Question 1

If a categorical independent variable contains 4 categories,then ________ dummy variable(s)will be needed to uniquely represent these categories.
A)1
B)2
C)3
D)4

Accepted Answer

When there are n categories in a categorical variable, we need to create n-1 dummy variables to represent all the categories uniquely. In this case, we have 4 categories, so we need to create 3 dummy variables to represent them uniquely.

Question 2

Instruction 13-9 A weight-loss clinic wants to use regression analysis to build a model for weight-loss of a client (measured in kilograms).Two variables thought to effect weight-loss are client's length of time on the weight loss program and time of session.These variables are described below: Y = Weight-loss (in kilograms) XS1U1B11 S1U1B0= Length of time in weight-loss program (in months) XS1U1B12S1U1B0 = 1 if morning session,0 if not XS1U1B13S1U1B0 = 1 if afternoon session,0 if not (Base level = evening session) Data for 12 clients on a weight-loss program at the clinic were collected and used to fit the interaction model: Y = β0 + βS1U1B11S1U1B0XS1U1B11S1U1B0 + βS1U1B12S1U1B0XS1U1B12S1U1B0 + βS1U1B13S1U1B0XS1U1B13S1U1B0 + βS1U1B14S1U1B0XS1U1B11S1U1B0XS1U1B12S1U1B0 + βS1U1B15S1U1B0XS1U1B11S1U1B0XS1U1B13S1U1B0 + ε Partial output from Microsoft Excel follows: Regression Statistics $\begin{array} { l l } \text { Multiple R } & 0.73514 \ \text { R Square } & 0.540438 \ \text { Adjusted R Square } & 0.157469 \ \text { Standard Error } & 12.4147 \ \text { Observations } & 12 \end{array}$ ANOVA $\begin{array} { c c c c c } F = 5.41118 & \text { Significance } F = 0.040201 & & \ & & & & \ \text { Intercept } & \text { Coeff } & \text { StdError } & t \text { Stat } & P \text {-value } \ \text { Length } \left( X _ { 1 } \right) & 0.089744 & 14.127 & 0.0060 & 0.9951 \ \text { Morn Ses } \left( X _ { 2 } \right) & 6.22538 & 2.43473 & 2.54956 & 0.0479 \ \text { Aft Ses } \left( X _ { 3 } \right) & 2.217272 & 22.1416 & 0.100141 & 0.9235 \ \text { Length*Morn Ses } & 11.8233 & 3.1545 & 3.558901 & 0.0165 \ \text { Length*Aft Ses } & 0.77058 & 3.562 & 0.216334 & 0.8359 \ & - 0.54147 & 3.35988 & - 0.161158 & 0.8773 \end{array}$ -Referring to Instruction 13-9,what null hypothesis would you test to determine whether the slope of the linear relationship between weight-loss (Y)and time in the program (X₁)varies according to time of session? A)H₀: ?₂ = ?₃ = 0 B)H₀: ?₄ = ?₅ = 0 C)H₀: ?₁ = ?₂ = ?₃= ?₄ = ?₅ = 0 D)H₀: ?₂ = ?₃= ?₄ = ?₅ = 0

Accepted Answer

The null hypothesis to test whether the slope of the linear relationship between weight-loss and time in the program varies according to the time of session involves testing the interaction terms. Therefore, we test if the coefficients of the interaction terms (β4 and β5) are equal to zero.

Question 3

Instruction 13-12 An automotive engineer would like to be able to predict automobile fuel economy.She believes that the two most important characteristics that affect economy are engine power and the number of cylinders (4 or 6)of a car.She believes that the appropriate model is Y = 40 - 0.05XS1U1B11S1U1B0 + 20XS1U1B12S1U1B0 - 0.1XS1U1B11S1U1B0XS1U1B12S1U1B0 where XS1U1B11S1U1B0 = engine power XS1U1B12S1U1B0 = 1 if 4 cylinders,0 if 6 cylinders Y = economy expressed as kilometres. -Referring to Instruction 13-12,the fitted model for predicting economy for 4-cylinder cars is ________. A)60 - 0.15X₁ B)40 - 0.10X₁ C)40 - 0.05X₁ D)60 - 0.10X₁

Accepted Answer

The answer of Instruction 13-12
An automotive engineer would like to...

Question 4

If a categorical independent variable contains 2 categories,then ________ dummy variable(s)will be needed to uniquely represent these categories.
A)1
B)2
C)3
D)4

Accepted Answer

One dummy variable is needed to represent a binary categorical variable, as it only has two categories.

Question 5

A dummy variable is used as an independent variable in a regression model when
A)2 independent variables interact.
B)the variable involved is categorical.
C)the variable involved is numerical.
D)a curvilinear relationship is suspected.

Accepted Answer

Dummy variables are used to represent categorical variables in a regression model. They allow us to assign numerical values to categorical variables, making them easier to include in a regression equation.

Question 6

Instruction 13-9 A weight-loss clinic wants to use regression analysis to build a model for weight-loss of a client (measured in kilograms).Two variables thought to effect weight-loss are client's length of time on the weight loss program and time of session.These variables are described below: Y = Weight-loss (in kilograms) XS1U1B11 S1U1B0= Length of time in weight-loss program (in months) XS1U1B12S1U1B0 = 1 if morning session,0 if not XS1U1B13S1U1B0 = 1 if afternoon session,0 if not (Base level = evening session) Data for 12 clients on a weight-loss program at the clinic were collected and used to fit the interaction model: Y = β0 + βS1U1B11S1U1B0XS1U1B11S1U1B0 + βS1U1B12S1U1B0XS1U1B12S1U1B0 + βS1U1B13S1U1B0XS1U1B13S1U1B0 + βS1U1B14S1U1B0XS1U1B11S1U1B0XS1U1B12S1U1B0 + βS1U1B15S1U1B0XS1U1B11S1U1B0XS1U1B13S1U1B0 + ε Partial output from Microsoft Excel follows: Regression Statistics $\begin{array} { l l } \text { Multiple R } & 0.73514 \ \text { R Square } & 0.540438 \ \text { Adjusted R Square } & 0.157469 \ \text { Standard Error } & 12.4147 \ \text { Observations } & 12 \end{array}$ ANOVA $\begin{array} { c c c c c } F = 5.41118 & \text { Significance } F = 0.040201 & & \ & & & & \ \text { Intercept } & \text { Coeff } & \text { StdError } & t \text { Stat } & P \text {-value } \ \text { Length } \left( X _ { 1 } \right) & 0.089744 & 14.127 & 0.0060 & 0.9951 \ \text { Morn Ses } \left( X _ { 2 } \right) & 6.22538 & 2.43473 & 2.54956 & 0.0479 \ \text { Aft Ses } \left( X _ { 3 } \right) & 2.217272 & 22.1416 & 0.100141 & 0.9235 \ \text { Length*Morn Ses } & 11.8233 & 3.1545 & 3.558901 & 0.0165 \ \text { Length*Aft Ses } & 0.77058 & 3.562 & 0.216334 & 0.8359 \ & - 0.54147 & 3.35988 & - 0.161158 & 0.8773 \end{array}$ -Referring to Instruction 13-9,in terms of the ?'s in the model,give the mean change in weight-loss (Y)for every 1 month increase in time in the program (X₁)when attending the evening session. A)?₁ + ?₄ B)?₁ + ?₅ C)?₁ D)?₄ + ?₅

Accepted Answer

When attending the evening session, both interaction terms (Length*Morn Ses and Length*Aft Ses) are zero, so the mean change in weight-loss for every 1 month increase in time in the program is represented by the coefficient of Length, which is β1.

Question 7

Instruction 13-12 An automotive engineer would like to be able to predict automobile fuel economy.She believes that the two most important characteristics that affect economy are engine power and the number of cylinders (4 or 6)of a car.She believes that the appropriate model is Y = 40 - 0.05XS1U1B11S1U1B0 + 20XS1U1B12S1U1B0 - 0.1XS1U1B11S1U1B0XS1U1B12S1U1B0 where XS1U1B11S1U1B0 = engine power XS1U1B12S1U1B0 = 1 if 4 cylinders,0 if 6 cylinders Y = economy expressed as kilometres. -Referring to Instruction 13-12,the fitted model for predicting economy for 6-cylinder cars is ________. A)60 - 0.10X₁ B)40 - 0.10X₁ C)40 - 0.05X₁ D)60 - 0.15X₁

Accepted Answer

The fitted model for predicting economy for 6-cylinder cars is 40 - 0.05X₁. This is because the term 20XS1U1B12S1U1B0 - 0.1XS1U1B11S1U1B0XS1U1B12S1U1B0 is equal to 0 when XS1U1B12S1U1B0 = 0 (i.e., for 6-cylinder cars).

Question 8

Instruction 13-11 An econometrician is interested in evaluating the relation of demand for building materials to mortgage rates in Sydney and Melbourne.He believes that the appropriate model is Y = 10 + 5XS1U1B11S1U1B0 + 8XS1U1B12S1U1B0 where XS1U1B11S1U1B0 = mortgage rate in % XS1U1B12S1U1B0 = 1 if Sydney,0 if Melbourne Y = demand in $100 per capita -Referring to Instruction 13-11,the fitted model for predicting demand in Melbourne is ________. A)15 + 8X₂ B)10 + 13X₁ C)18 + 5X₂ D)10 + 5X₁

Accepted Answer

In Melbourne, XS1U1B12S1U1B0 = 0, so the model simplifies to Y = 10 + 5XS1U1B11S1U1B0, which corresponds to option D.

Question 9

Instruction 13-10
As a project for his business statistics class,a student examined the factors that determined parking meter rates throughout the campus area.Data were collected for the price per hour of parking,number of city blocks to the centre of the university,and one of the three jurisdictions: on campus,in the CBD and off campus,or outside of the CBD and off campus.The population regression model hypothesised is:
Yi = α + βS1U1B11S1U1B0xS1U1B11S1U1B0S1U1B1iS1U1B0 + βS1U1B12S1U1B0xS1U1B12S1U1B0S1U1B1iS1U1B0 + βS1U1B13S1U1B0xS1U1B12S1U1B0S1U1B1iS1U1B0 + εS1U1B1iS1U1B0
Where
Y is the meter price
xS1U1B11S1U1B0 is the number of blocks to the centre of the university
xS1U1B12S1U1B0 is a dummy variable that takes the value 1 if the meter is located in the CBD and off campus and the value 0 otherwise
xS1U1B13S1U1B0 is a dummy variable that takes the value 1 if the meter is located outside of the CBD and off campus,and the value 0 otherwise
The following Excel results are obtained.
 $\begin{array}{l}
\text { Regression Statistics }\
\begin{array}{lr}
\hline \text { Multiple R } & 0.9659 \
\text { R Square } & 0.9331 \
\text { Adjusted R Square } & 0.9294 \
\text { Standard Error } & 0.0327 \
\text { Observations } & 58
\end{array}
\end{array}$
ANOVA
$\begin{array}{lrrrrr} 
& D f & S S & M S & F & \text { Significance F } \
\hline \text { Regression } & 3 & 0.8094 & 0.2698 & 251.1995 & 0.0000 \
\text { Residual } & 54 & 0.0580 & 0.0010 & & \
\text { Total } & 57 & 0.8675 & & &
\end{array}$

$\begin{array}{lrrrr} 
& \text { Coefficients } & \text { Standard Error } & {t \text { Stat }} & {P \text {-value }} \
\hline \text { Intercept } & 0.5118 & 0.0136 & 37.4675 & 2.4904 \
\mathrm{X}_{1} & -0.0045 & 0.0034 & -1.3276 & 0.1898 \
\mathrm{X}_{2} & -0.2392 & 0.0123 & -19.3942 & 0.0000 \
\mathrm{X}_{3} & -0.0002 & 0.0123 & -0.0214 & 0.9829
\end{array}$
-Referring to Instruction 13-10,if one is already outside of the CBD and off campus but decides to park three more blocks from the centre of the university,the estimated mean parking meter rate will
A)decrease by 0.0135 .
B)decrease by 0.0139.
C)decrease by 0.0045.
D)decrease by 0.4979.

Accepted Answer

The coefficient of x1 is -0.0045, which means that for each additional block from the center of the university, the estimated mean parking meter rate decreases by 0.0045.

Question 10

Instruction 13-11 An econometrician is interested in evaluating the relation of demand for building materials to mortgage rates in Sydney and Melbourne.He believes that the appropriate model is Y = 10 + 5XS1U1B11S1U1B0 + 8XS1U1B12S1U1B0 where XS1U1B11S1U1B0 = mortgage rate in % XS1U1B12S1U1B0 = 1 if Sydney,0 if Melbourne Y = demand in $100 per capita -Referring to Instruction 13-11,the fitted model for predicting demand in Sydney is ________. A)10 + 5X₁ B)10 + 13X₁ C)18 + 5X₁ D)15 + 8X₂

Accepted Answer

The answer of Instruction 13-11
An econometrician is interested in evaluating...

Question 11

Instruction 13-16
Given below are results from the regression analysis where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Unemploy)and the independent variables are the age of the worker (Age),the number of years of education received (Edu),the number of years at the previous job (Job Yr),a dummy variable for marital status (Married: 1 = married,0 = otherwise),a dummy variable for head of household (Head: 1 = yes,0 = no)and a dummy variable for management position (Manager: 1 = yes,0 = no).We shall call this Model 1.
 $$\begin{array} { l r } 
\hline  { \text { Regression Statistics } } \
\hline \text { Multiple R } & 0.7035 \
\text { R Square } & 0.4949 \
\text { Adjusted R } & 0.4030 \
\text { Square } & \
\text { Standard } & 18.4861 \
\text { Error } \
\text { Observations } & 40 \
\hline
\end{array}$$ ANOVA
$\begin{array}{lrrrrr}
\hline & d f & { S S } &  { M S } & F & \text { Significance } F \
\hline \text { Regression } & 6 & 11048.6415 & 1841.4402 & 5.3885 & 0.00057 \
\text { Residual } & 33 & 11277.2586 & 341.7351 & & \
\text { Total } & 39 & 22325.9 & & &
\end{array}$

$\begin{array}{lrrrrrr} 
& \text { Coefficients } & \text { Standard Error } & t \text { Stat } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \
\hline \text { Intercept } & 32.6595 & 23.18302 & 1.4088 & 0.1683 & -14.5067& 79.8257 \
\text { Age } & 1.2915 & 0.3599 & 3.5883 & 0.0011 & 0.5592 &2.0238 \
\text { Edu } & -1.3537 & 1.1766 & -1.1504 & 0.2582 & -3.7476 &1.0402\
\text { JobYr } & 0.6171 & 0.5940 & 1.0389 & 0.3064 & -0.5914 & 1.8257 \
\text { Married } & -5.2189 & 7.6068 & -0.6861 & 0.4974 & -20.6950 & 10.2571 \
\text { Head } & -14.2978 & 7.6479 & -1.8695 & 0.0704 & -29.8575 & 1.2618 \
\text { Manager } & -24.8203 & 11.6932 & -2.1226 & 0.0414 & -48.6102 & -1.0303
\end{array}$ Model 2 is the regression analysis where the dependent variable is Unemploy and the independent variables are Age and Manager.The results of the regression analysis are given below:
 $$\begin{array} { l r } 
\hline{ \text { Regression Statistics } } \
\hline \text { Multiple R } & 0.6391 \
\text { R Square } & 0.4085 \
\text { Adjusted R } & 0.3765 \
\text { Square } & \
\text { Standard Error } &  18.8929 \
\text { Observations } &40 \
\hline
\end{array}$$ $$\begin{array}{l}
\text { ANOVA }\
\begin{array} { l r r r l r } 
\hline & d f & { S S } & { M S } & F & \text { Significance } F \
\hline \text { Regression } & 2 & 9119.0897 & 4559.5448 & 12.7740 & 0.0000 \
\text { Residual } & 37 & 13206.8103 & 356.9408 & & \
\text { Total } & 39 & 22325.9 & & & \
\hline
\end{array}\
\begin{array} { l r r r r } 
\hline & \text { Coefficients } & \text { Standard Error } & { t \text { Stat } } & P \text {-value } \
\hline \text { Intercept } & - 0.2143 & 11.5796 & - 0.0185 & 0.9853 \
\text { Age } & 1.4448 & 0.3160 & 4.5717 & 0.0000 \
\text { Manager } & - 22.5761 & 11.3488 & - 1.9893 & 0.0541 \
\hline
\end{array}
\end{array}$$
-Referring to Instruction 13-16 Model 1,which of the following is a correct statement?
A)On average,those who are in a management position are estimated to stay jobless shorter by approximately 5.22 weeks,while holding constant the effects of all the remaining independent variables.
B)On average,those who are in a management position are estimated to stay jobless shorter by approximately 14.30 weeks,while holding constant the effects of all the remaining independent variables.
C)On average,those who are in a management position are estimated to stay jobless shorter by approximately 1.35 weeks,while holding constant the effects of all the remaining independent variables.
D)On average,those who are in a management position are estimated to stay jobless shorter by approximately 24.82 weeks,while holding constant the effects of all the remaining independent variables.

Accepted Answer

The coefficient for the Manager variable in Model 1 is -24.8203, indicating that, on average, those in a management position are estimated to stay jobless shorter by approximately 24.82 weeks, holding constant the effects of all other variables.

Question 12

Instruction 13-9 A weight-loss clinic wants to use regression analysis to build a model for weight-loss of a client (measured in kilograms).Two variables thought to effect weight-loss are client's length of time on the weight loss program and time of session.These variables are described below: Y = Weight-loss (in kilograms) XS1U1B11 S1U1B0= Length of time in weight-loss program (in months) XS1U1B12S1U1B0 = 1 if morning session,0 if not XS1U1B13S1U1B0 = 1 if afternoon session,0 if not (Base level = evening session) Data for 12 clients on a weight-loss program at the clinic were collected and used to fit the interaction model: Y = β0 + βS1U1B11S1U1B0XS1U1B11S1U1B0 + βS1U1B12S1U1B0XS1U1B12S1U1B0 + βS1U1B13S1U1B0XS1U1B13S1U1B0 + βS1U1B14S1U1B0XS1U1B11S1U1B0XS1U1B12S1U1B0 + βS1U1B15S1U1B0XS1U1B11S1U1B0XS1U1B13S1U1B0 + ε Partial output from Microsoft Excel follows: Regression Statistics $\begin{array} { l l } \text { Multiple R } & 0.73514 \ \text { R Square } & 0.540438 \ \text { Adjusted R Square } & 0.157469 \ \text { Standard Error } & 12.4147 \ \text { Observations } & 12 \end{array}$ ANOVA $\begin{array} { c c c c c } F = 5.41118 & \text { Significance } F = 0.040201 & & \ & & & & \ \text { Intercept } & \text { Coeff } & \text { StdError } & t \text { Stat } & P \text {-value } \ \text { Length } \left( X _ { 1 } \right) & 0.089744 & 14.127 & 0.0060 & 0.9951 \ \text { Morn Ses } \left( X _ { 2 } \right) & 6.22538 & 2.43473 & 2.54956 & 0.0479 \ \text { Aft Ses } \left( X _ { 3 } \right) & 2.217272 & 22.1416 & 0.100141 & 0.9235 \ \text { Length*Morn Ses } & 11.8233 & 3.1545 & 3.558901 & 0.0165 \ \text { Length*Aft Ses } & 0.77058 & 3.562 & 0.216334 & 0.8359 \ & - 0.54147 & 3.35988 & - 0.161158 & 0.8773 \end{array}$ -Referring to Instruction 13-9,which of the following statements is supported by the analysis shown? A)There is sufficient evidence (at ? = 0.05)of curvature in the relationship between weight-loss (Y)and months in program(X₁). B)There is sufficient evidence (at ? = 0.10)to indicate that the session time (morning,afternoon,evening)affects weight-loss (Y). C)There is sufficient evidence (at ? = 0.05)to indicate that the relationship between weight-loss (Y)and months in program (X₁)depends on session time. D)There is insufficient evidence (at ? = 0.10)to indicate that the relationship between weight-loss (Y)and months in program(X₁)depends on session time.

Accepted Answer

The answer of Instruction 13-9
A weight-loss clinic wants to use...

Question 13

Instruction 13-9 A weight-loss clinic wants to use regression analysis to build a model for weight-loss of a client (measured in kilograms).Two variables thought to effect weight-loss are client's length of time on the weight loss program and time of session.These variables are described below: Y = Weight-loss (in kilograms) XS1U1B11 S1U1B0= Length of time in weight-loss program (in months) XS1U1B12S1U1B0 = 1 if morning session,0 if not XS1U1B13S1U1B0 = 1 if afternoon session,0 if not (Base level = evening session) Data for 12 clients on a weight-loss program at the clinic were collected and used to fit the interaction model: Y = β0 + βS1U1B11S1U1B0XS1U1B11S1U1B0 + βS1U1B12S1U1B0XS1U1B12S1U1B0 + βS1U1B13S1U1B0XS1U1B13S1U1B0 + βS1U1B14S1U1B0XS1U1B11S1U1B0XS1U1B12S1U1B0 + βS1U1B15S1U1B0XS1U1B11S1U1B0XS1U1B13S1U1B0 + ε Partial output from Microsoft Excel follows: Regression Statistics $\begin{array} { l l } \text { Multiple R } & 0.73514 \ \text { R Square } & 0.540438 \ \text { Adjusted R Square } & 0.157469 \ \text { Standard Error } & 12.4147 \ \text { Observations } & 12 \end{array}$ ANOVA $\begin{array} { c c c c c } F = 5.41118 & \text { Significance } F = 0.040201 & & \ & & & & \ \text { Intercept } & \text { Coeff } & \text { StdError } & t \text { Stat } & P \text {-value } \ \text { Length } \left( X _ { 1 } \right) & 0.089744 & 14.127 & 0.0060 & 0.9951 \ \text { Morn Ses } \left( X _ { 2 } \right) & 6.22538 & 2.43473 & 2.54956 & 0.0479 \ \text { Aft Ses } \left( X _ { 3 } \right) & 2.217272 & 22.1416 & 0.100141 & 0.9235 \ \text { Length*Morn Ses } & 11.8233 & 3.1545 & 3.558901 & 0.0165 \ \text { Length*Aft Ses } & 0.77058 & 3.562 & 0.216334 & 0.8359 \ & - 0.54147 & 3.35988 & - 0.161158 & 0.8773 \end{array}$ -Referring to Instruction 13-9,in terms of the ?'s in the model,give the mean change in weight-loss (Y)for every 1 month increase in time in the program (X₁)when attending the morning session. A)?₁ + ?₄ B)?₁ + ?₅ C)?₁ D)?₄ + ?₅

Accepted Answer

The mean change in weight-loss for every 1 month increase in time in the program when attending the morning session is given by the coefficient of the length of time in the program (β1) plus the interaction term for length and morning session (β4).

Question 14

Instruction 13-10 As a project for his business statistics class,a student examined the factors that determined parking meter rates throughout the campus area.Data were collected for the price per hour of parking,number of city blocks to the centre of the university,and one of the three jurisdictions: on campus,in the CBD and off campus,or outside of the CBD and off campus.The population regression model hypothesised is: Yi = α + βS1U1B11S1U1B0xS1U1B11S1U1B0S1U1B1iS1U1B0 + βS1U1B12S1U1B0xS1U1B12S1U1B0S1U1B1iS1U1B0 + βS1U1B13S1U1B0xS1U1B12S1U1B0S1U1B1iS1U1B0 + εS1U1B1iS1U1B0 Where Y is the meter price xS1U1B11S1U1B0 is the number of blocks to the centre of the university xS1U1B12S1U1B0 is a dummy variable that takes the value 1 if the meter is located in the CBD and off campus and the value 0 otherwise xS1U1B13S1U1B0 is a dummy variable that takes the value 1 if the meter is located outside of the CBD and off campus,and the value 0 otherwise The following Excel results are obtained. $\begin{array}{l} \text { Regression Statistics }\ \begin{array}{lr} \hline \text { Multiple R } & 0.9659 \ \text { R Square } & 0.9331 \ \text { Adjusted R Square } & 0.9294 \ \text { Standard Error } & 0.0327 \ \text { Observations } & 58 \end{array} \end{array}$ ANOVA $\begin{array}{lrrrrr} & D f & S S & M S & F & \text { Significance F } \ \hline \text { Regression } & 3 & 0.8094 & 0.2698 & 251.1995 & 0.0000 \ \text { Residual } & 54 & 0.0580 & 0.0010 & & \ \text { Total } & 57 & 0.8675 & & & \end{array}$ $\begin{array}{lrrrr} & \text { Coefficients } & \text { Standard Error } & {t \text { Stat }} & {P \text {-value }} \ \hline \text { Intercept } & 0.5118 & 0.0136 & 37.4675 & 2.4904 \ \mathrm{X}_{1} & -0.0045 & 0.0034 & -1.3276 & 0.1898 \ \mathrm{X}_{2} & -0.2392 & 0.0123 & -19.3942 & 0.0000 \ \mathrm{X}_{3} & -0.0002 & 0.0123 & -0.0214 & 0.9829 \end{array}$ -Referring to Instruction 13-10,what is the correct interpretation for the estimated coefficient for x₂? A)Holding the effect of the other independent variables constant,the estimated mean difference in costs between parking on campus,and parking outside of the CBD and off campus is $0.24 per hour. B)Holding the effect of the other independent variables constant,the estimated mean difference in costs between parking in the CBD and off campus,and parking on campus is $0.24 per hour. C)Holding the effect of the other independent variables constant,the estimated mean difference in costs between parking in the CBD and off campus,and parking either outside of the CBD and off campus or on campus is $0.24 per hour. D)Holding the effect of the other independent variables constant,the estimated mean difference in costs between parking in the CBD and off campus,and parking outside of the CBD and off campus is $0.24 per hour.

Accepted Answer

Holding the effect of the other independent variables constant, the estimated mean difference in costs between parking in the CBD and off campus, and parking on campus is $0.24 per hour.

Question 15

Instruction 13-9 A weight-loss clinic wants to use regression analysis to build a model for weight-loss of a client (measured in kilograms).Two variables thought to effect weight-loss are client's length of time on the weight loss program and time of session.These variables are described below: Y = Weight-loss (in kilograms) XS1U1B11 S1U1B0= Length of time in weight-loss program (in months) XS1U1B12S1U1B0 = 1 if morning session,0 if not XS1U1B13S1U1B0 = 1 if afternoon session,0 if not (Base level = evening session) Data for 12 clients on a weight-loss program at the clinic were collected and used to fit the interaction model: Y = β0 + βS1U1B11S1U1B0XS1U1B11S1U1B0 + βS1U1B12S1U1B0XS1U1B12S1U1B0 + βS1U1B13S1U1B0XS1U1B13S1U1B0 + βS1U1B14S1U1B0XS1U1B11S1U1B0XS1U1B12S1U1B0 + βS1U1B15S1U1B0XS1U1B11S1U1B0XS1U1B13S1U1B0 + ε Partial output from Microsoft Excel follows: Regression Statistics $\begin{array} { l l } \text { Multiple R } & 0.73514 \ \text { R Square } & 0.540438 \ \text { Adjusted R Square } & 0.157469 \ \text { Standard Error } & 12.4147 \ \text { Observations } & 12 \end{array}$ ANOVA $\begin{array} { c c c c c } F = 5.41118 & \text { Significance } F = 0.040201 & & \ & & & & \ \text { Intercept } & \text { Coeff } & \text { StdError } & t \text { Stat } & P \text {-value } \ \text { Length } \left( X _ { 1 } \right) & 0.089744 & 14.127 & 0.0060 & 0.9951 \ \text { Morn Ses } \left( X _ { 2 } \right) & 6.22538 & 2.43473 & 2.54956 & 0.0479 \ \text { Aft Ses } \left( X _ { 3 } \right) & 2.217272 & 22.1416 & 0.100141 & 0.9235 \ \text { Length*Morn Ses } & 11.8233 & 3.1545 & 3.558901 & 0.0165 \ \text { Length*Aft Ses } & 0.77058 & 3.562 & 0.216334 & 0.8359 \ & - 0.54147 & 3.35988 & - 0.161158 & 0.8773 \end{array}$ -Referring to Instruction 13-9,in terms of the ?'s in the model,give the mean change in weight-loss (Y)for every 1 month increase in time in the program (X₁)when attending the afternoon session. A)?₁ + ?₄ B)?₁ + ?₅ C)?₁ D)?₄ + ?₅

Accepted Answer

The mean change in weight-loss for every 1 month increase in time in the program when attending the afternoon session is given by the coefficient of the length of time in the program plus the interaction term for length and afternoon session, which is β1 + β5.

Question 16

An interaction term in a multiple regression model may be used when A)neither one of 2 independent variables contribute significantly to the regression model. B)there is a curvilinear relationship between the dependent and independent variables. C)the relationship between X₁ and Y changes for differing values of X₂. D)the coefficient of determination is small.

Accepted Answer

An interaction term is used when the relationship between the independent and dependent variable changes for differing values of another independent variable. This is represented by the formula Y = b0 + b1X1 + b2X2 + b3(X1*X2). Therefore, choice C is the correct answer. Choices A, B, and D are incorrect as they do not accurately describe when an interaction term is used.

Quiz 13: Introduction to Multiple Regression

If a categorical independent variable contains 4 categories,then ________ dummy variable(s) will be needed to uniquely represent these categories.

If a categorical independent variable contains 2 categories,then ________ dummy variable(s) will be needed to uniquely represent these categories.

A dummy variable is used as an independent variable in a regression model when

An interaction term in a multiple regression model may be used when