Question 1

The manager of a fast food restaurant wants to determine how sales in a given week are related to the number of discount vouchers (#) printed in the local newspaper during the week. The number of vouchers and sales ($000s) from 10 randomly selected weeks is given below with Excel regression output. $$\begin{array} { | c | c | } 
\hline \text { Number of vo uchers } & \text { Sales } \
\hline 4 & 12.8 \
\hline 7 & 15.4 \
\hline 5 & 13.9 \
\hline 3 & 11.2 \
\hline 19 & 18.7 \
\hline 10 & 17.9 \
\hline 8 & 16.8 \
\hline 6 & 15.9 \
\hline 3 & 11.5 \
\hline 5 & 13.9 \
\hline
\end{array}$$  a. Write down the regression equation
b. Interpret the slope.

Accepted Answer

The answer of The manager of a fast food restaurant...

Question 2

The value of the sum of squares for regression, SSR, can never be smaller than 0.0.

Accepted Answer

A) True 
 B)False

Question 3

At a recent music concert, a survey was conducted that asked a random sample of 20 people their age and how many concerts they have attended since the beginning of the year. The following data were collected. $$\begin{array}{l}
\begin{array} { | l | c | c | c | c | c | c | c | c | c | c | } 
\hline \text { Age } & 62 & 57 & 40 & 49 & 67 & 54 & 43 & 65 & 54 & 41 \
\hline \text { Number of concerts } & 6 & 5 & 4 & 3 & 5 & 5 & 2 & 6 & 3 & 1 \
\hline
\end{array}\\
\begin{array} { | l | c | c | c | c | c | c | c | c | c | c | } 
\hline \text { Age } & 44 & 48 & 55 & 60 & 59 & 63 & 69 & 40 & 38 & 52 \
\hline \text { Number of Concerts } & 3 & 2 & 4 & 5 & 4 & 5 & 4 & 2 & 1 & 3 \
\hline
\end{array}
\end{array}$$  a. Determine the standard error of estimate and describe what this statistic tells you about the model's fit.
b. Interpret the coefficient of correlation.
c. Interpret the coefficient of determination, and discuss what its value tells you about the two variables.

Accepted Answer

The answer of At a recent music concert, a survey...

Question 4

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. $$\begin{array} { | c | c | c | } 
\hline \text { Movie } & \begin{array} { c } 
\text { Cost of two highest- } \
\text { paid performers } ( \$ \mathrm {~m} )
\end{array} & \begin{array} { c } 
\text { Gross revenue } \
( \$ \mathrm {~m} )
\end{array} \
\hline 1 & 5.3 & 48 \
\hline 2 & 7.2 & 65 \
\hline 3 & 1.3 & 18 \
\hline 4 & 1.8 & 20 \
\hline 5 & 3.5 & 31 \
\hline 6 & 2.6 & 26 \
\hline 7 & 8.0 & 73 \
\hline 8 & 2.4 & 23 \
\hline 9 & 4.5 & 39 \
\hline 10 & 6.7 & 58 \
\hline
\end{array}$$ Calculate the Pearson correlation coefficient. What sign does it have? Why?

Accepted Answer

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Question 5

An ardent fan of television game shows has observed that, in general, the more educated the contestant, the less money he or she wins. To test her belief, she gathers data about the last eight winners of her favourite game show. She records their winnings in dollars and their years of education. The results are as follows. $$\begin{array} { | c | c | c | } 
\hline \text { Contestant } & \begin{array} { c } 
\text { Years of } \
\text { education }
\end{array} & \text { Winnings } \
\hline 1 & 11 & 750 \
\hline 2 & 15 & 400 \
\hline 3 & 12 & 600 \
\hline 4 & 16 & 350 \
\hline 5 & 11 & 800 \
\hline 6 & 16 & 300 \
\hline 7 & 13 & 650 \
\hline 8 & 14 & 400 \
\hline
\end{array}$$ Predict with 95% confidence the winnings of a contestant who has 10 years of education.

Accepted Answer

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Question 6

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. Excel regression output given below.  (a) Estimate daily hot coffee sales revenue on a day of 38 degrees Celsius.
(b) Is your prediction in part (a) reasonable?

Accepted Answer

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Question 7

If the value of the sum of squares for error, SSE, equals zero, then the coefficient of determination must equal zero.

Accepted Answer

A) True 
 B)False

Question 8

Given that cov(x,y) = 8, $$S _ { y } ^ { 2 }$$ = 14, $$S _ { x } ^ { 2 }$$ = 10 and n = 6, the value of the sum of squares for error, SSE, is 38.

Accepted Answer

A) True 
 B)False

Question 9

A regression analysis between weight $$y$$ (in kilograms) and height $$x$$ (in centimetres) yielded the least squares line 
 = 135 + 6 $$x$$ . We estimate that for each 1 cm in height, that weight will cedrease by 6 kilograms, on average.

Accepted Answer

A) True 
 B)False

Question 10

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. $$\begin{array} { | c | c | c | } 
\hline \text { Movie } & \begin{array} { c } 
\text { Cost of two highest- } \
\text { paid performers } ( \$ \mathrm {~m} )
\end{array} & \begin{array} { c } 
\text { Gross revenue } \
( \$ \mathrm {~m} )
\end{array} \
\hline 1 & 5.3 & 48 \
\hline 2 & 7.2 & 65 \
\hline 3 & 1.3 & 18 \
\hline 4 & 1.8 & 20 \
\hline 5 & 3.5 & 31 \
\hline 6 & 2.6 & 26 \
\hline 7 & 8.0 & 73 \
\hline 8 & 2.4 & 23 \
\hline 9 & 4.5 & 39 \
\hline 10 & 6.7 & 58 \
\hline
\end{array}$$ Conduct a test of the population slope to determine at the 5% significance level whether a linear relationship exists between payment to the two highest-paid performers and gross revenue.

Accepted Answer

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Question 11

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. $$\begin{array} { | l | c | c | c | c | c | c | c | c | } 
\hline \text { Education } & 16 & 11 & 15 & 8 & 12 & 10 & 13 & 14 \
\hline \text { Income } & 58 & 40 & 55 & 35 & 43 & 41 & 52 & 49 \
\hline
\end{array}$$ 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 years of education and income are linearly related?

Accepted Answer

The answer of A professor of economics wants to study...

Question 12

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. Excel regression output given below. $$\begin{array} { | c | c | } 
\hline \text { Coffee sales revenue } & \text { Temperature } \
\hline 6.50 & 25 \
\hline 10.00 & 17 \
\hline 5.50 & 30 \
\hline 4.50 & 35 \
\hline 3.50 & 40 \
\hline 28.00 & 9 \
\hline
\end{array}$$  Test the significance of the slope, against a two-tailed alternative, at the 5% level of significance.

Accepted Answer

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

Question 13

Given that ssx = 2500, ssy = 3750, ssxy = 500 and n = 6, the standard error of estimate is:

Accepted Answer

A)  12.247. 
B)  24.933. 
C)  30.2076. 
D)  11.180.

Question 14

If the error variable $$\varepsilon$$ is normally distributed, the test statistic for testing $$H _ { 0 } : \beta _ { 1 } = 0$$ in a simple linear regression follows the Student t-distribution with n - 1 degrees of freedom.

Accepted Answer

A) True 
 B)False

Question 15

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. $$\begin{array} { | l | c | c | c | c | c | c | c | c | } 
\hline \text { Education } & 16 & 11 & 15 & 8 & 12 & 10 & 13 & 14 \
\hline \text { Income } & 58 & 40 & 55 & 35 & 43 & 41 & 52 & 49 \
\hline
\end{array}$$ Calculate the Pearson correlation coefficient. What sign does it have? Why?

Accepted Answer

The answer of A professor of economics wants to study...

Question 16

A direct relationship between an independent variable x and a dependent variably y means that x and y move in the same directions.

Accepted Answer

A) True 
 B)False

Question 17

In simple linear regression, which of the following statements indicates no linear relationship between the variables x and y?

Accepted Answer

A)  The coefficient of determination is 1.0. 
B)  The coefficient of correlation is 0.0. 
C)  The sum of squares for error is 0.0. 
D)  The sum of squares for regression is relatively large.

Question 18

In a simple linear regression model, testing whether the slope, $$\beta _ { 1 }$$ , of the population regression line is zero is the same as testing whether the population coefficient of correlation, $$P$$ , equals zero.

Accepted Answer

A) True 
 B)False

Question 19

In a simple linear regression, which of the following is equivalent to testing the significance of the population slope?

Accepted Answer

A)  Testing the significance of the population intercept. 
B)  Testing the significance of the mean. 
C)  Testing the significance of the coefficient of correlation. 
D)  All of these choices are correct.

Question 20

Which of the following best describes the value of the slope, if the coefficient of determination is 0.95?

Accepted Answer

A)  Slope must be 1. 
B)  Slope must be negative. 
C)  Slope must be 0.95. 
D)  Slope must be positive.

Exam 18: Simple Linear Regression and Correlation

The value of the sum of squares for regression, SSR, can never be smaller than 0.0.

If the value of the sum of squares for error, SSE, equals zero, then the coefficient of determination must equal zero.

Given that cov(x,y) = 8, $S _ { y } ^ { 2 }$ = 14, $S _ { x } ^ { 2 }$ = 10 and n = 6, the value of the sum of squares for error, SSE, is 38.

A regression analysis between weight $y$ (in kilograms) and height $x$ (in centimetres) yielded the least squares line = 135 + 6 $x$ . We estimate that for each 1 cm in height, that weight will cedrease by 6 kilograms, on average.

Given that ss_x = 2500, ss_y = 3750, ss_xy = 500 and n = 6, the standard error of estimate is:

If the error variable $\varepsilon$ is normally distributed, the test statistic for testing $H _ { 0 } : \beta _ { 1 } = 0$ in a simple linear regression follows the Student t-distribution with n - 1 degrees of freedom.

A direct relationship between an independent variable x and a dependent variably y means that x and y move in the same directions.

In simple linear regression, which of the following statements indicates no linear relationship between the variables x and y?

In a simple linear regression model, testing whether the slope, $\beta _ { 1 }$ , of the population regression line is zero is the same as testing whether the population coefficient of correlation, $P$ , equals zero.

In a simple linear regression, which of the following is equivalent to testing the significance of the population slope?

Which of the following best describes the value of the slope, if the coefficient of determination is 0.95?

Exam 18: Simple Linear Regression and Correlation

The value of the sum of squares for regression, SSR, can never be smaller than 0.0.

If the value of the sum of squares for error, SSE, equals zero, then the coefficient of determination must equal zero.

Given that cov(x,y) = 8, Sy2S _ { y } ^ { 2 }Sy2​ = 14, Sx2S _ { x } ^ { 2 }Sx2​ = 10 and n = 6, the value of the sum of squares for error, SSE, is 38.

A regression analysis between weight yyy (in kilograms) and height xxx (in centimetres) yielded the least squares line = 135 + 6 xxx . We estimate that for each 1 cm in height, that weight will cedrease by 6 kilograms, on average.

Given that ssx = 2500, ssy = 3750, ssxy = 500 and n = 6, the standard error of estimate is:

If the error variable ε\varepsilonε is normally distributed, the test statistic for testing H0:β1=0H _ { 0 } : \beta _ { 1 } = 0H0​:β1​=0 in a simple linear regression follows the Student t-distribution with n - 1 degrees of freedom.

A direct relationship between an independent variable x and a dependent variably y means that x and y move in the same directions.

In simple linear regression, which of the following statements indicates no linear relationship between the variables x and y?

In a simple linear regression model, testing whether the slope, β1\beta _ { 1 }β1​ , of the population regression line is zero is the same as testing whether the population coefficient of correlation, PPP , equals zero.

In a simple linear regression, which of the following is equivalent to testing the significance of the population slope?

Which of the following best describes the value of the slope, if the coefficient of determination is 0.95?

Given that cov(x,y) = 8, $S _ { y } ^ { 2 }$ = 14, $S _ { x } ^ { 2 }$ = 10 and n = 6, the value of the sum of squares for error, SSE, is 38.

A regression analysis between weight $y$ (in kilograms) and height $x$ (in centimetres) yielded the least squares line = 135 + 6 $x$ . We estimate that for each 1 cm in height, that weight will cedrease by 6 kilograms, on average.

Given that ss_x = 2500, ss_y = 3750, ss_xy = 500 and n = 6, the standard error of estimate is:

If the error variable $\varepsilon$ is normally distributed, the test statistic for testing $H _ { 0 } : \beta _ { 1 } = 0$ in a simple linear regression follows the Student t-distribution with n - 1 degrees of freedom.

In a simple linear regression model, testing whether the slope, $\beta _ { 1 }$ , of the population regression line is zero is the same as testing whether the population coefficient of correlation, $P$ , equals zero.