Question 1

Which of the following is used to test the significance of the overall regression equation?

Accepted Answer

A)  t-test.. 
B)  z-test. 
C)  χ2 test 
D)  F-test 
A)  t-test.. 
B)  z-test. 
C)  χ2 test 
D)  F-test D

Question 2

In testing the validity of a multiple regression model involving 5 independent variables and 30 observations, the numbers of degrees of freedom for the numerator and denominator (respectively) for the critical value of F will be:

Accepted Answer

A)  5 and 25. 
B)  24 and 5. 
C)  25 and 5. 
D)  5 and 24. 
A)  5 and 25. 
B)  24 and 5. 
C)  25 and 5. 
D)  5 and 24. D

Question 3

In a multiple regression analysis involving 20 observations and 5 independent variables, total variation in y = SSY = 250 and SSE = 35. The multiple coefficient of determination, adjusted for degrees of freedom, is:

Accepted Answer

A)  0.810. 
B)  0.860. 
C)  0.835. 
D)  0.831. 
A)  0.810. 
B)  0.860. 
C)  0.835. 
D)  0.831. A

Question 4

The multiple coefficient of determination is defined as:

Accepted Answer

A)  SSE/SSY. 
B)  MSE/MSR. 
C)  1 - (SSE/SSY). 
D)  1 - (MSE/MSR). 
A)  SSE/SSY. 
B)  MSE/MSR. 
C)  1 - (SSE/SSY). 
D)  1 - (MSE/MSR).

Question 5

Pop-up coffee vendors have been popular in the city of Adelaide in 2013. A vendor is interested in knowing how temperature (in degrees Celsius) and number of different pastries and biscuits offered to customers impacts daily hot coffee sales revenue (in $00's).
A random sample of 6 days was taken, with the daily hot coffee sales revenue and the corresponding temperature and number of different pastries and biscuits offered on that day, noted.
Excel output for a multiple linear regression is given below: $$\begin{array} { | c | c | r | } 
\hline \text { Coffee sales revenue } & \text { Temperature } & \text { Pastries/biscuits } \
\hline 6.5 & 25 & 7 \
\hline 10 & 17 & 13 \
\hline 5.5 & 30 & 5 \
\hline 4.5 & 35 & 6 \
\hline 3.5 & 40 & 3 \
\hline 28 & 9 & 15 \
\hline
\end{array}$$   Test the significance of the overall regression model, at α of 5%.

Accepted Answer

Ho: β₁ = β₂ = 0 H_A: β₁ ≠ 0 and/or

Question 6

A multiple regression model involves 40 observations and 4 independent variables produces
SST = 100 000 and SSR = 82,500. The value of MSE is 500.

Accepted Answer

A) True 
 B)False

Question 7

In a regression model involving 50 observations, the following estimated regression model was obtained: ŷ = 10.5 + 3.2x1 + 5.8x2 + 6.5x3. For this model, SSR = 450 and SSE = 175. The value of MSE is:

Accepted Answer

A)  9.783. 
B)  58.333. 
C)  150.000. 
D)  3.804. 
A)  9.783. 
B)  58.333. 
C)  150.000. 
D)  3.804.

Question 8

An actuary wanted to develop a model to predict how long individuals will live. After consulting a number of physicians, she collected the age at death (y), the average number of hours of exercise per week ( $$x _ { 1 }$$ ), the cholesterol level ( $x _ { 2 }$ ), and the number of points by which the individual's blood pressure exceeded the recommended value ( $X _ { 3 }$ ). A random sample of 40 individuals was selected. The computer output of the multiple regression model is shown below:
THE REGRESSION EQUATION IS $y =$ $55.8 + 1.79 x _ { 1 } - 0.021 x _ { 2 } - 0.016 x _ { 3 }$ $$\begin{array} { | c | c c c | } 
\hline \text { Predictor } & \text { Coef } & \text { StDev } & \text { T } \
\hline \text { Constant } & 55.8 & 11.8 & 4.729 \
x _ { 1 } & 1.79 & 0.44 & 4.068 \
x _ { 2 } & - 0.021 & 0.011 & - 1.909 \
x _ { 3 } & - 0.016 & 0.014 & - 1.143 \
\hline
\end{array}$$ S = 9.47 R-Sq = 22.5%. $$\begin{array}{l}
\text { ANALYSIS OF VARIANCE }\
\begin{array} { | l | c c c c | } 
\hline \text { Source of Variation } & \text { df } & \text { SS } & \text { MS } & \text { F } \
\hline \text { Regression } & 3 & 936 & 312 & 3.477 \
\text { Error } & 36 & 3230 & 89.722 & \
\hline \text { Total } & 39 & 4166 & & \
\hline
\end{array}
\end{array}$$ Is there enough evidence at the 10% significance level to infer that the model is useful in predicting length of life?

Accepted Answer

@#LAT-DLM& . @#LAT-DLM& At least one @#LAT-DLM& is not equal

Question 9

For the multiple regression model   $= 40 + 15 x _ { 1 } - 10 x _ { 2 } + 5 x _ { 3 }$ , if $x _ { 2 }$ were to increase by 5 units, holding $x _ { 1 }$ and $X _ { 3 }$ constant, the value of $y$ would decrease by 50 units, on average.

Accepted Answer

A) True 
 B)False

Question 10

In a multiple regression model, the error variable $ { \varepsilon }$ 
 is assumed to have a mean of:

Accepted Answer

A)  -1.0. 
B)  0.0. 
C)  1.0. 
D)  any value smaller than -1.0. 
A)  -1.0. 
B)  0.0. 
C)  1.0. 
D)  any value smaller than -1.0.

Question 11

The problem of multicollinearity arises when the:

Accepted Answer

A)  dependent variables are highly correlated with one another. 
B)  independent variables are highly correlated with one another. 
C)  independent variables are highly correlated with the dependent variable. 
D)  dependent variables are highly correlated with one another or independent variables are highly correlated with one another.. 
A)  dependent variables are highly correlated with one another. 
B)  independent variables are highly correlated with one another. 
C)  independent variables are highly correlated with the dependent variable. 
D)  dependent variables are highly correlated with one another or independent variables are highly correlated with one another..

Question 12

An economist wanted to develop a multiple regression model to enable him to predict the annual family expenditure on clothes. After some consideration, he developed the multiple regression model: $y = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 3 } + \varepsilon$ .
Where:
y = annual family clothes expenditure (in $1000s) $x _ { 1 }$ = annual household income (in $1000s) $x _ { 2 }$ = number of family members $X _ { 3 }$ = number of children under 10 years of age
The computer output is shown below.
THE REGRESSION EQUATION IS $y=1.74+0.091 x_{1}+0.93 x_{2}+0.26 x_{3}$
$\begin{array}{|c|ccc|}
\hline \text { Predictor } & \text { Coef } & \text { StDev } & \mathrm{T} \
\hline \text { Constant } & 1.74 & 0.630 & 2.762 \
x_{1} & 0.091 & 0.025 & 3.640 \
x_{2} & 0.93 & 0.290 & 3.207 \
x_{3} & 0.26 & 0.180 & 1.444 \
\hline
\end{array}$

$$\mathrm { S } = 2.06 \quad \mathrm { R } - \mathrm { Sq } = 59.6 \%$$
ANALYSIS OF VARIANCE
$\begin{array}{|l|cccc|}
\hline \text { Source of Variation } & \text { df } & \text { SS } & \text { MS } & \mathrm{F} \
\hline \text { Regression } & 3 & 288 & 96 & 22.647 \
\text { Error } & 46 & 195 & 4.239 & \
\hline \text { Total } & 49 & 483 & & \
\hline
\end{array}$
 Interpret the coefficient $b _ { 2 }$ .

Accepted Answer

@#LAT-DLM& = 0.93. This tells us that for each add

Question 13

A statistics professor investigated some of the factors that affect an individual student's final grade in his or her course. He proposed the multiple regression model: $y = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 3 } + \varepsilon$ .
Where:
y = final mark (out of 100). $x _ { 1 }$ = number of lectures skipped. $x _ { 2 }$ = number of late assignments. $X _ { 3 }$ = 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  
 = $$41.6 - 3.18 x _ { 1 } - 1.17 x _ { 2 } + .63 x _ { 3 }$$ $$\begin{array} { | c | c c c | } 
\hline \text { Predictor } & \text { Coef } & \text { StDev } & \text { T } \
\hline \text { Constant } & 41.6 & 17.8 & 2.337 \
x _ { 1 } & - 3.18 & 1.66 & - 1.916 \
x _ { 2 } & - 1.17 & 1.13 & - 1.035 \
x _ { 3 } & 0.63 & 0.13 & 4.846 \
\hline
\end{array}$$ S = 13.74 R-Sq = 30.0%. $$\begin{array}{l}
\text { ANALYSIS OF VARIANCE }\
\begin{array} { | l | c c c c | } 
\hline \text { Source of Variation } & \text { df } & \text { SS } & \text { MS } & \text { F } \
\hline \text { Regression } & 3 & 3716 & 1238.667 & 6.558 \
\text { Error } & 46 & 8688 & 188.870 & \
\hline \text { Total } & 49 & 12404 & & \
\hline
\end{array}
\end{array}$$ Interpret the coefficients $b _ { 1 }$ and $b _ { 3 }$ .

Accepted Answer

@#LAT-DLM& = -3.18. This tells us that for each ad

Question 14

In regression analysis, we judge the magnitude of the standard error of estimate relative to the values of the dependent variable, and particularly to the mean of y.

Accepted Answer

A) True 
 B)False

Question 15

A multiple regression model involves 5 independent variables and the sample size is 30. If we want to test the validity of the model at the 5% significance level, the critical value is:

Accepted Answer

A)  2.59. 
B)  2.53. 
C)  2.62. 
D)  2.56. 
A)  2.59. 
B)  2.53. 
C)  2.62. 
D)  2.56.

Question 16

For the multiple regression model  $ = 75 + 25 x _ { 1 } - 15 x _ { 2 } + 10 x _ { 3 }$ , if $x _ { 2 }$ were to increase by 5, holding $x _ { 1 }$ and $X _ { 3 }$ constant, the value of y would:

Accepted Answer

A)  increase by 5. 
B)  increase by 75. 
C)  decrease on average by 5. 
D)  decrease on average by 75. 
A)  increase by 5. 
B)  increase by 75. 
C)  decrease on average by 5. 
D)  decrease on average by 75.

Question 17

In multiple regression, the standard error of estimate is defined by $s _ { \varepsilon } = \sqrt { \alpha n E / ( n - k ) }$ , where n is the sample size and k is the number of independent variables.

Accepted Answer

A) True 
 B)False

Question 18

Pop-up coffee vendors have been popular in the city of Adelaide in 2013. A vendor is interested in knowing how temperature (in degrees Celsius) and number of different pastries and biscuits offered to customers impacts daily hot coffee sales revenue (in $00's).
A random sample of 6 days was taken, with the daily hot coffee sales revenue and the corresponding temperature and number of different pastries and biscuits offered on that day, noted.
Excel output for a multiple linear regression is given below: $$\begin{array} { | c | c | r | } 
\hline \text { Coffee sales revenue } & \text { Temperature } & \text { Pastries/biscuits } \
\hline 6.5 & 25 & 7 \
\hline 10 & 17 & 13 \
\hline 5.5 & 30 & 5 \
\hline 4.5 & 35 & 6 \
\hline 3.5 & 40 & 3 \
\hline 28 & 9 & 15 \
\hline
\end{array}$$   Interpret the intercept. Does this make sense?

Accepted Answer

We estimate that if the temperature were

Question 19

An estimated multiple regression model has the form ? = 8 + 3x1 - 5x2 - 4x3. As x1 increases by 1 unit, with x2 and x3 held constant, the value of y, on average, is estimated to:

Accepted Answer

A)  decrease by 3 unit. 
B)  increase by 3 units. 
C)  decrease by 6 units. 
D)  increase by 11 units. 
A)  decrease by 3 unit. 
B)  increase by 3 units. 
C)  decrease by 6 units. 
D)  increase by 11 units.

Question 20

Multicollinearity is a situation in which the independent variables are highly correlated with the dependent variable.

Accepted Answer

A) True 
 B)False

Which of the following is used to test the significance of the overall regression equation?

In testing the validity of a multiple regression model involving 5 independent variables and 30 observations, the numbers of degrees of freedom for the numerator and denominator (respectively) for the critical value of F will be:

In a multiple regression analysis involving 20 observations and 5 independent variables, total variation in y = SSY = 250 and SSE = 35. The multiple coefficient of determination, adjusted for degrees of freedom, is:

The multiple coefficient of determination is defined as:

A multiple regression model involves 40 observations and 4 independent variables produces SST = 100 000 and SSR = 82,500. The value of MSE is 500.

In a regression model involving 50 observations, the following estimated regression model was obtained: ŷ = 10.5 + 3.2x₁+ 5.8x₂+ 6.5x₃. For this model, SSR = 450 and SSE = 175. The value of MSE is:

In a multiple regression model, the error variable ${ \varepsilon }$ is assumed to have a mean of:

The problem of multicollinearity arises when the:

In regression analysis, we judge the magnitude of the standard error of estimate relative to the values of the dependent variable, and particularly to the mean of y.

A multiple regression model involves 5 independent variables and the sample size is 30. If we want to test the validity of the model at the 5% significance level, the critical value is:

In multiple regression, the standard error of estimate is defined by $s _ { \varepsilon } = \sqrt { \alpha n E / ( n - k ) }$ , where n is the sample size and k is the number of independent variables.

An estimated multiple regression model has the form ? = 8 + 3x₁- 5x₂- 4x₃. As x₁ increases by 1 unit, with x₂ and x₃ held constant, the value of y, on average, is estimated to:

Multicollinearity is a situation in which the independent variables are highly correlated with the dependent variable.

What Is Statistics

Types of Data, Data Collection and Sampling

Graphical Descriptive Methods Nominal Data

Graphical Descriptive Techniques Numerical Data

Numerical Descriptive Measures

Probability

Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Statistical Inference: Introduction

Sampling Distributions

Estimation: Describing a Single Population

Estimation: Comparing Two Populations

Hypothesis Testing: Describing a Single Population

Hypothesis Testing: Comparing Two Populations

Inference About Population Variances

Analysis of Variance

Additional Tests for Nominal Data: Chi-Squared Tests

Simple Linear Regression and Correlation

Model Building

Nonparametric Techniques

Statistical Inference: Conclusion

Time-Series Analysis and Forecasting

Index Numbers

Decision Analysis

Filters

Exam 19: Multiple Regression

Which of the following is used to test the significance of the overall regression equation?

In testing the validity of a multiple regression model involving 5 independent variables and 30 observations, the numbers of degrees of freedom for the numerator and denominator (respectively) for the critical value of F will be:

In a multiple regression analysis involving 20 observations and 5 independent variables, total variation in y = SSY = 250 and SSE = 35. The multiple coefficient of determination, adjusted for degrees of freedom, is:

The multiple coefficient of determination is defined as:

A multiple regression model involves 40 observations and 4 independent variables produces SST = 100 000 and SSR = 82,500. The value of MSE is 500.

In a regression model involving 50 observations, the following estimated regression model was obtained: ŷ = 10.5 + 3.2x1 + 5.8x2 + 6.5x3. For this model, SSR = 450 and SSE = 175. The value of MSE is:

For the multiple regression model =40+15x1−10x2+5x3= 40 + 15 x _ { 1 } - 10 x _ { 2 } + 5 x _ { 3 }=40+15x1​−10x2​+5x3​ , if x2x _ { 2 }x2​ were to increase by 5 units, holding x1x _ { 1 }x1​ and X3X _ { 3 }X3​ constant, the value of yyy would decrease by 50 units, on average.

In a multiple regression model, the error variable ε { \varepsilon }ε is assumed to have a mean of:

The problem of multicollinearity arises when the:

In regression analysis, we judge the magnitude of the standard error of estimate relative to the values of the dependent variable, and particularly to the mean of y.

A multiple regression model involves 5 independent variables and the sample size is 30. If we want to test the validity of the model at the 5% significance level, the critical value is:

For the multiple regression model =75+25x1−15x2+10x3 = 75 + 25 x _ { 1 } - 15 x _ { 2 } + 10 x _ { 3 }=75+25x1​−15x2​+10x3​ , if x2x _ { 2 }x2​ were to increase by 5, holding x1x _ { 1 }x1​ and X3X _ { 3 }X3​ constant, the value of y would:

In multiple regression, the standard error of estimate is defined by sε=αnE/(n−k)s _ { \varepsilon } = \sqrt { \alpha n E / ( n - k ) }sε​=αnE/(n−k)​ , where n is the sample size and k is the number of independent variables.

An estimated multiple regression model has the form ? = 8 + 3x1 - 5x2 - 4x3. As x1 increases by 1 unit, with x2 and x3 held constant, the value of y, on average, is estimated to:

Multicollinearity is a situation in which the independent variables are highly correlated with the dependent variable.

What Is Statistics

Types of Data, Data Collection and Sampling

Graphical Descriptive Methods Nominal Data

Graphical Descriptive Techniques Numerical Data

Numerical Descriptive Measures

Probability

Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Statistical Inference: Introduction

Sampling Distributions

Estimation: Describing a Single Population

Estimation: Comparing Two Populations

Hypothesis Testing: Describing a Single Population

Hypothesis Testing: Comparing Two Populations

Inference About Population Variances

Analysis of Variance

Additional Tests for Nominal Data: Chi-Squared Tests

Simple Linear Regression and Correlation

Model Building

Nonparametric Techniques

Statistical Inference: Conclusion

Time-Series Analysis and Forecasting

Index Numbers

Decision Analysis

Filters

In a regression model involving 50 observations, the following estimated regression model was obtained: ŷ = 10.5 + 3.2x₁+ 5.8x₂+ 6.5x₃. For this model, SSR = 450 and SSE = 175. The value of MSE is:

In a multiple regression model, the error variable ${ \varepsilon }$ is assumed to have a mean of:

In multiple regression, the standard error of estimate is defined by $s _ { \varepsilon } = \sqrt { \alpha n E / ( n - k ) }$ , where n is the sample size and k is the number of independent variables.

An estimated multiple regression model has the form ? = 8 + 3x₁- 5x₂- 4x₃. As x₁ increases by 1 unit, with x₂ and x₃ held constant, the value of y, on average, is estimated to: