline
\end{array}$ Note: Std.Error = Standard Error
-Referring to Instruction 16-2,does the quadratic term appear to be significant in the response curve relating the demand (Y)and the price (X)at 10% level of significance?

Accepted Answer

A) No,sine the value of ?2 is near 0. 
B) No,since the p-value for the test is greater than 0.10. 
C) Yes,since the p-value for the test is less than 0.10. 
D) Yes,since the value of ?2 is positive. 
A) No,sine the value of ?2 is near 0. 
B) No,since the p-value for the test is greater than 0.10. 
C) Yes,since the p-value for the test is less than 0.10. 
D) Yes,since the value of ?2 is positive.

Question 14

In stepwise regression,an independent variable is not allowed to be removed from the model once it has entered into the model.

Accepted Answer

A) True 
 B)False

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,what is the value of the variance inflationary factor of Age?

Accepted Answer

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

Question 16

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

Accepted Answer

The answer of In multiple regression,the ________ procedure permits variables...

Question 17

Which of the following will NOT change a nonlinear model into a linear model?

Accepted Answer

A) Logarithmic transformation. 
B) Square-root transformation. 
C) Variance inflationary factor . 
D) Quadratic regression model. 
A) Logarithmic transformation. 
B) Square-root transformation. 
C) Variance inflationary factor . 
D) Quadratic regression model.

Question 18

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 Head of Household?

Accepted Answer

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

Question 19

If a group of independent variables are not significant individually but are significant as a group at a specified level of significance,this is most likely due to

Accepted Answer

A) collinearity. 
B) the absence of dummy variables. 
C) the presence of dummy variables. 
D) autocorrelation. 
A) collinearity. 
B) the absence of dummy variables. 
C) the presence of dummy variables. 
D) autocorrelation.

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,what is the value of the Mallow's Cp statistic for the model that includes X1,X2,X5 and X6?

Accepted Answer

Collinearity will result in excessively low standard errors of the parameter estimates reported in the regression output.

The parameter estimates are biased when collinearity is present in a multiple regression equation.

The stepwise regression approach takes into consideration all possible models.

The goals of model building are to find a good model with the fewest independent variables that is easier to interpret and has lower probability of collinearity.

Which of the following is used to determine observations that have influential effect on the fitted model?

Which of the following is used to find a "best" model?

A regression diagnostic tool used to study the possible effects of collinearity is

The Variance Inflationary Factor (VIF)measures the

In stepwise regression,an independent variable is not allowed to be removed from the model once it has entered into the model.

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

Which of the following will NOT change a nonlinear model into a linear model?

If a group of independent variables are not significant individually but are significant as a group at a specified level of significance,this is most likely due to

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

Collinearity will result in excessively low standard errors of the parameter estimates reported in the regression output.

The parameter estimates are biased when collinearity is present in a multiple regression equation.

The stepwise regression approach takes into consideration all possible models.

The goals of model building are to find a good model with the fewest independent variables that is easier to interpret and has lower probability of collinearity.

Which of the following is used to determine observations that have influential effect on the fitted model?

Which of the following is used to find a "best" model?

A regression diagnostic tool used to study the possible effects of collinearity is

The Variance Inflationary Factor (VIF)measures the

In stepwise regression,an independent variable is not allowed to be removed from the model once it has entered into the model.

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

Which of the following will NOT change a nonlinear model into a linear model?

If a group of independent variables are not significant individually but are significant as a group at a specified level of significance,this is most likely due to

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