Question 1

In a regression model involving more than one independent variable, which of the following tests must be used in order to determine if the relationship between the dependent variable and the set of independent variables is significant?

Accepted Answer

A)  t test 
B)  F test 
C)  Either a t test or a chi-square test can be used. 
D)  chi-square test

Question 2

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 multiple coefficient of determination is

Accepted Answer

A)  0.2 
B)  0.5 
C)  0.333 
D)  5

Question 3

The following regression model has been proposed to predict monthly sales at a shoe store.
 $\hat { Y }$ = 40 - 3X1 + 12X2 + 10X3
where
X1 = competitor's previous month's sales in $1,000s) X2 = store's previous month's sales in $1,000s)
X3 =
= sales in $1,000s)
 $\hat { Y }$ 
a. Predict sales in dollars) for the shoe store if the competitor's previous month's sales were
$9,000, the store's previous month's sales were $30,000, and no radio advertisements were run.
b. Predict sales in dollars) for the shoe store if the competitor's previous month's sales were
$9,000, the store's previous month's sales were $30,000, and 10 radio advertisements were run.

Accepted Answer

The answer of The following regression model has been proposed...

Question 4

Exhibit 13-7
A regression model involving 4 independent variables and a sample of 15 periods resulted in the following sum of squares.
SSR = 165
SSE = 60
-Refer to Exhibit 13-7. The coefficient of determination is

Accepted Answer

A)  0.3636 
B)  0.7333 
C)  0.275 
D)  0.5

Question 5

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. MSR for this model is

Accepted Answer

A)  200 
B)  10 
C)  1,000 
D)  43

Question 6

Exhibit 13-5
Below you are given a partial Minitab output based on a sample of 25 observations.
 $\begin{array}{lcc}&\text { Coefficient }&\text { Standard Error }\
\text { Constant } & 145.321 & 48.682 \
\mathrm{X}_{1} & 25.625 & 9.150 \
\mathrm{X}_{2} & -5.720 & 3.575 \
\mathrm{X}_{3} & 0.823 & 0.183
\end{array}$
-Refer to Exhibit 13-5. The interpretation of the coefficient on X1 is that

Accepted Answer

A)  a one unit change in X1 will lead to a 25.625 unit change in Y 
B)  a one unit change in X1 will lead to a 25.625 unit increase in Y when all other variables are held constant 
C)  a one unit change in X1 will lead to a 25.625 unit increase in X2 when all other variables are held constant 
D)  It is impossible to interpret the coefficient.

Question 7

A variable that takes on the values of 0 or 1 and is used to incorporate the effect of qualitative variables in a regression model is called

Accepted Answer

A)  an interaction 
B)  a constant variable 
C)  a dummy variable 
D)  None of these alternatives is correct.

Question 8

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 p-value for testing the significance of the regression model is

Accepted Answer

A)  less than 0.01 
B)  between 0.01 and 0.025 
C)  between 0.025 and 0.05 
D)  between 0.05 and 0.10

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 test statistic F for testing the significance of the above model is

Accepted Answer

A)  32.12 
B)  6.69 
C)  4.8 
D)  58

Question 10

In order to test for the significance of a regression model involving 4 independent variables and 36 observations, the numerator and denominator degrees of freedom respectively) for the critical value of F are

Accepted Answer

A)  4 and 36 
B)  3 and 35 
C)  4 and 31 
D)  4 and 32

Question 11

Exhibit 13-7
A regression model involving 4 independent variables and a sample of 15 periods resulted in the following sum of squares.
SSR = 165
SSE = 60
-Refer to Exhibit 13-7. The test statistic from the information provided is

Accepted Answer

A)  2.110 
B)  3.480 
C)  4.710 
D)  6.875

Question 12

A multiple regression model has the form Y = 70 - 14X1 + 5X2 As X1decreases by 1 unit holding X2 constant), Y is expected to

Accepted Answer

A)  increase by 5 units 
B)  decrease by 5 units 
C)  increase by 14 units 
D)  decrease by 14 units

Question 13

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 life expectancy of a rat that was not given any protein and that did not take agent X2 is

Accepted Answer

A)  36.7 
B)  34.3 
C)  36 
D)  38.4

Question 14

Exhibit 13-3
In a regression model involving 30 observations, the following estimated regression equation was obtained:
 $\hat { Y }$ =17+4X1 - 3X2+8X3+8X4
For this model SSR = 700 and SSE = 100.
-Refer to Exhibit 13-3. The computed F statistic for testing the significance of the above model is

Accepted Answer

A)  43.75 
B)  0.875 
C)  50.19 
D)  7.00

Question 15

A regression model involving 8 independent variables for a sample of 69 periods resulted in the following sum of squares.
SSE = 306
SST = 1800
a. Compute the coefficient of determination.
b. At α = 0.05, test to determine whether or not the model is significant.

Accepted Answer

The answer of A regression model involving 8 independent variables...

Question 16

A student used multiple regression analysis to study how family spending Y) is influenced by income X1), family size X2), and additions to savings X3). The variables Y, X1, and X3 are measured in thousands of dollars. The following results were obtained.
ANOVA
DF SS
Regression 3 45.9634
Residual 11 2.6218 Total
 $\begin{array}{lr}
&\text { Coefilicient }&\text { Standard Error }\
\text { Intercept } & 0.0136 \
\mathrm{X}_{1} & 0.7992&0.074 \
\mathrm{X}_{2} & 0.2280&0.190 \
\mathrm{X}_{3} & -0.5796&0.920
\end{array}$ 
a. Write out the estimated regression equation for the relationship between the variables.
b. Compute R². What can you say about the strength of this relationship?
c. Carry out a test of whether Y is significantly related to the independent variables. Use a .05 level of significance.
d. Carry out a test to see if X3 and Y are significantly related. Use a .05 level of significance.

Accepted Answer

The answer of A student used multiple regression analysis to...

Question 17

Sherri Cola Company has developed a regression model relating its sales Y in $10,000s) with four independent variables. The four independent variables are price per unit PRICE, in dollars), competitor's price COMPRICE, in dollars), advertising ADV, in $1,000s) and type of container used CONTAIN; 1 = Cans and 0 = Bottles). Part of the regression results is shown below. Assume n = 25)
 $\begin{array}{lr}
&\text { Coefilicient }&\text { Standard Error }\
\text { Intercept } & 443.143 & \
\text { PRICE } & -57.170 & 20.426 \
\text { COMPRICE } & 27.681 & 19.991 \
\text { ADV } & 0.025 & 0.023 \
\text { CONTAIN } & -95.353 &91.027
\end{array}$ 
a. If the manufacturer uses can containers, his price is $1.25, advertising $200,000, and his competitor's price is $1.50, what is your estimate of his sales? Give your answer in dollars.
b. Test to see if there is a significant relationship between sales and unit price. Let α = 0.05.
c. Test to see if there is a significant relationship between sales and advertising. Let α = 0.05.
d. Is the type of container a significant variable? Let α = 0.05.
e. Test to see if there is a significant relationship between sales and competitor's price. Let α = 0.05.

Accepted Answer

The answer of Sherri Cola Company has developed a regression...

Question 18

The Brock Juice Company has developed a regression model relating sales Y in $10,000s) with four independent variables. The four independent variables are price per unit X1, in dollars), competitor's price X2, in dollars), advertising X3, in $1,000s) and type of container used X4) 1 = Cans and 0 = Bottles). Part of the regression results are shown below:
Analysis of Variance
Source of Variation
Degrees of Freedom
Sum of Squares
Regression 4 283,940.60
Error Residuals) 18 621,735.14
a. Compute the coefficient of determination and fully interpret its meaning.
b. Is the regression model significant? Explain what your answer implies. Let α = 0.05.
c. What has been the sample size for this analysis?

Accepted Answer

The answer of The Brock Juice Company has developed a...

Question 19

In order to test for the significance of a regression model involving 14 independent variables and 255 observations, the numerator and denominator degrees of freedom respectively) for the critical value of F are

Accepted Answer

A)  14 and 255 
B)  255 and 14 
C)  13 and 240 
D)  14 and 240

Question 20

Multiple regression analysis was used to study the relationship between a dependent variable, Y, and three independent variables X1, X2 and, X3. The following is a partial result of the regression analysis involving 20 observations.
F
 $\begin{array}{lcc} 
& \text { Coefficient } & \text { Standard Error } \
\text { Intercept } & 20.00 & 5.00 \
\mathrm{X}_{1} & 15.00 & 3.00 \
\mathrm{X}_{2} & 8.00 & 5.00 \
\mathrm{X}_{3} & -18.00 & 10.00
\end{array}$
$\text { Analysis of Variance }$
$\begin{array}{lllc}
\text { Source } & \text { DF } & \text { SS } & \text { MS } \
\text { Regression } & & & 80\
\text { Error }&&320
\end{array}$ $\begin{array}{lcc} 
& \text { Coefficient } & \text { Standard Error } \
\text { Intercept } & 20.00 & 5.00 \
\mathrm{X}_{1} & 15.00 & 3.00 \
\mathrm{X}_{2} & 8.00 & 5.00 \
\mathrm{X}_{3} & -18.00 & 10.00
\end{array}$
$\text { Analysis of Variance }$
$\begin{array}{lllc}
\text { Source } & \text { DF } & \text { SS } & \text { MS } \
\text { Regression } & & & 80\
\text { Error }&&320
\end{array}$ 
a. Compute the coefficient of determination.
b. Perform a t test and determine whether or not β₁ is significantly different from zero α = 0.05).
c. Perform a t test and determine whether or not β2 is significantly different from zero α = 0.05).
d. Perform a t test and determine whether or not β3 is significantly different from zero α = 0.05).
e. At α = 0.05, perform an F test and determine whether or not the regression model is significant.

Accepted Answer

The answer of Multiple regression analysis was used to study...

Exam 13: Multiple Regression

In a regression model involving more than one independent variable, which of the following tests must be used in order to determine if the relationship between the dependent variable and the set of independent variables is significant?

Exhibit 13-7 A regression model involving 4 independent variables and a sample of 15 periods resulted in the following sum of squares. SSR = 165 SSE = 60 -Refer to Exhibit 13-7. 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. MSR for this model is

A variable that takes on the values of 0 or 1 and is used to incorporate the effect of qualitative variables in a regression model is called

In order to test for the significance of a regression model involving 4 independent variables and 36 observations, the numerator and denominator degrees of freedom respectively) for the critical value of F are

Exhibit 13-7 A regression model involving 4 independent variables and a sample of 15 periods resulted in the following sum of squares. SSR = 165 SSE = 60 -Refer to Exhibit 13-7. The test statistic from the information provided is

A multiple regression model has the form Y = 70 - 14X1 + 5X2 As X1decreases by 1 unit holding X2 constant) , Y is expected to

Exhibit 13-3 In a regression model involving 30 observations, the following estimated regression equation was obtained: $\hat { Y }$ =17+4X1 - 3X2+8X3+8X4 For this model SSR = 700 and SSE = 100. -Refer to Exhibit 13-3. The computed F statistic for testing the significance of the above model is

A regression model involving 8 independent variables for a sample of 69 periods resulted in the following sum of squares. SSE = 306 SST = 1800 a. Compute the coefficient of determination. b. At α = 0.05, test to determine whether or not the model is significant.

In order to test for the significance of a regression model involving 14 independent variables and 255 observations, the numerator and denominator degrees of freedom respectively) for the critical value of F are

Exam 13: Multiple Regression

In a regression model involving more than one independent variable, which of the following tests must be used in order to determine if the relationship between the dependent variable and the set of independent variables is significant?

Exhibit 13-7 A regression model involving 4 independent variables and a sample of 15 periods resulted in the following sum of squares. SSR = 165 SSE = 60 -Refer to Exhibit 13-7. 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. MSR for this model is

A variable that takes on the values of 0 or 1 and is used to incorporate the effect of qualitative variables in a regression model is called

In order to test for the significance of a regression model involving 4 independent variables and 36 observations, the numerator and denominator degrees of freedom respectively) for the critical value of F are

Exhibit 13-7 A regression model involving 4 independent variables and a sample of 15 periods resulted in the following sum of squares. SSR = 165 SSE = 60 -Refer to Exhibit 13-7. The test statistic from the information provided is

A multiple regression model has the form Y = 70 - 14X1 + 5X2 As X1decreases by 1 unit holding X2 constant) , Y is expected to

Exhibit 13-3 In a regression model involving 30 observations, the following estimated regression equation was obtained: Y^\hat { Y }Y^ =17+4X1 - 3X2+8X3+8X4 For this model SSR = 700 and SSE = 100. -Refer to Exhibit 13-3. The computed F statistic for testing the significance of the above model is

A regression model involving 8 independent variables for a sample of 69 periods resulted in the following sum of squares. SSE = 306 SST = 1800 a. Compute the coefficient of determination. b. At α = 0.05, test to determine whether or not the model is significant.

In order to test for the significance of a regression model involving 14 independent variables and 255 observations, the numerator and denominator degrees of freedom respectively) for the critical value of F 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. MSR for this model is

Exhibit 13-3 In a regression model involving 30 observations, the following estimated regression equation was obtained: $\hat { Y }$ =17+4X1 - 3X2+8X3+8X4 For this model SSR = 700 and SSE = 100. -Refer to Exhibit 13-3. The computed F statistic for testing the significance of the above model is