Question 1

The method of least squares requires that the sum of the squared deviations between actual y values in the scatter diagram and y values predicted by the regression line be minimised.

Accepted Answer

A) True 
 B)False

Question 2

Given the data points (x,y)  = (3,3) , (4,4) , (5,5) , (6,6) , (7,7) , the least squares estimates of the y-intercept and slope are respectively:

Accepted Answer

A)   0 and 1.
B)   -1 and 0.
C)   5 and 5.
D)   5 and 0.E) B) and D)
F) None of the above

Question 3

Which of the following statements best describes why a linear regression is also called a least squares regression model?

Accepted Answer

A)   A linear regression is also called a least squares regression model because the regression line is calculated by minimizing the square of the difference between each actual x data value and the predicted x value.
B)   A linear regression is also called a least squares regression model because the regression line is calculated by minimizing the sum of the difference between each actual y data value and the predicted y value.
C)   A linear regression is also called a least squares regression model because the regression line is calculated by minimizing the square of each actual y data value and the predicted y value.
D)   why a A linear regression is also called a least squares regression model because the regression line is calculated by minimizing the sum of the square of the differences between each actual y data value and the predicted y value.E) A) and C)
F) B) and D)

Question 4

The standard error of estimate,  SεS _  { \varepsilon }Sε​  , is given by:

Accepted Answer

A)   SSE/(n - 2) .
B)    SSE/(n−2) \sqrt { S S E } / ( n - 2 ) SSEc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​/(n−2)   .
C)    SSE/(n−2) \sqrt { S S E / ( n - 2 )  }SSE/(n−2) c34,79.3,68.167,158.7,102.5,238c34.3,79.3,51.8,119.3,52.5,120c340,-704.7,510.7,-1060.3,512,-1067l0 -0c4.7,-7.3,11,-11,19,-11H40000v40H1012.3s-271.3,567,-271.3,567c-38.7,80.7,-84,175,-136,283c-52,108,-89.167,185.3,-111.5,232c-22.3,46.7,-33.8,70.3,-34.5,71c-4.7,4.7,-12.3,7,-23,7s-12,-1,-12,-1s-109,-253,-109,-253c-72.7,-168,-109.3,-252,-110,-252c-10.7,8,-22,16.7,-34,26c-22,17.3,-33.3,26,-34,26s-26,-26,-26,-26s76,-59,76,-59s76,-60,76,-60zM1001 80h400000v40h-400000z'/>​  .
D)   SSE/  n−2\sqrt { n - 2 }n−2c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​  . E) None of the above
F) A) and B)

Question 5

A financier whose specialty is investing in movie productions has observed that, in general, movies with 'big-name' stars seem to generate more revenue than those movies whose stars are less well known. To examine his belief, he records the gross revenue and the payment (in $ million) given to the two highest-paid performers in the movie for 10 recently released movies. $$\begin{array} { | c | c | c | } 
\hline \text { Movie } & \begin{array} { c } 
\text { Cost of two highest- } \
\text { paid performers } ( \$ \mathrm {~m} )
\end{array} & \begin{array} { c } 
\text { Gross revenue } \
( \$ \mathrm {~m} )
\end{array} \
\hline 1 & 5.3 & 48 \
\hline 2 & 7.2 & 65 \
\hline 3 & 1.3 & 18 \
\hline 4 & 1.8 & 20 \
\hline 5 & 3.5 & 31 \
\hline 6 & 2.6 & 26 \
\hline 7 & 8.0 & 73 \
\hline 8 & 2.4 & 23 \
\hline 9 & 4.5 & 39 \
\hline 10 & 6.7 & 58 \
\hline
\end{array}$$ a. Determine the least squares regression line.
b. Interpret the value of the slope of the regression line.
c. Determine the standard error of estimate, and describe what this statistic tells you about the regression line.

Accepted Answer

a.

4.225 + 8.285x
b. For eac...

Question 6

The editor of a major academic book publisher claims that a large part of the cost of books is the cost of paper. This implies that larger books will cost more money. As an experiment to analyse the claim, a university student visits the bookstore and records the number of pages and the selling price of 12 randomly selected books. These data are listed below. $$\begin{array} { | c | c | c | } 
\hline \text { Book } & \text { Number of pages } & \text { Selling price (\$) } \
\hline 1 & 844 & 55 \
\hline 2 & 727 & 50 \
\hline 3 & 360 & 35 \
\hline 4 & 915 & 60 \
\hline 5 & 295 & 30 \
\hline 6 & 706 & 50 \
\hline 7 & 410 & 40 \
\hline 8 & 905 & 53 \
\hline 9 & 1058 & 65 \
\hline 10 & 865 & 54 \
\hline 11 & 677 & 42 \
\hline 12 & 912 & 58 \
\hline
\end{array}$$ Draw a scatter diagram of the data and plot the least squares regression line on it.

Accepted Answer

The answer of The editor of a major academic book...

Question 7

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) 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 of that day noted. $$\begin{array} { | c | c | } 
\hline \text { Coffee sales revenue } & \text { Temperature } \
\hline 6.50 & 25 \
\hline 10.00 & 17 \
\hline 5.50 & 30 \
\hline 4.50 & 35 \
\hline 3.50 & 40 \
\hline 28.00 & 9 \
\hline
\end{array}$$ a. Find the least squares regression line.
b. Interpret the slope.

Accepted Answer

<img  loading="lazy" src="/assets/images/blured-textbook.svg" class="d-inline m-1" alt="blured image" width="139" height="30"> a. Estimated daily hot coffee sales rev...

Question 8

When the variance,  σε2\sigma _ { \varepsilon } ^ { 2 }σε2​  , of the error variable  ε\varepsilonε  is a constant no matter what the value of x is, this condition is called:

Accepted Answer

A)   homocausality.
B)   heteroscedasticity.
C)   homoscedasticity.
D)   heterocausality. E) None of the above
F) A) and C)

Question 9

Given the least squares regression line y-hat = 3.52 - 1.27x, and a coefficient of determination of 0.81, the coefficient of correlation is:

Accepted Answer

A)   -0.85.
B)   0.85.
C)   -0.90.
D)   0.90.E) B) and C)
F) A) and D)

Question 10

Which of the following best describes the relationship of the least squares regression line: Estimated y = 2 - x?

Accepted Answer

A)   As x increases by 1 unit, y increases by 1 unit, estimated, on average.
B)   As x increases by 1 unit y decreases by (2 -x)  units, estimated, on average.
C)   As x increases by 1 unit, y decreases by 1 unit, estimated, on average.
D)   All of these choices are correct.E) A) and B)
F) A) and C)

Question 11

In regression analysis, if the coefficient of determination is 1.0, then:

Accepted Answer

A)   the sum of squares for error must be 1.0.
B)   the sum of squares for regression must be 1.0.
C)   the sum of squares for error must be 0.0.
D)   the sum of squares for regression must be 0.0.E) B) and C)
F) C) and D)

Question 12

A professor of economics wants to study the relationship between income y (in $1000s) and education x (in years). A random sample of eight individuals is taken and the results are shown below. $$\begin{array} { | l | c | c | c | c | c | c | c | c | } 
\hline \text { Education } & 16 & 11 & 15 & 8 & 12 & 10 & 13 & 14 \
\hline \text { Income } & 58 & 40 & 55 & 35 & 43 & 41 & 52 & 49 \
\hline
\end{array}$$ Conduct a test of the population slope to determine at the 5% significance level whether a linear relationship exists between years of education and income.

Accepted Answer

.

.
Rejection region: | t | ...

Question 13

A financier whose specialty is investing in movie productions has observed that, in general, movies with 'big-name' stars seem to generate more revenue than those movies whose stars are less well known. To examine his belief, he records the gross revenue and the payment (in $ million) given to the two highest-paid performers in the movie for 10 recently released movies. $$\begin{array} { | c | c | c | } 
\hline \text { Movie } & \begin{array} { c } 
\text { Cost of two highest- } \
\text { paid performers } ( \$ \mathrm {~m} )
\end{array} & \begin{array} { c } 
\text { Gross revenue } \
( \$ \mathrm {~m} )
\end{array} \
\hline 1 & 5.3 & 48 \
\hline 2 & 7.2 & 65 \
\hline 3 & 1.3 & 18 \
\hline 4 & 1.8 & 20 \
\hline 5 & 3.5 & 31 \
\hline 6 & 2.6 & 26 \
\hline 7 & 8.0 & 73 \
\hline 8 & 2.4 & 23 \
\hline 9 & 4.5 & 39 \
\hline 10 & 6.7 & 58 \
\hline
\end{array}$$ Assume that the conditions for the tests conducted in the previous two questions are not met. Do the data allow us to infer at the 5% significance level that payment to the two highest-paid performers and gross revenue are linearly related?

Accepted Answer

H₀ :

_s = 0.
H₁ :

_s

0.
Rejection...

Question 14

A direct relationship between an independent variable x and a dependent variably y means that the variables x and y increase or decrease together.

Accepted Answer

A) True 
 B)False

Question 15

Which of the following statements is correct when all the actual values of y are on an upward sloping regression line?

Accepted Answer

A)   The coefficient of correlation is equal to one and the sign of the coefficient of correlation will be negative but the sign of the slope with be positive.
B)   The coefficient of correlation and the slope must both be equal to 1.
C)   The coefficient of correlation is equal to one and the sign of the coefficient of correlation and the sign of the slope will both be positive.
D)   The coefficient of correlation and the slope must be equal to - 1.E) None of the above
F) A) and B)

Question 16

The Pearson coefficient of correlation r equals 1 when there is/are no:

Accepted Answer

A)   explained variation.
B)   unexplained variation.
C)   y-intercept in the model.
D)   outliers.E) B) and C)
F) A) and D)

Question 17

A professor of economics wants to study the relationship between income y (in $1000s) and education x (in years). A random sample of eight individuals is taken and the results are shown below. $$\begin{array} { | l | c | c | c | c | c | c | c | c | } 
\hline \text { Education } & 16 & 11 & 15 & 8 & 12 & 10 & 13 & 14 \
\hline \text { Income } & 58 & 40 & 55 & 35 & 43 & 41 & 52 & 49 \
\hline
\end{array}$$ Predict with 95% confidence the average income of all individuals with 10 years of education.

Accepted Answer

39.715 ± 1...

Question 18

In the first-order linear regression model, the population parameters of the y-intercept and the slope are:

Accepted Answer

A)    b0b _ { 0 }b0​  and  b1b _ { 1 }b1​  .
B)    b0b _ { 0 }b0​  and  β1\beta _ { 1 }β1​  .
C)    β0\beta _ { 0 }β0​  and  b1b _ { 1 }b1​  .
D)    β0\beta _ { 0 }β0​  and  β1\beta _ { 1 }β1​  . E) B) and D)
F) A) and C)

Question 19

The value of the sum of squares for regression, SSR, can never be larger than the value of sum of squares for error, SSE.

Accepted Answer

A) True 
 B)False

Question 20

If all the points in a scatter diagram lie on the least squares regression line, then the coefficient of correlation must be:

Accepted Answer

A)   1.0.
B)   -1.0.
C)   either 1.0 or -1.0.
D)   0.0.E) B) and D)
F) All of the above

Exam 18: Simple Linear Regression and Correlation

A direct relationship between an independent variable x and a dependent variably y means that the variables x and y increase or decrease together.

Correct Answer
verified

In the first-order linear regression model, the population parameters of the y-intercept and the slope are:

Correct Answer
verified

Which of the following statements is correct when all the actual values of y are on an upward sloping regression line?

Correct Answer
verified

The standard error of estimate, $S _ { \varepsilon }$ , is given by:

Correct Answer
verified

Correct Answer
verified
H₀ : _s = 0.
H₁ : _s 0.
Rejection...
View Answer

If all the points in a scatter diagram lie on the least squares regression line, then the coefficient of correlation must be:

Correct Answer
verified

The method of least squares requires that the sum of the squared deviations between actual y values in the scatter diagram and y values predicted by the regression line be minimised.

Correct Answer
verified

Which of the following best describes the relationship of the least squares regression line: Estimated y = 2 - x?

Correct Answer
verified

In regression analysis, if the coefficient of determination is 1.0, then:

Correct Answer
verified

The Pearson coefficient of correlation r equals 1 when there is/are no:

Correct Answer
verified

Which of the following statements best describes why a linear regression is also called a least squares regression model?

Correct Answer
verified

When the variance, $\sigma _ { \varepsilon } ^ { 2 }$ , of the error variable $\varepsilon$ is a constant no matter what the value of x is, this condition is called:

Correct Answer
verified

Correct Answer
verified

Correct Answer
verified
a. 4.225 + 8.285x
b. For eac...
View Answer

Correct Answer
verified
. .
Rejection region: | t | ...
View Answer

Correct Answer
verified
39.715 ± 1...
View Answer

Correct Answer
verified
a. Estimated daily hot coffee sales rev...
View Answer

Given the data points (x,y) = (3,3) , (4,4) , (5,5) , (6,6) , (7,7) , the least squares estimates of the y-intercept and slope are respectively:

Correct Answer
verified

The value of the sum of squares for regression, SSR, can never be larger than the value of sum of squares for error, SSE.

Correct Answer
verified

Given the least squares regression line y-hat = 3.52 - 1.27x, and a coefficient of determination of 0.81, the coefficient of correlation is:

Correct Answer
verified

Exam 18: Simple Linear Regression and Correlation

A direct relationship between an independent variable x and a dependent variably y means that the variables x and y increase or decrease together.

Correct AnswerverifiedShow Answer

In the first-order linear regression model, the population parameters of the y-intercept and the slope are:

Correct AnswerverifiedShow Answer

Which of the following statements is correct when all the actual values of y are on an upward sloping regression line?

Correct AnswerverifiedShow Answer

The standard error of estimate, SεS _ { \varepsilon }Sε​ , is given by:

Correct AnswerverifiedShow Answer

Correct AnswerverifiedH0 : s = 0.H1 : s 0.Rejection...View AnswerShow Answer

If all the points in a scatter diagram lie on the least squares regression line, then the coefficient of correlation must be:

Correct AnswerverifiedShow Answer

The method of least squares requires that the sum of the squared deviations between actual y values in the scatter diagram and y values predicted by the regression line be minimised.

Correct AnswerverifiedShow Answer

Which of the following best describes the relationship of the least squares regression line: Estimated y = 2 - x?

Correct AnswerverifiedShow Answer

In regression analysis, if the coefficient of determination is 1.0, then:

Correct AnswerverifiedShow Answer

The Pearson coefficient of correlation r equals 1 when there is/are no:

Correct AnswerverifiedShow Answer

Which of the following statements best describes why a linear regression is also called a least squares regression model?

Correct AnswerverifiedShow Answer

When the variance, σε2\sigma _ { \varepsilon } ^ { 2 }σε2​ , of the error variable ε\varepsilonε is a constant no matter what the value of x is, this condition is called:

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Correct Answerverifieda. 4.225 + 8.285xb. For eac...View AnswerShow Answer

Correct Answerverified . .Rejection region: | t | ...View AnswerShow Answer

Correct Answerverified39.715 ± 1...View AnswerShow Answer

Correct Answerverified a. Estimated daily hot coffee sales rev...View AnswerShow Answer

Given the data points (x,y) = (3,3) , (4,4) , (5,5) , (6,6) , (7,7) , the least squares estimates of the y-intercept and slope are respectively:

Correct AnswerverifiedShow Answer

The value of the sum of squares for regression, SSR, can never be larger than the value of sum of squares for error, SSE.

Correct AnswerverifiedShow Answer

Given the least squares regression line y-hat = 3.52 - 1.27x, and a coefficient of determination of 0.81, the coefficient of correlation is:

Correct AnswerverifiedShow Answer

Correct Answer
verified

Correct Answer
verified

Correct Answer
verified

The standard error of estimate, $S _ { \varepsilon }$ , is given by:

Correct Answer
verified

Correct Answer
verified
H₀ : _s = 0.
H₁ : _s 0.
Rejection...
View Answer

Correct Answer
verified

Correct Answer
verified

Correct Answer
verified

Correct Answer
verified

Correct Answer
verified

Correct Answer
verified

When the variance, $\sigma _ { \varepsilon } ^ { 2 }$ , of the error variable $\varepsilon$ is a constant no matter what the value of x is, this condition is called:

Correct Answer
verified

Correct Answer
verified

Correct Answer
verified
a. 4.225 + 8.285x
b. For eac...
View Answer

Correct Answer
verified
. .
Rejection region: | t | ...
View Answer

Correct Answer
verified
39.715 ± 1...
View Answer

Correct Answer
verified
a. Estimated daily hot coffee sales rev...
View Answer

Correct Answer
verified

Correct Answer
verified

Correct Answer
verified