Question 1

A multiple regression model has the form $\hat { Y }$ = b0 + b1x1 + b2x2.The coefficient b1 is interpreted as the:

Accepted Answer

A)  estimated change in y per unit change in x1. 
B)  estimated change in y per unit change in x1,holding x2constant. 
C)  estimated change in y per unit change in x1,when x1 and x2 values are correlated. 
D)  estimated change in y per unit change in x2,holding x1 constant. 
A)  estimated change in y per unit change in x1. 
B)  estimated change in y per unit change in x1,holding x2constant. 
C)  estimated change in y per unit change in x1,when x1 and x2 values are correlated. 
D)  estimated change in y per unit change in x2,holding x1 constant.

Question 2

Professor
A statistics professor investigated some of the factors that affect an individual student's final grade in his course.He proposed the multiple regression model $$y = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 3 } + \epsilon$$ where:
y = final mark (out of 100)
xS1U1B11S1U1B0 = number of lectures skipped
xS1U1B12S1U1B0 = number of late assignments
xS1U1B13S1U1B0 = mid-term test mark (out of 100)
The professor recorded the data for 50 randomly selected students.The computer output is shown below. The regression equation is:
$$\hat { y } = 41.6 - 3.18 x _ { 1 } - 1.17 x _ { 2 } + .63 x _ { 3 }$$
$\begin{array}{l|lll|}
\hline \text { Predictor } & \text { Coef } & \text { StDev } & T \
\hline \text { Constant } & 41.6 & 17.8 & 2.337 \
x_{1} & -3.18 & 1.66 & -1.916 \
x_{2} & -1.17 & 1.13 & -1.035 \
x_{3} & 0.63 & 0.13 & 4.846 \
\hline
\end{array}$
$$S = 13.74$$
$$\mathrm { R } - \mathrm { Sq } = 30.0 \%$$
Analysis of Variance
$\begin{array}{l|llll}
\hline \text { Source of Variation } & \text { df } & \text { SS } & M S & F \
\hline \text { Regression } & 3 & 3716 & 1238.667 & 6.558 \
\text { Error } & 46 & 8688 & 188.870 & \
\hline \text { Total } & 49 & 12404 & & \
\hline
\end{array}$
-Do these data provide enough evidence to conclude at the 5% significance level that the final mark and the number of skipped lectures are linearly related?
Test statistic = ____________________
Critical Value = ____________________
Conclusion: ____________________

Accepted Answer

t = -1.916

Question 3

Salary
Data was collected from 40 employees to develop a regression model to predict the employee's annual salary using their years with the company (Years),their starting salary (Starting),and their Gender (Male = 0,Female = 1).The results from Excel regression analysis are shown below:
 $$\begin{array}{l}
\begin{array} { l r } 
\hline  { \text { RegresionSlalinlics } } \
\hline \text { Multiple R } & \text { 0.719714957 } \
\text { R Square } & \text { 0.516551199 } \
\text { Adjusted R Square } & 0.476253780 \
\text { Standard Errar } & 10515.63461 \
\text { Dbservations } & 40 \
\hline
\end{array}\
\end{array}$$

$\text { ANOVA }$
$\begin{array}{lrrrrrr}
\hline & \text { of } & & \text { SS } & \text { MS } & F & \text { Significance } F \
\hline \text { Regression } & 3 & 4334682510 & 1444894170 & 12.82165585 & 7.48476 \mathrm{E}-06 \
\text { Residual } & 36 & 4056901131 & 112691698.1 & & \
\text { Total } & 39 & 8391583641 & & & \
\hline
\end{array}$

$\begin{array}{lcrrr}
\hline & \text { Coefficients } &{\text { Standard Error }} & {t \text { Stat }} &{P \text {-value }} \
\hline \text { Intercept } & 27946.57894 & 4832.438706 & 5.783121245 & 1.35464 \mathrm{E}-06 \
\text { Years } & 1665.251558 & 425.0829092 & 3.917474737 & 0.000383313 \
\text { Starting } & 0.266374185 & 0.12610443 & 2.112330112 & 0.041661598 \
\text { Gender } & -3285.541043 & 5617.145392 & -0.584912943 & 0.56225464
\end{array}$

-In testing the null hypothesis that the regression equation is not significant at the 0.05 level,what is the appropriate conclusion?

Accepted Answer

The answer of Salary
Data was collected from 40 employees to...

Question 4

Explain each of the terms in the multiple regression model: $$y _ { i } = \beta _ { 0 } + \beta _ { 1 } x _ { 1 i } + \beta _ { 2 } x _ { 2 i } + \ldots \ldots + \beta _ { \mathrm { ki } } x _ { \mathrm { ki } } + \epsilon _ { 1 }$$ .

Accepted Answer

y_i = a value of the dependent v

Question 5

A multiple regression model has the form: $\hat { Y }$ = 5.25 + 2.5x1 + 4x2.As x2 increases by 1 unit,holding x1 constant,then the value of y will increase by:

Accepted Answer

A)  2.5 units. 
B)  7.75 units. 
C)  4 units on average. 
D)  11.75 units on average. 
A)  2.5 units. 
B)  7.75 units. 
C)  4 units on average. 
D)  11.75 units on average.

Question 6

States
Concern over the number of car thefts grew into a project to determine the relationship between car thefts by state and these variables:
xS1U1B11S1U1B0 = Police per 10,000 persons,by state
xS1U1B12S1U1B0 = Expenditure by local government for police protection,in thousands,by state
xS1U1B13S1U1B0 = New passenger car registrations,in thousands,by state.
Data from 13 states were collected.The MINITAB regression results are: 
The regression equation is car-thf $= - 25.3 + 1.28$ police $+ 0.0188$ polexp $+ 0.0969$ registr
$\begin{array} { l l l c l } \text { Predictor } & \text { Coef } & \text { Stdev } & \text { t-ratio } & p \ \text { Constant } & - 25.29 & 17.85 & - 1.42 & 0.190 \ \text { police } & 1.2831 & 0.9275 & 1.38 & 0.200 \ \text { polexp } & 0.018827 & 0.008460 & 2.23 & 0.053 \ \text { registr } & 0.09686 & 0.03536 & 2.74 & 0.023 \end{array}$
$$s = ? ? \quad \mathrm { R } - s q = ? ? \% \quad \mathrm { R } - s q ( a d j ) = ? ? \%$$
Analysis of Variance
$\begin{array} { l l l l c l } \text { SOURCE } & \text { DF } & \text { SS } & \text { MS } & F & p \ \text { Regression } & 3 & 33007 & 11002 & 107.14 & 0.000 \ \text { Error } & 9 & 924 & 103 & & \ \text { Total } & 12 & 33932 & & & \end{array}$
Correlation between the variables:
$\begin{array} { l c c c c } & \text { car-thf } & \text { police } & \text { polexp } & \text { registr } \ \text { car-thf } & 1.000 & & & \ \text { police } & 0.466 & 1.000 & & \ \text { polexp } & 0.970 & 0.390 & 1.000 & \ \text { registr } & 0.976 & 0.406 & 0.958 & 1.000 \end{array}$
-Do the partial regression coefficients have the algebraic sign you might expect?

Accepted Answer

The sign for b₁ is questionable since it

Question 7

In testing the significance of a multiple regression model in which there are three independent variables,the null hypothesis is:

Accepted Answer

A) $H _ { 0 } : \beta _ { 1 } = \beta _ { 2 } = \beta _ { 3 } = 1$ 
B)  $H _ { 0 } : \beta _ { 0 } = \beta _ { 1 } = \beta _ { 2 } = \beta _ { 3 }$ 
C)  $H _ { 0 } : \beta _ { 1 } = \beta _ { 2 } = \beta _ { 3 } = 0$ 
D)  $H _ { 0 } : \beta _ { 0 } = \beta _ { 1 } = \beta _ { 2 } = \beta _ { 3 } \neq 0$ 
A) $H _ { 0 } : \beta _ { 1 } = \beta _ { 2 } = \beta _ { 3 } = 1$ 
B)  $H _ { 0 } : \beta _ { 0 } = \beta _ { 1 } = \beta _ { 2 } = \beta _ { 3 }$ 
C)  $H _ { 0 } : \beta _ { 1 } = \beta _ { 2 } = \beta _ { 3 } = 0$ 
D)  $H _ { 0 } : \beta _ { 0 } = \beta _ { 1 } = \beta _ { 2 } = \beta _ { 3 } \neq 0$

Question 8

States
Concern over the number of car thefts grew into a project to determine the relationship between car thefts by state and these variables:
xS1U1B11S1U1B0 = Police per 10,000 persons,by state
xS1U1B12S1U1B0 = Expenditure by local government for police protection,in thousands,by state
xS1U1B13S1U1B0 = New passenger car registrations,in thousands,by state.
Data from 13 states were collected.The MINITAB regression results are: 
The regression equation is car-thf $= - 25.3 + 1.28$ police $+ 0.0188$ polexp $+ 0.0969$ registr
$\begin{array} { l l l c l } \text { Predictor } & \text { Coef } & \text { Stdev } & \text { t-ratio } & p \ \text { Constant } & - 25.29 & 17.85 & - 1.42 & 0.190 \ \text { police } & 1.2831 & 0.9275 & 1.38 & 0.200 \ \text { polexp } & 0.018827 & 0.008460 & 2.23 & 0.053 \ \text { registr } & 0.09686 & 0.03536 & 2.74 & 0.023 \end{array}$
$$s = ? ? \quad \mathrm { R } - s q = ? ? \% \quad \mathrm { R } - s q ( a d j ) = ? ? \%$$
Analysis of Variance
$\begin{array} { l l l l c l } \text { SOURCE } & \text { DF } & \text { SS } & \text { MS } & F & p \ \text { Regression } & 3 & 33007 & 11002 & 107.14 & 0.000 \ \text { Error } & 9 & 924 & 103 & & \ \text { Total } & 12 & 33932 & & & \end{array}$
Correlation between the variables:
$\begin{array} { l c c c c } & \text { car-thf } & \text { police } & \text { polexp } & \text { registr } \ \text { car-thf } & 1.000 & & & \ \text { police } & 0.466 & 1.000 & & \ \text { polexp } & 0.970 & 0.390 & 1.000 & \ \text { registr } & 0.976 & 0.406 & 0.958 & 1.000 \end{array}$
-What,if any,multicollinearity do you detect?

Accepted Answer

Multicollinearity is correlati

Question 9

Marketing Analyst
A marketing analyst is interested in predicting prospective buyer's knowledge about compact disc players.A random sample of 36 buyers was taken,a questionnaire about compact disc players completed,and information about education,income and age was obtained.In estimating the equation,the variables were:
y = knowledge about compact disc players
xS1U1B11S1U1B0 = education (years)
xS1U1B12S1U1B0 = age
xS1U1B13S1U1B0 = income (thousands of dollars)
The resulting output using MINITAB was: $$\begin{array}{l}
\text { The regression equation is }\
\begin{array} { l c c r } 
Y = 50.2 + 4.36 \times 1 - 0.632 \times 2 - 0.068 \times 3 & \
& & \
\text { Predictor } & \text { Coef } & \text { Stdev } & \text { t-ratio } \
\text { Constant } & 50.168 & 4.977 & 10.08 \
X 1 & 4.3609 & 0.4064 & 10.73 \
X 2 & - 0.63169 & 0.08172 & - 7.73 \
X 3 & - 0.0682 & 0.1176 & - 0.58 \
s = 4.615 & \text { R-sq } = 85.0 \% & \text { R-sq(adj) } = 83.6 \%
\end{array}
\end{array}$$
-Identify the coefficient of multiple determination,R2.
Interpret the value.

Accepted Answer

0.85; It means that 85% of the

Question 10

A health science-kinesiology program to lose weight collected data from ten students.Sex was coded as 1 = female and 0 = male.The regression equation obtained was given by: Pounds lost = 15.8 + 0.65 time + 6.00 sex.For the same length of time in the program,compare the weight loss of a female to a male.What is your conclusion?

Accepted Answer

The weight loss of a

Question 11

Professor
A statistics professor investigated some of the factors that affect an individual student's final grade in his course.He proposed the multiple regression model $$y = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 3 } + \epsilon$$ where:
y = final mark (out of 100)
xS1U1B11S1U1B0 = number of lectures skipped
xS1U1B12S1U1B0 = number of late assignments
xS1U1B13S1U1B0 = mid-term test mark (out of 100)
The professor recorded the data for 50 randomly selected students.The computer output is shown below. The regression equation is:
$$\hat { y } = 41.6 - 3.18 x _ { 1 } - 1.17 x _ { 2 } + .63 x _ { 3 }$$
$\begin{array}{l|lll|}
\hline \text { Predictor } & \text { Coef } & \text { StDev } & T \
\hline \text { Constant } & 41.6 & 17.8 & 2.337 \
x_{1} & -3.18 & 1.66 & -1.916 \
x_{2} & -1.17 & 1.13 & -1.035 \
x_{3} & 0.63 & 0.13 & 4.846 \
\hline
\end{array}$
$$S = 13.74$$
$$\mathrm { R } - \mathrm { Sq } = 30.0 \%$$
Analysis of Variance
$\begin{array}{l|llll}
\hline \text { Source of Variation } & \text { df } & \text { SS } & M S & F \
\hline \text { Regression } & 3 & 3716 & 1238.667 & 6.558 \
\text { Error } & 46 & 8688 & 188.870 & \
\hline \text { Total } & 49 & 12404 & & \
\hline
\end{array}$
-Do these data provide enough evidence at the 5% significance level to conclude that the final mark and the number of late assignments are negatively linearly related?
Test statistic = ____________________
Critical Value = ____________________
Conclusion: ____________________

Accepted Answer

t = -1.035

Question 12

States
Concern over the number of car thefts grew into a project to determine the relationship between car thefts by state and these variables:
xS1U1B11S1U1B0 = Police per 10,000 persons,by state
xS1U1B12S1U1B0 = Expenditure by local government for police protection,in thousands,by state
xS1U1B13S1U1B0 = New passenger car registrations,in thousands,by state.
Data from 13 states were collected.The MINITAB regression results are: 
The regression equation is car-thf $= - 25.3 + 1.28$ police $+ 0.0188$ polexp $+ 0.0969$ registr
$\begin{array} { l l l c l } \text { Predictor } & \text { Coef } & \text { Stdev } & \text { t-ratio } & p \ \text { Constant } & - 25.29 & 17.85 & - 1.42 & 0.190 \ \text { police } & 1.2831 & 0.9275 & 1.38 & 0.200 \ \text { polexp } & 0.018827 & 0.008460 & 2.23 & 0.053 \ \text { registr } & 0.09686 & 0.03536 & 2.74 & 0.023 \end{array}$
$$s = ? ? \quad \text { R-sq } = ? ? \% \quad \text { R-sq(adj) } = ? ? \%$$
$\begin{array}{l}
\text { Analysis of Variance }\
\begin{array} { l l l l c l } 
\text { SOURCE } & \text { DF } & \text { SS } & \text { MS } & F & p \
\text { Regression } & 3 & 33007 & 11002 & 107.14 & 0.000 \
\text { Error } & 9 & 924 & 103 & & \
\text { Total } & 12 & 33932 & & &
\end{array}
\end{array}$
$\begin{array}{l}
\text { Correlation between the variables: }\
\begin{array} { l r c c c } 
& \text { car-thf } & \text { police } & \text { polexp } & \text { registr } \
\text { car-thf } & 1.000 & & & \
\text { police } & 0.466 & 1.000 & & \
\text { polexp } & 0.970 & 0.390 & 1.000 & \
\text { registr } & 0.976 & 0.406 & 0.958 & 1.000
\end{array}
\end{array}$
-How much of the variation in thefts is explained by the model?

Accepted Answer

The answer of States
Concern over the number of car thefts...

Question 13

A health science-kinesiology program to lose weight collected data from ten students.Sex was coded as 1 = female and 0 = male.The regression equation obtained was given by: Pounds lost = 15.8 + 0.65 time + 6.00 sex What is the estimated weight loss of a female who stayed in the program for 5 time periods?

Accepted Answer

The answer of A health science-kinesiology program to lose weight...

Question 14

For a multiple regression model the following statistics are given: SSE = 40,SST = 200,k = 4,n = 20.Calculate the coefficient of determination adjusted for degrees of freedom.

Accepted Answer

The answer of For a multiple regression model the following...

Question 15

Consider the multiple regression equation, $\hat { Y }$ = 80 + 15x1 - 5 x2 + 100x3.Identify the y-intercept and partial regression coefficients:
y-intercept: ____________________
x1: ____________________
x2: ____________________
x3: ____________________

Accepted Answer

Question 16

Salary
Data was collected from 40 employees to develop a regression model to predict the employee's annual salary using their years with the company (Years),their starting salary (Starting),and their Gender (Male = 0,Female = 1).The results from Excel regression analysis are shown below:
 $$\begin{array}{l}
\begin{array} { l r } 
\hline  { \text { RegresionSlalinlics } } \
\hline \text { Multiple R } & \text { 0.719714957 } \
\text { R Square } & \text { 0.516551199 } \
\text { Adjusted R Square } & 0.476253780 \
\text { Standard Errar } & 10515.63461 \
\text { Dbservations } & 40 \
\hline
\end{array}\
\end{array}$$

$\text { ANOVA }$
$\begin{array}{lrrrrrr}
\hline & \text { of } & & \text { SS } & \text { MS } & F & \text { Significance } F \
\hline \text { Regression } & 3 & 4334682510 & 1444894170 & 12.82165585 & 7.48476 \mathrm{E}-06 \
\text { Residual } & 36 & 4056901131 & 112691698.1 & & \
\text { Total } & 39 & 8391583641 & & & \
\hline
\end{array}$

$\begin{array}{lcrrr}
\hline & \text { Coefficients } &{\text { Standard Error }} & {t \text { Stat }} &{P \text {-value }} \
\hline \text { Intercept } & 27946.57894 & 4832.438706 & 5.783121245 & 1.35464 \mathrm{E}-06 \
\text { Years } & 1665.251558 & 425.0829092 & 3.917474737 & 0.000383313 \
\text { Starting } & 0.266374185 & 0.12610443 & 2.112330112 & 0.041661598 \
\text { Gender } & -3285.541043 & 5617.145392 & -0.584912943 & 0.56225464
\end{array}$

-What is the regression equation?

Accepted Answer

The answer of Salary
Data was collected from 40 employees to...

Question 17

What is multicollinearity?

Accepted Answer

A situation in which two or mo

Question 18

For the multiple regression model $\hat { Y }$ = 50 + 25x1 - 10x2 + 8x3,if x2 were to increase by 5,holding x1 and x3 constant,the value of y would:

Accepted Answer

A)  increase by 5. 
B)  increase by 50. 
C)  decrease on average by 5. 
D)  decrease on average by 50. 
A)  increase by 5. 
B)  increase by 50. 
C)  decrease on average by 5. 
D)  decrease on average by 50.

A multiple regression model has the form $\hat { Y }$ = b₀ + b₁x₁ + b₂x₂.The coefficient b₁ is interpreted as the:

Explain each of the terms in the multiple regression model: $y _ { i } = \beta _ { 0 } + \beta _ { 1 } x _ { 1 i } + \beta _ { 2 } x _ { 2 i } + \ldots \ldots + \beta _ { \mathrm { ki } } x _ { \mathrm { ki } } + \epsilon _ { 1 }$ .

A multiple regression model has the form: $\hat { Y }$ = 5.25 + 2.5x₁ + 4x₂.As x₂ increases by 1 unit,holding x₁ constant,then the value of y will increase by:

In testing the significance of a multiple regression model in which there are three independent variables,the null hypothesis is:

For a multiple regression model the following statistics are given: SSE = 40,SST = 200,k = 4,n = 20.Calculate the coefficient of determination adjusted for degrees of freedom.

Consider the multiple regression equation, $\hat { Y }$ = 80 + 15x₁ - 5 x₂ + 100x₃.Identify the y-intercept and partial regression coefficients: y-intercept: x₁: x₂: x₃:

What is multicollinearity?

For the multiple regression model $\hat { Y }$ = 50 + 25x₁ - 10x₂ + 8x₃,if x₂ were to increase by 5,holding x₁ and x₃ constant,the value of y would:

A Preview of Business Statistics

Visual Description of Data

Statistical Description of Data

Data Collection and Sampling Methods

Probability: Review of Basic Concepts

Discrete Probability Distributions

Continuous Probability Distributions

Sampling Distributions

Estimation From Sample Data

Hypothesis Tests Involving a Sample Mean or Proportion

Hypothesis Tests Involving Two Sample Means

Analysis of Variance Tests

Chi-Square Applications

Nonparametric Methods

Simple Linear Regression and Correlation

Model Building

Models for Time Series and Forecasting

Decision Theory

Total Quality Management

Filters

Exam 16: Multiple Regression and Correlation

A multiple regression model has the form Y^\hat { Y }Y^ = b0 + b1x1 + b2x2.The coefficient b1 is interpreted as the:

A multiple regression model has the form: Y^\hat { Y }Y^ = 5.25 + 2.5x1 + 4x2.As x2 increases by 1 unit,holding x1 constant,then the value of y will increase by:

In testing the significance of a multiple regression model in which there are three independent variables,the null hypothesis is:

For a multiple regression model the following statistics are given: SSE = 40,SST = 200,k = 4,n = 20.Calculate the coefficient of determination adjusted for degrees of freedom.

Consider the multiple regression equation, Y^\hat { Y }Y^ = 80 + 15x1 - 5 x2 + 100x3.Identify the y-intercept and partial regression coefficients: y-intercept: ____________________ x1: ____________________ x2: ____________________ x3: ____________________

What is multicollinearity?

For the multiple regression model Y^\hat { Y }Y^ = 50 + 25x1 - 10x2 + 8x3,if x2 were to increase by 5,holding x1 and x3 constant,the value of y would:

A Preview of Business Statistics

Visual Description of Data

Statistical Description of Data

Data Collection and Sampling Methods

Probability: Review of Basic Concepts

Discrete Probability Distributions

Continuous Probability Distributions

Sampling Distributions

Estimation From Sample Data

Hypothesis Tests Involving a Sample Mean or Proportion

Hypothesis Tests Involving Two Sample Means

Analysis of Variance Tests

Chi-Square Applications

Nonparametric Methods

Simple Linear Regression and Correlation

Model Building

Models for Time Series and Forecasting

Decision Theory

Total Quality Management

Filters

A multiple regression model has the form $\hat { Y }$ = b₀ + b₁x₁ + b₂x₂.The coefficient b₁ is interpreted as the:

A multiple regression model has the form: $\hat { Y }$ = 5.25 + 2.5x₁ + 4x₂.As x₂ increases by 1 unit,holding x₁ constant,then the value of y will increase by:

Consider the multiple regression equation, $\hat { Y }$ = 80 + 15x₁ - 5 x₂ + 100x₃.Identify the y-intercept and partial regression coefficients: y-intercept: x₁: x₂: x₃:

For the multiple regression model $\hat { Y }$ = 50 + 25x₁ - 10x₂ + 8x₃,if x₂ were to increase by 5,holding x₁ and x₃ constant,the value of y would: