Question 1

Instruction 13.41 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 $\begin{array}{l} Y = 40 - 0.05 X _ { 1 } + 20 X _ { 2 } - 0.1 X _ { 1 } X _ { 2 }\\ \text { where } \begin{aligned} X _ { 1 } & = \text { engine power } \ X _ { 2 } & = 1 \text { if } 4 \text { cylinders, } 0 \text { if } 6 \text { cylinders } \ Y & = \text { economy expressed as kilometres. } \end{aligned} \end{array}$ -Referring to Instruction 13.41,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 13.41
An automotive engineer would like to...

Question 2

Instruction 13.42
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.
 Model 1
Regression Statistics
$\begin{array} { l l } \text { Multiple R } & 0.7035 \ \text { R Square } & 0.4949 \ \text { Adj. R Square } & 0.4030 \ \text { Std. Error } & 18.4861 \ \text { Observations } & 40 \end{array}$

ANOVA
$\begin{array} { l l l l l l l } & d f & \text { SS } & \text { MS } & F & \text { Signif F} & \ \text { Regression } & 6 & 11048.6415 & 1841.4402 & 5.3885 & 0.00057 & \ \text { Residual } & 33 & 11277.2586 & 341.7351 & & & \ \text { Total } & 39 & 223325.9 & & & & \ & & & & & & \ & \text { Coeff } & \text { StdError } & \text { tStat } & p \text { value } & \text { Lower 95\% } & \text { Upper95\% } \ \text { Intercept } & 32.6595 & 23.18302 & 1.4088 & 0.1683 & - 14.5067 & 79.8257 \ \text { Age } & 1.2915 & 0.3599 & 3.5883 & 0.0011 & 0.5592 & 2.0238 \ \text { Edu } & - 1.3537 & 1.1766 & - 1.1504 & 0.2582 & - 3.7476 & 1.0402 \ \text { Job Yr } & 0.6171 & 0.5940 & 1.0389 & 0.3064 & - 0.5914 & 1.8257 \ \text { Married } & - 5.2189 & 7.6068 & - 0.6861 & 0.4974 & - 20.6950 & 10.2571 \ \text { Head } & - 14.2978 & 7.6479 & - 1.8695 & 0.0704 & - 29.8575 & 1.2618 \ \text { Manager } & - 24.8203 & 11.6932 & - 2.1226 & 0.0414 & - 48.6102 & - 1.0303 \end{array}$ 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:
 Mode 2
Regression Statistics
$\begin{array} { l l } \text { Multiple R } & 0.6391 \ \text { R Square } & 0.4085 \ \text { Adj. R Square } & 0.3765 \ \text { Std. Error } & 18.8929 \ \text { Observations } & 40 \end{array}$

ANOVA
$\begin{array} { l l l l l l } & d f & \text { SS } & \text { MS } & F & \text { Signif F} \ \text { Regression } & 2 & 9119.0897 & 4559.5448 & 12.7740 & 0.0000 \ \text { Residual } & 37 & 13206.8103 & 356.9408 & & \ \text { Total } & 39 & 22325.9 & & & \ & & & & & \ & \text { Coeff } & \text { StdError } & t \text { Stat } & p \text { value } & \ \text { Intercept } & - 0.2143 & 11.5796 & - 0.0185 & 0.9853 & \ \text { Age } & 1.4448 & 0.3160 & 4.5717 & 0.0000 & \ \text { Manager } & - 22.5761 & 11.3488 & - 1.9893 & 0.0541 & \end{array}$
-Referring to Instruction 13.42 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 unemployed for 24.82 weeks less, holding other variables constant.

Question 3

The potential for correlation within a set of independent X variables is known as ______.

Accepted Answer

The answer of The potential for correlation within a set...

Question 4

Instruction 13.40
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
$$Y = 10 + 5 X _ { 1 } + 8 X _ { 2 }$$
where
$\begin{array} { l } 
x _ { 1 } = \text { mortgage rate in } \% \
x _ { 2 } = 1 \text { if Sydney, } 0 \text { if Melbourne } \
Y = \text { demand in } \$ 100 \text { per capita }
\end{array}$
-Referring to Instruction 13.40,the fitted model for predicting demand in Melbourne is ______. 
A)S1U1B0S1U1B1 S1U1B015 + 8XS1U1B12S1U1B0
B)S1U1B0S1U1B1 S1U1B010 + 13XS1U1B11S1U1B0
C)S1U1B0S1U1B1 S1U1B018 + 5XS1U1B12S1U1B0
D)S1U1B0S1U1B1 S1U1B010 + 5XS1U1B11S1U1B0

Accepted Answer

For Melbourne, $x_2 = 0$, so the model simplifies to $Y = 10 + 5X_1$, which matches option D.

Question 5

Variance inflationary factor (VIF)states the degree to which collinearity among the predictors increases the precision of an estimate.

Accepted Answer

The variance inflation factor (VIF) actually measures the amount of multicollinearity among the predictors, and assesses how much the variance of the estimated regression coefficients are inflated as a result of this multicollinearity. A high VIF indicates high collinearity among the predictors, which can lead to challenges in interpreting the individual effects of each predictor variable. However, a high VIF does not necessarily increase the precision of an estimate; in fact, it can lead to decreased precision and reliability of the estimated regression coefficients.

Question 6

You need to proceed with extreme caution when using a multiple regression model that has one or more large VIF values.

Accepted Answer

When a multiple regression model has one or more large VIF (Variance Inflation Factor) values, it indicates high multicollinearity among the independent variables. This means that the independent variables are highly correlated with each other, which can lead to incorrect coefficient estimates, reduced model reliability, and difficulty in interpreting the results. Therefore, it is important to proceed with caution and address the issue of multicollinearity before using such a model for analysis or prediction.

Question 7

Instruction 13.40
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
$$Y = 10 + 5 X _ { 1 } + 8 X _ { 2 }$$
where
$\begin{array} { l } 
x _ { 1 } = \text { mortgage rate in } \% \
x _ { 2 } = 1 \text { if Sydney, } 0 \text { if Melbourne } \
Y = \text { demand in } \$ 100 \text { per capita }
\end{array}$
-Referring to Instruction 13.40,the fitted model for predicting demand in Sydney is ______. 
A)S1U1B0S1U1B1 S1U1B010 + 5XS1U1B11S1U1B0
B)S1U1B0S1U1B1 S1U1B010 + 13XS1U1B11S1U1B0
C)S1U1B0S1U1B1 S1U1B018 + 5XS1U1B11S1U1B0
D)S1U1B0S1U1B1 S1U1B015 + 8XS1U1B12S1U1B0

Accepted Answer

The answer of Instruction 13.40
An econometrician is interested in evaluating...

Question 8

Instruction 13.41 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 $\begin{array}{l} Y = 40 - 0.05 X _ { 1 } + 20 X _ { 2 } - 0.1 X _ { 1 } X _ { 2 }\\ \text { where } \begin{aligned} X _ { 1 } & = \text { engine power } \ X _ { 2 } & = 1 \text { if } 4 \text { cylinders, } 0 \text { if } 6 \text { cylinders } \ Y & = \text { economy expressed as kilometres. } \end{aligned} \end{array}$ -Referring to Instruction 13.41,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

For a 6-cylinder car, X₂ = 0, so the model simplifies to: Y = 40F1F1F1S1F1F1F10 - 0.05X₁ Substituting X₂ = 0 in the last term of the original model, we get: 20X₂F1F1F1S1F1F1F10 = 0 Therefore, the only term left in the simplified model for a 6-cylinder car is - 0.05X₁, which corresponds to choice C.

Question 9

Variance inflationary factor (VIF)measures the impact of collinearity among the Xs in a regression model.

Accepted Answer

VIF is used to quantify the severity of multicollinearity in a regression model. It measures how much the variance of the estimated regression coefficient is increased due to collinearity among the predictor variables. A high VIF value indicates that there is high correlation between the independent variables and the model may need to be adjusted to address this issue.

Quiz 13: Introduction to Multiple Regression

The potential for correlation within a set of independent X variables is known as ______.

Variance inflationary factor (VIF)states the degree to which collinearity among the predictors increases the precision of an estimate.

You need to proceed with extreme caution when using a multiple regression model that has one or more large VIF values.

Variance inflationary factor (VIF)measures the impact of collinearity among the Xs in a regression model.