Question 1

For y = annual household expenditure for appliances maintenance and repair,what independent variables could help explain the amount of money a household spends per year for this purpose?

Accepted Answer

Many variables could affect the annual household expenditure for appliances maintenance and repair: the number of appliances owned,the age(s)of the appliance(s),the make(s)of the appliance(s).These are just a few of the many variables that could have a notable effect.

Question 2

Under what circumstances would a multiple regression analysis be preferable to a simple regression analysis?

Accepted Answer

Multiple regression analysis is preferred whenever two or more independent variables have impact upon the single dependent variable.

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:
 $$\begin{array}{l}
\begin{array} { l r } 
\hline  { \text { RegresionSlalinlics } } \
\hline \text { Multiple R } & \text { 0.719714957 } \
\text { R Square } & \text { 0.516551199 } \
\text { Adjusted R Square } & 0.476253780 \
\text { Standard Errar } & 10515.63461 \
\text { Dbservations } & 40 \
\hline
\end{array}\
\end{array}$$

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

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

-For a male employee with 5 years of experience and a starting salary of $30,000,what is the approximate 95% confidence interval for his annual salary?

Accepted Answer

$$\$ 44264 \pm ( 2.028 ) ( 10615.6 / \sqrt { 40 } ) = ( \$ 40860 , \$ 47668 )$$

Question 4

What is the coefficient of multiple determination,and what does it tell us about the relationship between y and the independent variables.

Accepted Answer

The answer of What is the coefficient of multiple determination,and...

Question 5

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 model is useful in predicting the final mark?
Test statistic = ____________________
Critical Value = ____________________
Conclusion: ____________________

Accepted Answer

The answer of Professor
A statistics professor investigated some of the...

Question 6

Grade
A statistics teacher collected the following data to determine if the number of hours a student studied during the semester and the number of classes missed could be used to predict the final grade for the course.The following table shows the results of the model being applied to 8 students.
 $$\begin{array} { | c | c | c | } 
\hline \text { Student } & \text { Predicted Grade } & \text { Actural Grade } \
\hline 1 & 84 & 92 \
\hline 2 & 93 & 95 \
\hline 3 & 77 & 81 \
\hline 4 & 81 & 78 \
\hline 5 & 81 & 75 \
\hline 6 & 89 & 88 \
\hline 7 & 88 & 85 \
\hline \mathbf { 8 } & 85 & 85 \
\hline
\end{array}$$
-Calculate the residual sum of squares.

Accepted Answer

The answer of Grade
A statistics teacher collected the following data...

Question 7

It is a good idea to make point estimates based on x values that lie beyond the range of the underlying data.

Accepted Answer

A) True 
 B)False

Question 8

What is a dummy variable,and how is it useful to multiple regression? Give an example of three dummy variables that could be used in describing your home town.

Accepted Answer

The answer of What is a dummy variable,and how is...

Question 9

Regression Model
A multiple regression model was developed to predict the grade point average (GPA)for MBA students based on two entrance exam scores,verbal (VGMAT)and math (MGMAT).The following table shows the actual GPA and predicted GPA for 7 students.
 $$\begin{array} { | c | c | c | } 
\hline \text { Student } & \text { Actural CPA } & \text { Predicted CPA } \
\hline 1 & 3.5 & 3.71 \
\hline 2 & 3.1 & 3.19 \
\hline 3 & 3.2 & 3.10 \
\hline 4 & 4.0 & 3.74 \
\hline 5 & 3.6 & 3.52 \
\hline 6 & 3.2 & 3.27 \
\hline 7 & 3.7 & 3.78 \
\hline
\end{array}$$
-Calculate the total sum of squares.

Accepted Answer

The answer of Regression Model
A multiple regression model was developed...

Question 10

In order to test the significance of a multiple regression model involving 4 independent variables and 30 observations,the numerator and denominator degrees of freedom (respectively)for the critical value of F are:

Accepted Answer

A)   4 and 30.
B)   3 and 29.
C)   4 and 25.
D)   5 and 31.

Question 11

In interpreting the multiple regression equation,it can be a mistake to conclude that one independent variable is more important than another just because its partial regression coefficient happens to be large.

Accepted Answer

A) True 
 B)False

Question 12

Regression Model
A multiple regression model was developed to predict the grade point average (GPA)for MBA students based on two entrance exam scores,verbal (VGMAT)and math (MGMAT).The following table shows the actual GPA and predicted GPA for 7 students.
 $$\begin{array} { | c | c | c | } 
\hline \text { Student } & \text { Actural CPA } & \text { Predicted CPA } \
\hline 1 & 3.5 & 3.71 \
\hline 2 & 3.1 & 3.19 \
\hline 3 & 3.2 & 3.10 \
\hline 4 & 4.0 & 3.74 \
\hline 5 & 3.6 & 3.52 \
\hline 6 & 3.2 & 3.27 \
\hline 7 & 3.7 & 3.78 \
\hline
\end{array}$$
-Calculate the coefficient of multiple determination.

Accepted Answer

The answer of Regression Model
A multiple regression model was developed...

Question 13

Among the results of a multiple regression analysis are the following sum-of-squares terms: SST,SSR,and SSE.What does each term represent,and how do the terms contribute to our understanding of the relationship between y and the set of independent variables.

Accepted Answer

The answer of Among the results of a multiple regression...

Question 14

The amount of variation in the dependent variable that is not explained by the multiple regression equation is known as:

Accepted Answer

A)   total sum of squares.
B)   residual sum of squares.
C)   regression sum of squares.
D)   treatment sum of squares.

Question 15

In multiple regression,to what does the descriptor "multiple" refer?

Accepted Answer

The answer of In multiple regression,to what does the descriptor...

Question 16

A dummy variable is used to incorporate qualitative data into the analysis.

Accepted Answer

A) True 
 B)False

Question 17

Grade
A statistics teacher collected the following data to determine if the number of hours a student studied during the semester and the number of classes missed could be used to predict the final grade for the course.The following table shows the results of the model being applied to 8 students.
 $$\begin{array} { | c | c | c | } 
\hline \text { Student } & \text { Predicted Grade } & \text { Actural Grade } \
\hline 1 & 84 & 92 \
\hline 2 & 93 & 95 \
\hline 3 & 77 & 81 \
\hline 4 & 81 & 78 \
\hline 5 & 81 & 75 \
\hline 6 & 89 & 88 \
\hline 7 & 88 & 85 \
\hline \mathbf { 8 } & 85 & 85 \
\hline
\end{array}$$
-Calculate the total sum of squares.

Accepted Answer

The answer of Grade
A statistics teacher collected the following data...

Question 18

Grade
A statistics teacher collected the following data to determine if the number of hours a student studied during the semester and the number of classes missed could be used to predict the final grade for the course.The following table shows the results of the model being applied to 8 students.
 $$\begin{array} { | c | c | c | } 
\hline \text { Student } & \text { Predicted Grade } & \text { Actural Grade } \
\hline 1 & 84 & 92 \
\hline 2 & 93 & 95 \
\hline 3 & 77 & 81 \
\hline 4 & 81 & 78 \
\hline 5 & 81 & 75 \
\hline 6 & 89 & 88 \
\hline 7 & 88 & 85 \
\hline \mathbf { 8 } & 85 & 85 \
\hline
\end{array}$$
-Calculate the multiple standard error of estimate.

Accepted Answer

The answer of Grade
A statistics teacher collected the following data...

Question 19

Equation The regression equation, $\hat{ Y }$ = 4 + 1.5xS1U1B11S1U1B0 + 2.5xS1U1B12S1U1B0 has been fitted to 25 data points.The means of xS1U1B11S1U1B0 and xS1U1B12S1U1B0 are 30 and 46,respectively.The sum of the squared differences between observed and predicted values of y has been calculated as SSE = 175,and the sum of the squared differences between y values and mean of y is SST = 525. -What is the approximate 95% confidence interval for the mean of y whenever x₁ = 20 and x₂ = 25.

Accepted Answer

The answer of Equation
The regression equation, $\hat{ Y }$ =...

Question 20

A dummy variable will have a value of either ____________________ or ____________________,depending on whether a given characteristic is present or absent.

Accepted Answer

The answer of A dummy variable will have a value...

Exam 16: Multiple Regression and Correlation

For y = annual household expenditure for appliances maintenance and repair,what independent variables could help explain the amount of money a household spends per year for this purpose?

Under what circumstances would a multiple regression analysis be preferable to a simple regression analysis?

What is the coefficient of multiple determination,and what does it tell us about the relationship between y and the independent variables.

It is a good idea to make point estimates based on x values that lie beyond the range of the underlying data.

What is a dummy variable,and how is it useful to multiple regression? Give an example of three dummy variables that could be used in describing your home town.

In order to test the significance of a multiple regression model involving 4 independent variables and 30 observations,the numerator and denominator degrees of freedom (respectively) for the critical value of F are:

In interpreting the multiple regression equation,it can be a mistake to conclude that one independent variable is more important than another just because its partial regression coefficient happens to be large.

Among the results of a multiple regression analysis are the following sum-of-squares terms: SST,SSR,and SSE.What does each term represent,and how do the terms contribute to our understanding of the relationship between y and the set of independent variables.

The amount of variation in the dependent variable that is not explained by the multiple regression equation is known as:

In multiple regression,to what does the descriptor "multiple" refer?

A dummy variable is used to incorporate qualitative data into the analysis.

A dummy variable will have a value of either or ,depending on whether a given characteristic is present or absent.