Question 1

In a multiple regression analysis involving 10 independent variables and 81 observations, SST = 120 and SSE = 42. The coefficient of determination is

Accepted Answer

A)  0.81 
B)  0.11 
C)  0.35 
D)  0.65 
A)  0.81 
B)  0.11 
C)  0.35 
D)  0.65 D

Question 2

In a regression analysis involving 18 observations and four independent variables, the following information was obtained.
Multiple R = 0.6000 R Square = 0.3600
Standard Error = 4.8000
Based on the above information, fill in all the blanks in the following ANOVA table.
$\text { ANALYSIS OF VARIANCE }$
$\begin{array}{lcc}\text { Source of } & \text { Degrees } & \text { Sum of } & \text { Mean } \
\text { Variation } & \text { of Freedom } & \text { Squares } & \text { Square }&F\
\text { Regression } &\_\_\_?&\_\_\_? &\_\_\_?&\_\_\_? \
\text { Error } &\_\_\_? &\_\_\_?&\_\_\_?  \
\end{array}$

Accepted Answer

$\text { ANALYSIS OF VARIANCE }$
$\begin{array}{lcc}\text { Source of } & \text { Degrees } & \text { Sum of } & \text { Mean } \
\text { Variation } & \text { of Freedom } & \text { Squares } & \text { Square }&F\
\text { Regression } &4&168.48&42.12&1.828\
\text { Error } &13&299.52&23.04 \
\end{array}$

Question 3

Exhibit 13-8
The following estimated regression model was developed relating yearly income Y in $1,000s) of 30 individuals with their age X1) and their gender X2) 0 if male and 1 if female).
 $\hat { Y }$ =30+0.7X1+3X2
Also provided are SST = 1,200 and SSE = 384.
-Refer to Exhibit 13-8. From the above function, it can be said that the expected yearly income of

Accepted Answer

A)  males is $3 more than females 
B)  females is $3 more than males 
C)  males is $3,000 more than females 
D)  females is $3,000 more than males 
A)  males is $3 more than females 
B)  females is $3 more than males 
C)  males is $3,000 more than females 
D)  females is $3,000 more than males D

Question 4

Exhibit 13-1
In a regression model involving 44 observations, the following estimated regression equation was obtained.
 $\hat { Y }$ = 29+18X1+43X2+87X3
For this model SSR = 600 and SSE = 400.
-Refer to Exhibit 13-1. The computed F statistics for testing the significance of the above model is

Accepted Answer

A)  1.500 
B)  20.00 
C)  0.600 
D)  0.6667 
A)  1.500 
B)  20.00 
C)  0.600 
D)  0.6667

Question 5

In regression analysis, the response variable is the

Accepted Answer

A)  independent variable 
B)  dependent variable 
C)  slope of the regression function 
D)  intercept 
A)  independent variable 
B)  dependent variable 
C)  slope of the regression function 
D)  intercept

Question 6

Exhibit 13-10
In a regression model involving 30 observations, the following estimated regression equation was obtained.
 $\hat { Y }$ =170+34X1 - 3X2+8X3+58X4+3X5
For this model, SSR = 1,740 and SST = 2,000.
-Refer to Exhibit 13-10. The coefficient of determination for this model is

Accepted Answer

A)  0.6923 
B)  0.1494 
C)  0.1300 
D)  0.8700 
A)  0.6923 
B)  0.1494 
C)  0.1300 
D)  0.8700

Question 7

The ratio of MSE/MSR yields

Accepted Answer

A)  SST 
B)  the F statistic 
C)  SSR 
D)  None of these alternatives is correct. 
A)  SST 
B)  the F statistic 
C)  SSR 
D)  None of these alternatives is correct.

Question 8

A regression model involved 5 independent variables and 136 observations. The critical value of t for testing the significance of each of the independent variable's coefficients will have

Accepted Answer

A)  121 degrees of freedom 
B)  135 degrees of freedom 
C)  130 degrees of freedom 
D)  4 degrees of freedom 
A)  121 degrees of freedom 
B)  135 degrees of freedom 
C)  130 degrees of freedom 
D)  4 degrees of freedom

Question 9

Exhibit 13-10
In a regression model involving 30 observations, the following estimated regression equation was obtained.
 $\hat { Y }$ =170+34X1 - 3X2+8X3+58X4+3X5
For this model, SSR = 1,740 and SST = 2,000.
-Refer to Exhibit 13-10. The degrees of freedom associated with SSR are

Accepted Answer

A)  24 
B)  6 
C)  19 
D)  5 
A)  24 
B)  6 
C)  19 
D)  5

Question 10

Exhibit 13-9
In a regression analysis involving 25 observations, the following estimated regression equation was developed.
 $\hat { Y }$ =10 - 18X1+3X2+14X3
Also, the following standard errors and the sum of squares were obtained.
Sb₁ = 3 Sb2 = 6 Sb3 = 7
SST = 4,800 SSE = 1,296
-Refer to Exhibit 13-9. The multiple coefficient of determination is

Accepted Answer

A)  0.27 
B)  0.73 
C)  0.50 
D)  0.33 
A)  0.27 
B)  0.73 
C)  0.50 
D)  0.33

Question 11

Exhibit 13-1
In a regression model involving 44 observations, the following estimated regression equation was obtained.
 $\hat { Y }$ = 29+18X1+43X2+87X3
For this model SSR = 600 and SSE = 400.
-Refer to Exhibit 13-1. The coefficient of determination for the above model is

Accepted Answer

A)  0.667 
B)  0.600 
C)  0.336 
D)  o.400 
A)  0.667 
B)  0.600 
C)  0.336 
D)  o.400

Question 12

Exhibit 13-6
Below you are given a partial computer output based on a sample of 16 observations.
 $\begin{array}{lcc} 
& \text { Coefficient } & \text { Standard Error } \
\text { Intercept } & 12.924&4.425\
\mathrm{X}_{1} & -3.682&2.63. \
\mathrm{X}_{2} &45.216&12.560\
\end{array}$
$\text { Analysis of Variance }$

$\begin{array}{lccc}
\text { Source of } & \text { Degrees } &\text { Sum of } &\text { Mean }\
\text { Variation } & \text { of Freedom }&\text { Squares } & \text { Square }&F\
\text { Regression }&&4,853&2,426.5\
\text {Error }&&&485.3
\end{array}$
-Refer to Exhibit 13-6. The interpretation of the coefficient of X1 is that

Accepted Answer

A)  a one unit change in X1 will lead to a 3.682 unit decrease in Y 
B)  a one unit increase in X1 will lead to a 3.682 unit decrease in Y when all other variables are held constant 
C)  a one unit increase in X1 will lead to a 3.682 unit decrease in X2 when all other variables are held constant 
D)  It is impossible to interpret the coefficient. 
A)  a one unit change in X1 will lead to a 3.682 unit decrease in Y 
B)  a one unit increase in X1 will lead to a 3.682 unit decrease in Y when all other variables are held constant 
C)  a one unit increase in X1 will lead to a 3.682 unit decrease in X2 when all other variables are held constant 
D)  It is impossible to interpret the coefficient.

Question 13

A regression model in which more than one independent variable is used to predict the dependent variable is called

Accepted Answer

A)  a simple linear regression model 
B)  a multiple regression model 
C)  an independent model 
D)  None of these alternatives is correct. 
A)  a simple linear regression model 
B)  a multiple regression model 
C)  an independent model 
D)  None of these alternatives is correct.

Question 14

Exhibit 13-11
Below you are given a partial computer output based on a sample of 25 observations.
 $\begin{array}{lcc}&\text { Coefficient }&\text { Standard Error }\
\text { Constant } & 145 & 29 \
\mathrm{X}_{1} & 20 & 5 \
\mathrm{X}_{2} & -18 & 6 \
\mathrm{X}_{3} & 4 & 4
\end{array}$
-Refer to Exhibit 13-11. The critical t value obtained from the table to test an individual parameter at the 5% level is

Accepted Answer

A)  2.06 
B)  2.069 
C)  2.074 
D)  2.080 
A)  2.06 
B)  2.069 
C)  2.074 
D)  2.080

Question 15

Exhibit 13-6
Below you are given a partial computer output based on a sample of 16 observations.
 $\begin{array}{lcc} 
& \text { Coefficient } & \text { Standard Error } \
\text { Intercept } & 12.924&4.425\
\mathrm{X}_{1} & -3.682&2.63. \
\mathrm{X}_{2} &45.216&12.560\
\end{array}$
$\text { Analysis of Variance }$

$\begin{array}{lccc}
\text { Source of } & \text { Degrees } &\text { Sum of } &\text { Mean }\
\text { Variation } & \text { of Freedom }&\text { Squares } & \text { Square }&F\
\text { Regression }&&4,853&2,426.5\
\text {Error }&&&485.3
\end{array}$
-Refer to Exhibit 13-6. The estimated regression equation is

Accepted Answer

A)  Y = ?? + ??X1 + ?2X2 + ? 
B)  EY) = ?? + ??X1 + ?2X2 
C)  =12.924 - 3.682X1 + 45.216X2 
D)  =4.425+2.63X1+12.56X2 
A)  Y = ?? + ??X1 + ?2X2 + ? 
B)  EY) = ?? + ??X1 + ?2X2 
C)  =12.924 - 3.682X1 + 45.216X2 
D)  =4.425+2.63X1+12.56X2

Question 16

Exhibit 13-10
In a regression model involving 30 observations, the following estimated regression equation was obtained.
 $\hat { Y }$ =170+34X1 - 3X2+8X3+58X4+3X5
For this model, SSR = 1,740 and SST = 2,000.
-Refer to Exhibit 13-10. The value of SSE is

Accepted Answer

A)  3,740 
B)  170 
C)  260 
D)  2000 
A)  3,740 
B)  170 
C)  260 
D)  2000

Question 17

Exhibit 13-9
In a regression analysis involving 25 observations, the following estimated regression equation was developed.
 $\hat { Y }$ =10 - 18X1+3X2+14X3
Also, the following standard errors and the sum of squares were obtained.
Sb₁ = 3 Sb2 = 6 Sb3 = 7
SST = 4,800 SSE = 1,296
-Refer to Exhibit 13-9. The coefficient of X1

Accepted Answer

A)  is significant 
B)  is not significant 
C)  can not be tested, because not enough information is provided 
D)  None of these alternatives is correct. 
A)  is significant 
B)  is not significant 
C)  can not be tested, because not enough information is provided 
D)  None of these alternatives is correct.

Question 18

A regression analysis involved 8 independent variables and 99 observations. The critical value of t for testing the significance of each of the independent variable's coefficients will have

Accepted Answer

A)  98 degrees of freedom 
B)  97 degrees of freedom 
C)  90 degrees of freedom 
D)  7 degrees of freedom 
A)  98 degrees of freedom 
B)  97 degrees of freedom 
C)  90 degrees of freedom 
D)  7 degrees of freedom

Question 19

Shown below is a partial computer output from a regression analysis.
Coefficient Standard Error
Constant 10.00 2.00
X1 -2.00 1.50
X2 6.00 2.00
X3 -4.00 1.00
Analysis of Variance
Source of Variation
Degrees of Freedom
Sum of Squares
Mean
Square F
Regression 60
Error
Total 19 140
a. Use the above results and write the regression equation.
b. Compute the coefficient of determination and fully interpret its meaning.
c. At α = 0.05, test to see if there is a relation between X1 and Y.
d. At α = 0.05, test to see if there is a relation between X3 and Y.
e. Is the regression model significant? Perform an F test and let α = 0.05.

Accepted Answer

a. @#IMG-DLM& = 10 - 2X1 + 6X2 - 4X3
b. 0.4286; 42

Question 20

Exhibit 13-12
In a laboratory experiment, data were gathered on the life span Y in months) of 33 rats, units of daily protein intake X1), and whether or not agent X2 a proposed life extending agent) was added to the rats diet X2 = 0 if agent X2 was not added, and X2 = 1 if agent was added.) From the results of the experiment, the following regression model was developed.
 $\hat { Y }$ =36+0.8X1 - 1.7X2
Also provided are SSR = 60 and SST = 180.
-Refer to Exhibit 13-12. The test statistic for testing the significance of the model is

Accepted Answer

A)  0.50 
B)  5.00 
C)  0.25 
D)  0.33 
A)  0.50 
B)  5.00 
C)  0.25 
D)  0.33

In a multiple regression analysis involving 10 independent variables and 81 observations, SST = 120 and SSE = 42. The coefficient of determination is

Exhibit 13-1 In a regression model involving 44 observations, the following estimated regression equation was obtained. $\hat { Y }$ = 29+18X1+43X2+87X3 For this model SSR = 600 and SSE = 400. -Refer to Exhibit 13-1. The computed F statistics for testing the significance of the above model is

In regression analysis, the response variable is the

Exhibit 13-10 In a regression model involving 30 observations, the following estimated regression equation was obtained. $\hat { Y }$ =170+34X1 - 3X2+8X3+58X4+3X5 For this model, SSR = 1,740 and SST = 2,000. -Refer to Exhibit 13-10. The coefficient of determination for this model is

The ratio of MSE/MSR yields

A regression model involved 5 independent variables and 136 observations. The critical value of t for testing the significance of each of the independent variable's coefficients will have

Exhibit 13-10 In a regression model involving 30 observations, the following estimated regression equation was obtained. $\hat { Y }$ =170+34X1 - 3X2+8X3+58X4+3X5 For this model, SSR = 1,740 and SST = 2,000. -Refer to Exhibit 13-10. The degrees of freedom associated with SSR are

Exhibit 13-1 In a regression model involving 44 observations, the following estimated regression equation was obtained. $\hat { Y }$ = 29+18X1+43X2+87X3 For this model SSR = 600 and SSE = 400. -Refer to Exhibit 13-1. The coefficient of determination for the above model is

A regression model in which more than one independent variable is used to predict the dependent variable is called

Exhibit 13-11 Below you are given a partial computer output based on a sample of 25 observations. Coefficient Standard Error Constant 145 29 20 5 -18 6 4 4 -Refer to Exhibit 13-11. The critical t value obtained from the table to test an individual parameter at the 5% level is

Exhibit 13-10 In a regression model involving 30 observations, the following estimated regression equation was obtained. $\hat { Y }$ =170+34X1 - 3X2+8X3+58X4+3X5 For this model, SSR = 1,740 and SST = 2,000. -Refer to Exhibit 13-10. The value of SSE is

A regression analysis involved 8 independent variables and 99 observations. The critical value of t for testing the significance of each of the independent variable's coefficients will have

Data and Statistics

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Descriptive Statistics: Numerical Measures

Introduction to Probability

Discrete Probability Distributions

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Exam 13: Multiple Regression

In a multiple regression analysis involving 10 independent variables and 81 observations, SST = 120 and SSE = 42. The coefficient of determination is

Exhibit 13-1 In a regression model involving 44 observations, the following estimated regression equation was obtained. Y^\hat { Y }Y^ = 29+18X1+43X2+87X3 For this model SSR = 600 and SSE = 400. -Refer to Exhibit 13-1. The computed F statistics for testing the significance of the above model is

In regression analysis, the response variable is the

Exhibit 13-10 In a regression model involving 30 observations, the following estimated regression equation was obtained. Y^\hat { Y }Y^ =170+34X1 - 3X2+8X3+58X4+3X5 For this model, SSR = 1,740 and SST = 2,000. -Refer to Exhibit 13-10. The coefficient of determination for this model is

The ratio of MSE/MSR yields

A regression model involved 5 independent variables and 136 observations. The critical value of t for testing the significance of each of the independent variable's coefficients will have

Exhibit 13-10 In a regression model involving 30 observations, the following estimated regression equation was obtained. Y^\hat { Y }Y^ =170+34X1 - 3X2+8X3+58X4+3X5 For this model, SSR = 1,740 and SST = 2,000. -Refer to Exhibit 13-10. The degrees of freedom associated with SSR are

Exhibit 13-1 In a regression model involving 44 observations, the following estimated regression equation was obtained. Y^\hat { Y }Y^ = 29+18X1+43X2+87X3 For this model SSR = 600 and SSE = 400. -Refer to Exhibit 13-1. The coefficient of determination for the above model is

A regression model in which more than one independent variable is used to predict the dependent variable is called

Exhibit 13-11 Below you are given a partial computer output based on a sample of 25 observations. Coefficient Standard Error Constant 145 29 20 5 -18 6 4 4 -Refer to Exhibit 13-11. The critical t value obtained from the table to test an individual parameter at the 5% level is

Exhibit 13-10 In a regression model involving 30 observations, the following estimated regression equation was obtained. Y^\hat { Y }Y^ =170+34X1 - 3X2+8X3+58X4+3X5 For this model, SSR = 1,740 and SST = 2,000. -Refer to Exhibit 13-10. The value of SSE is

A regression analysis involved 8 independent variables and 99 observations. The critical value of t for testing the significance of each of the independent variable's coefficients will have

Data and Statistics

Descriptive Statistics: Tabular and Graphical Displays

Descriptive Statistics: Numerical Measures

Introduction to Probability

Discrete Probability Distributions

Continuous Probability Distributions

Sampling and Sampling Distributions

Interval Estimation

Hypothesis Tests

Comparisons Involving Means, Experimental Design, and Analysis of Variance

Comparisons Involving Proportions and a Test of Independence

Simple Linear Regression

Filters

Exhibit 13-1 In a regression model involving 44 observations, the following estimated regression equation was obtained. $\hat { Y }$ = 29+18X1+43X2+87X3 For this model SSR = 600 and SSE = 400. -Refer to Exhibit 13-1. The computed F statistics for testing the significance of the above model is

Exhibit 13-10 In a regression model involving 30 observations, the following estimated regression equation was obtained. $\hat { Y }$ =170+34X1 - 3X2+8X3+58X4+3X5 For this model, SSR = 1,740 and SST = 2,000. -Refer to Exhibit 13-10. The coefficient of determination for this model is

Exhibit 13-10 In a regression model involving 30 observations, the following estimated regression equation was obtained. $\hat { Y }$ =170+34X1 - 3X2+8X3+58X4+3X5 For this model, SSR = 1,740 and SST = 2,000. -Refer to Exhibit 13-10. The degrees of freedom associated with SSR are

Exhibit 13-1 In a regression model involving 44 observations, the following estimated regression equation was obtained. $\hat { Y }$ = 29+18X1+43X2+87X3 For this model SSR = 600 and SSE = 400. -Refer to Exhibit 13-1. The coefficient of determination for the above model is

Exhibit 13-10 In a regression model involving 30 observations, the following estimated regression equation was obtained. $\hat { Y }$ =170+34X1 - 3X2+8X3+58X4+3X5 For this model, SSR = 1,740 and SST = 2,000. -Refer to Exhibit 13-10. The value of SSE is