Question 1

A multiple regression analysis that includes 25 data points and 4 independent variables produces SST = 400 and SSR = 300. The multiple standard error of estimate will be 5.

Accepted Answer

A) True 
 B)False

Question 2

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 $y=1.74+0.091 x_{1}+0.93 x_{2}+0.26 x_{3}$
$\begin{array}{|c|ccc|}
\hline \text { Predictor } & \text { Coef } & \text { StDev } & \text { T } \
\hline \text { Constant } & 1.74 & 0.630 & 2.762 \
x_{1} & 0.091 & 0.025 & 3.640 \
x_{2} & 0.93 & 0.290 & 3.207 \
x_{3} & 0.26 & 0.180 & 1.444 \
\hline
\end{array}$

$$\mathrm { S } = 2.06 \quad \mathrm { R } - \mathrm { Sq } = 59.6 \%$$
ANALYSIS OF VARIANCE
$\begin{array}{|l|cccc|}
\hline \text { Source of Variation } & \mathrm{df} & \mathrm{SS} & \mathrm{MS} & \mathrm{F} \
\hline \text { Regression } & 3 & 288 & 96 & 22.647 \
\text { Error } & 46 & 195 & 4.239 & \
\hline \text { Total } & 49 & 483 & & \
\hline
\end{array}$
 Test at the 1% significance level to determine whether the number of family members and annual family clothes expenditure are linearly related.

Accepted Answer

The answer of An economist wanted to develop a multiple...

Question 3

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
$= 41.6 - 3.18 x _ { 1 } - 1.17 x _ { 2 } + .63 x _ { 3 }$

$\begin{array}{|c|ccc|}
\hline \text { Predictor } & \text { Coef } & \text { StDev } & \text { T } \
\hline \text { Constant } & 41.6 & 17.8 & 2.337 \
x_{1} & -3.18 & 1.66 & -1.916 \
x_{2} & -1.17 & 1.13 & -1.035 \
x_{3} & 0.63 & 0.13 & 4.846 \
\hline
\end{array}$
$$\mathrm { S } = 13.74 \quad \mathrm { R } - \mathrm { Sq } = 30.0 \%$$
ANALYSIS OF VARIANCE
$\begin{array}{|l|cccc|}
\hline \text { Source of Variation } & \text { df } & \mathrm{SS} & \mathrm{MS} & \mathrm{F} \
\hline \text { Regression } & 3 & 3716 & 1238.667 & 6.558 \
\text { Error } & 46 & 8688 & 188.870 & \
\hline \text { Total } & 49 & 12404 & & \
\hline
\end{array}$
 Do these data provide enough evidence to conclude at the 5% significance level that the model is useful in predicting the final mark?

Accepted Answer

The answer of A statistics professor investigated some of the...

Question 4

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 $y =$ $$1.74 + 0.091 x _ { 1 } + 0.93 x _ { 2 } + 0.26 x _ { 3 }$$ $$\begin{array} { | c | c c c | } 
\hline \text { Predictor } & \text { Coef } & \text { StDev } & \mathrm { T } \
\hline \text { Constant } & 1.74 & 0.630 & 2.762 \
x _ { 1 } & 0.091 & 0.025 & 3.640 \
x _ { 2 } & 0.93 & 0.290 & 3.207 \
x _ { 3 } & 0.26 & 0.180 & 1.444 \
\hline
\end{array}$$ S = 2.06 R-Sq = 59.6%. $$\begin{array}{l}
\text { ANALYSIS OF VARIANCE }\
\begin{array} { | l | c c c c | } 
\hline \text { Source of Variation } & \text { df } & \text { SS } & \text { MS } & \text { F } \
\hline \text { Regression } & 3 & 288 & 96 & 22.647 \
\text { Error } & 46 & 195 & 4.239 & \
\hline \text { Total } & 49 & 483 & & \
\hline
\end{array}
\end{array}$$ Test the overall model's validity at the 5% significance level.

Accepted Answer

The answer of An economist wanted to develop a multiple...

Question 5

Consider the following statistics of a multiple regression model: n = 30 k = 4 SS_y = 1500 SSE = 260. a. Determine the standard error of estimate. b. Determine the multiple coefficient of determination. c. Determine the F-statistic.

Accepted Answer

The answer of Consider the following statistics of a multiple...

Question 6

In a regression model involving 60 observations, the following estimated regression model was obtained: $= 51.4 + 0.70 x _ { 1 } + 0.679 x _ { 2 } - 0.378 x _ { 3 }$ For this model, total variation in y = SSY = 119,724 and SSR = 29,029.72. The value of MSE is:

Accepted Answer

A)  1619.541. 
B)  9676.572. 
C)  1995.400. 
D)  5020.235.

Question 7

For the estimated multiple regression model  = 30 -4x1 + 5x2 +3 x3, a one unit increase in x3, holding x1 and x2 constant, will result in which of the following changes in y?

Accepted Answer

A)  y will increase by 3 units. 
B)  y will increase by 2 units, estimated, on average. 
C)  y will increase by 33 units 
D)  y will increase by 3 units, estimated, on average.

Question 8

In testing the validity of a multiple regression model in which there are four independent variables, the null hypothesis is:

Accepted Answer

A)  $H _ { 0 } : \beta _ { 1 } = \beta _ { 2 } = \beta _ { 3 } = \beta _ { 4 } = 1$ . 
B)  $H _ { 0 } : \beta _ { 0 } = \beta _ { 1 } = \beta _ { 2 } = \beta _ { 3 } = \beta _ { 4 }$ . 
C)  $H _ { 0 } : \beta _ { 1 } = \beta _ { 2 } = \beta _ { 3 } = \beta _ { 4 } = 0$ . 
D)  $H _ { 0 } : \beta _ { 0 } = \beta _ { 1 } = \beta _ { 2 } = \beta _ { 3 } = \beta _ { 4 } \neq 0$ .

Question 9

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%. $$\begin{array}{l}
\text { ANALYSIS OF VARIANCE }\
\begin{array} { | l | c c c c | } 
\hline \text { Source of Variation } & \text { df } & \text { SS } & \text { MS } & \text { F } \
\hline \text { Regression } & 3 & 936 & 312 & 3.477 \
\text { Error } & 36 & 3230 & 89.722 & \
\hline \text { Total } & 39 & 4166 & & \
\hline
\end{array}
\end{array}$$ What is the coefficient of determination? What does this statistic tell you?

Accepted Answer

The answer of An actuary wanted to develop a model...

Question 10

In multiple regression, the problem of multicollinearity affects the t-tests of the individual coefficients as well as the F-test in the analysis of variance for regression, since the F-test combines these t-tests into a single test.

Accepted Answer

A) True 
 B)False

Question 11

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
$$y = 1.74 + 0.091 x _ { 1 } + 0.93 x _ { 2 } + 0.26 x _ { 3 }$$
$\begin{array}{|c|ccc|}
\hline \text { Predictor } & \text { Coef } & \text { StDev } & \text { T } \
\hline \text { Constant } & 1.74 & 0.630 & 2.762 \
x_{1} & 0.091 & 0.025 & 3.640 \
x_{2} & 0.93 & 0.290 & 3.207 \
x_{3} & 0.26 & 0.180 & 1.444 \
\hline
\end{array}$

$$\mathrm { S } = 2.06 \quad \mathrm { R } - \mathrm { Sq } = 59.6 \%$$
ANALYSIS OF VARIANCE
$\begin{array}{|l|cccc|}
\hline \text { Source of Variation } & \mathrm{df} & \mathrm{SS} & \mathrm{MS} & \mathrm{F} \
\hline \text { Regression } & 3 & 288 & 96 & 22.647 \
\text { Error } & 46 & 195 & 4.239 & \
\hline \text { Total } & 49 & 483 & & \
\hline
\end{array}$
 What is the coefficient of determination? What does this statistic tell you?

Accepted Answer

The answer of An economist wanted to develop a multiple...

Question 12

In reference to the equation $ = 1.86 - 0.51 x _ { 1 } + 0.60 \quad x _ { 2 }$
 , the value 0.60 is the change in $y$ per unit change in $x _ { 2 }$ , regardless of the value of $x _ { 1 }$ .

Accepted Answer

A) True 
 B)False

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%. $$\begin{array}{l}
\text { ANALYSIS OF VARIANCE }\
\begin{array} { | l | c c c c | } 
\hline \text { Source of Variation } & \text { df } & \text { SS } & \text { MS } & \text { F } \
\hline \text { Regression } & 3 & 3716 & 1238.667 & 6.558 \
\text { Error } & 46 & 8688 & 188.870 & \
\hline \text { Total } & 49 & 12404 & & \
\hline
\end{array}
\end{array}$$ Do these data provide enough evidence at the 1% significance level to conclude that the final mark and the mid-term mark are positively linearly related?

Accepted Answer

The answer of A statistics professor investigated some of the...

Question 14

A multiple regression analysis that includes 4 independent variables results in a sum of squares for regression of 1200 and a sum of squares for error of 800. The multiple coefficient of determination will be:

Accepted Answer

A)  0.667. 
B)  0.600. 
C)  0.400. 
D)  0.200.

Question 15

Test the hypotheses: $H _ { 0 } :$ There is no first-order autocorrelation $H _ { 1 } :$ There is first-order autocorrelation,
given that the Durbin-Watson statistic d = 1.89, n = 28, k = 3 and $\alpha =$ 0.05.

Accepted Answer

The answer of Test the hypotheses: \(H _ { 0...

Question 16

Which of the following best describes a multiple linear regression model?

Accepted Answer

A)  A multiple linear regression model has more than one dependent variable. 
B)  A multiple linear regression model has more than one independent variable. 
C)  A multiple linear regression model must have more than one independent variable and more than one independent variable. 
D)  A multiple linear regression model has one independent variable.

Question 17

A multiple regression model has the form ŷ = b0 + b1x1 + b2x2. The coefficient b2 is interpreted as the change in $y$ per unit change in x2.

Accepted Answer

A) True 
 B)False

Question 18

In a multiple regression model, the standard deviation of the error variable $\varepsilon$ is assumed to be:

Accepted Answer

A)  constant for all values of the independent variables. 
B)  constant for all values of the dependent variable. 
C)  1.0. 
D)  None of these choices are correct.

Question 19

A multiple regression analysis that includes 20 data points and 4 independent variables results in total variation in y = SSY = 200 and SSR = 160. The multiple standard error of estimate will be:

Accepted Answer

A)  0.80. 
B)  3.266. 
C)  3.651. 
D)  1.633.

Question 20

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 coefficient on Pasties/biscuits against a two tailed alternative. Use the 5% level of significance.

Accepted Answer

The answer of Pop-up coffee vendors have been popular in...

Exam 19: Multiple Regression

A multiple regression analysis that includes 25 data points and 4 independent variables produces SST = 400 and SSR = 300. The multiple standard error of estimate will be 5.

Consider the following statistics of a multiple regression model: n = 30 k = 4 SS_y = 1500 SSE = 260. a. Determine the standard error of estimate. b. Determine the multiple coefficient of determination. c. Determine the F-statistic.

For the estimated multiple regression model = 30 -4x₁+ 5x₂+3 x₃, a one unit increase in x₃, holding x₁ and x₂ constant, will result in which of the following changes in y?

In testing the validity of a multiple regression model in which there are four independent variables, the null hypothesis is:

In multiple regression, the problem of multicollinearity affects the t-tests of the individual coefficients as well as the F-test in the analysis of variance for regression, since the F-test combines these t-tests into a single test.

A multiple regression analysis that includes 4 independent variables results in a sum of squares for regression of 1200 and a sum of squares for error of 800. The multiple coefficient of determination will be:

Test the hypotheses: $H _ { 0 } :$ There is no first-order autocorrelation $H _ { 1 } :$ There is first-order autocorrelation, given that the Durbin-Watson statistic d = 1.89, n = 28, k = 3 and $\alpha =$ 0.05.

Which of the following best describes a multiple linear regression model?

A multiple regression model has the form ŷ = b₀+ b₁x₁ + b₂x₂. The coefficient b₂ is interpreted as the change in $y$ per unit change in x₂.

In a multiple regression model, the standard deviation of the error variable $\varepsilon$ is assumed to be:

A multiple regression analysis that includes 20 data points and 4 independent variables results in total variation in y = SSY = 200 and SSR = 160. The multiple standard error of estimate will be:

Exam 19: Multiple Regression

A multiple regression analysis that includes 25 data points and 4 independent variables produces SST = 400 and SSR = 300. The multiple standard error of estimate will be 5.

Consider the following statistics of a multiple regression model: n = 30 k = 4 SSy = 1500 SSE = 260. a. Determine the standard error of estimate. b. Determine the multiple coefficient of determination. c. Determine the F-statistic.

For the estimated multiple regression model = 30 -4x1 + 5x2 +3 x3, a one unit increase in x3, holding x1 and x2 constant, will result in which of the following changes in y?

In testing the validity of a multiple regression model in which there are four independent variables, the null hypothesis is:

In multiple regression, the problem of multicollinearity affects the t-tests of the individual coefficients as well as the F-test in the analysis of variance for regression, since the F-test combines these t-tests into a single test.

In reference to the equation =1.86−0.51x1+0.60x2 = 1.86 - 0.51 x _ { 1 } + 0.60 \quad x _ { 2 }=1.86−0.51x1​+0.60x2​ , the value 0.60 is the change in yyy per unit change in x2x _ { 2 }x2​ , regardless of the value of x1x _ { 1 }x1​ .

A multiple regression analysis that includes 4 independent variables results in a sum of squares for regression of 1200 and a sum of squares for error of 800. The multiple coefficient of determination will be:

Test the hypotheses: H0:H _ { 0 } :H0​: There is no first-order autocorrelation H1:H _ { 1 } :H1​: There is first-order autocorrelation, given that the Durbin-Watson statistic d = 1.89, n = 28, k = 3 and α=\alpha =α= 0.05.

Which of the following best describes a multiple linear regression model?

A multiple regression model has the form ŷ = b0 + b1x1 + b2x2. The coefficient b2 is interpreted as the change in yyy per unit change in x2.

In a multiple regression model, the standard deviation of the error variable ε\varepsilonε is assumed to be:

A multiple regression analysis that includes 20 data points and 4 independent variables results in total variation in y = SSY = 200 and SSR = 160. The multiple standard error of estimate will be:

Consider the following statistics of a multiple regression model: n = 30 k = 4 SS_y = 1500 SSE = 260. a. Determine the standard error of estimate. b. Determine the multiple coefficient of determination. c. Determine the F-statistic.

For the estimated multiple regression model = 30 -4x₁+ 5x₂+3 x₃, a one unit increase in x₃, holding x₁ and x₂ constant, will result in which of the following changes in y?

Test the hypotheses: $H _ { 0 } :$ There is no first-order autocorrelation $H _ { 1 } :$ There is first-order autocorrelation, given that the Durbin-Watson statistic d = 1.89, n = 28, k = 3 and $\alpha =$ 0.05.

A multiple regression model has the form ŷ = b₀+ b₁x₁ + b₂x₂. The coefficient b₂ is interpreted as the change in $y$ per unit change in x₂.

In a multiple regression model, the standard deviation of the error variable $\varepsilon$ is assumed to be: