Question 1

The regression line Estimated y = 3 + 2x has been fitted to the data points (4,8), (2,5), and (1,2). The sum of the squared residuals will be:

Accepted Answer

A)  7. 
B)  15. 
C)  8. 
D)  22.

Question 2

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. $$\begin{array} { | c | c | c | } 
\hline \text { Contestant } & \begin{array} { c } 
\text { Years of } \
\text { education }
\end{array} & \text { Winnings } \
\hline 1 & 11 & 750 \
\hline 2 & 15 & 400 \
\hline 3 & 12 & 600 \
\hline 4 & 16 & 350 \
\hline 5 & 11 & 800 \
\hline 6 & 16 & 300 \
\hline 7 & 13 & 650 \
\hline 8 & 14 & 400 \
\hline
\end{array}$$ Compute the standardised residuals.

Accepted Answer

The answer of An ardent fan of television game shows...

Question 3

In simple linear regression, the coefficient of correlation r and the least squares estimate $\hat { \beta } _ { 1 }$ of the population slope $\beta _ { 1 }$ :

Accepted Answer

A) Must be the same size and sign. 
B) May have a different size and different sign. 
C) May be the same size but have different sign. 
D) May be different sizes but will have the same sign.

Question 4

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. $$\begin{array} { | c | c | } 
\hline \text { Number of vouchers } & \text { Sales } \
\hline 4 & 12.8 \
\hline 7 & 15.4 \
\hline 5 & 13.9 \
\hline 3 & 11.2 \
\hline 19 & 18.7 \
\hline 10 & 17.9 \
\hline 8 & 16.8 \
\hline 6 & 15.9 \
\hline 3 & 11.5 \
\hline 5 & 13.9 \
\hline
\end{array}$$ $\begin{array}{|l|c|c|c|c|c|c|}
\hline \text { SUMMARY OUTPUT } & & \
\hline & & \
\hline \text { RegressionStatistics } & & \
\hline \text { Multiple R } & 0.8524 & \
\hline \text { RSquare } & 0.7267 & \
\hline \text { Adjusted R Square } & 0.6925 & \
\hline \text { Standard Error } & 1.4301 & \
\hline \text { Observations } & 10 & \\hline & & \
\hline \text { ANOvA } & & & & & & \
\hline & d f & S S & \text { MS } & F & \text { significance } F & \
\hline \text { Regression } & 1 & 43.4982 & 43.4982 & 21.2682 & 0.0017 & \
\hline \text { Residual } & 8 & 16.3618 & 2.0452 & & & \
\hline \text { Total } & 9 & 59.8600 & & & & \\hline & & \
\hline & \text { Coefficients } & \text { Standard Error } & \text { t Stat } & \text { P-value } & \text { Lower } 95 \% & \text { Upper 95\% } \
\hline \text { Intercept } & 11.5676 & 0.8341 & 13.6579 & 0.0000 & 9.6441 & 13.4912 \
\hline \text { Number of vouchers } & 0.4618 & 0.1001 & 4.6117 & 0.0017 & 0.2309 & 0.6927 \
\hline
\end{array}$ Test the significance of the slope against a suitable alternative, at the 5% level of significance. Justify your choice of the direction in your alternative hypothesis.

Accepted Answer

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

Question 5

A television rating wants to determine whether married couples tend to agree about the quality of the television shows they watch. Ten couples are asked to rate a particular comedy series on a 7-point scale where 1 = terrible and 7 = excellent. The results are shown below. $$\begin{array} { | l | l | l | l | l | l | l | l | l | l | l | } 
\hline \text { Husband's rating } & 3 & 6 & 6 & 5 & 4 & 5 & 7 & 4 & 5 & 5 \
\hline \text { Wife's rating } & 5 & 5 & 4 & 5 & 4 & 4 & 6 & 3 & 4 & 5 \
\hline
\end{array}$$ Do these data provide sufficient evidence at the 5% significance level to conclude that the husband's and the wife's ratings are positively related?

Accepted Answer

The answer of A television rating wants to determine whether...

Question 6

In developing a 95% confidence interval for the expected value of y from a simple linear regression problem involving a sample of size 10, the appropriate table value would be 2.306.

Accepted Answer

A) True 
 B)False

Question 7

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. $$\begin{array} { | l | c | c | c | c | c | c | c | c | c | c | } 
\hline \text { Age } & 62 & 57 & 40 & 49 & 67 & 54 & 43 & 65 & 54 & 41 \
\hline \text { Number of concerts } & 6 & 5 & 4 & 3 & 5 & 5 & 2 & 6 & 3 & 1 \
\hline
\end{array}$$ $$\begin{array} { | l | c | c | c | c | c | c | c | c | c | c | } 
\hline \text { Age } & 44 & 48 & 55 & 60 & 59 & 63 & 69 & 40 & 38 & 52 \
\hline \text { Number of Concerts } & 3 & 2 & 4 & 5 & 4 & 5 & 4 & 2 & 1 & 3 \
\hline
\end{array}$$  a. Draw a scatter diagram of the data to determine whether a linear model appears to be appropriate to describe the relationship between the age and number of concerts attended by the respondents.
b. Determine the least squares regression line.
c. Plot the least squares regression line.
d. Interpret the value of the slope of the regression line.

Accepted Answer

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Question 8

Correlation analysis is used to determine the strength of a non-linear relationship between an independent variable x and a dependent variable y.

Accepted Answer

A) True 
 B)False

Question 9

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.

Question 10

In simple linear regression, most often we perform a two-tail test of the population slope $\beta _ { 1 }$ to determine whether there is sufficient evidence to infer that a linear relationship exists. Which of the following best describes the null and alternative hypotheses needed for a test of significance?

Accepted Answer

A) Ho: ?0 = 0 HA: ?0 ? 0 
B) Ho: ?1 ? 0 HA: ?1 = 0 
C) Ho: ?0 = 0 HA: ?0 ? 1 
D) Ho: ?1 = 0 HA: ?1 ? 0

Question 11

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. $$\begin{array} { | c | c | } 
\hline \text { Number of vouchers } & \text { Sales } \
\hline 4 & 12.8 \
\hline 7 & 15.4 \
\hline 5 & 13.9 \
\hline 3 & 11.2 \
\hline 19 & 18.7 \
\hline 10 & 17.9 \
\hline 8 & 16.8 \
\hline 6 & 15.9 \
\hline 3 & 11.5 \
\hline 5 & 13.9 \
\hline
\end{array}$$  Identify possible outliers.

Accepted Answer

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

Question 12

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. $$\begin{array} { | c | c | c | } 
\hline \text { Book } & \text { Number of pages } & \text { Selling price } ( \$ ) \
\hline 1 & 844 & 55 \
\hline 2 & 727 & 50 \
\hline 3 & 360 & 35 \
\hline 4 & 915 & 60 \
\hline 5 & 295 & 30 \
\hline 6 & 706 & 50 \
\hline 7 & 410 & 40 \
\hline 8 & 905 & 53 \
\hline 9 & 1058 & 65 \
\hline 10 & 865 & 54 \
\hline 11 & 677 & 42 \
\hline 12 & 912 & 58 \
\hline
\end{array}$$ Determine the least squares regression line.

Accepted Answer

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

Question 13

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 14

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

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

Question 15

The smallest value that the standard error of estimate $S _ { ? }$ can assume is:

Accepted Answer

A) -1. 
B) 0. 
C) 1. 
D) -2.

Question 16

On the least squares regression line Estimated y= 2 - 3x, the predicted value of y equals:

Accepted Answer

A) -1.0 when x = -1.0. 
B) 1.0 when x = 1.0. 
C) 5.0 when x = -1.0. 
D) 5.0 when x = 1.0.

Question 17

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 the predicted sales.
Calculate the residuals. $$\begin{array} { | c | c | c | c | } 
\hline \text { Observation } & \text { Sales } & \text { Predicted Sales } & \text { Residuals } \
\hline 1 & 12.8 & 13.4147 & - 0.6147 \
\hline 2 & 15.4 & 14.8000 & 0.6000 \
\hline 3 & 13.9 & 13.8765 & 0.0235 \
\hline 4 & 11.2 & 12.9529 & - 1.7529 \
\hline 5 & 18.7 & 20.3412 & - 1.6412 \
\hline 6 & 17.9 & 16.1853 & 1.7147 \
\hline 7 & 16.8 & 15.2618 & 1.5382 \
\hline 8 & 15.9 & 14.3382 & 1.5618 \
\hline 9 & 11.5 & 12.9529 & - 1.4529 \
\hline 10 & 13.9 & 13.8765 & 0.0235 \
\hline
\end{array}$$ Compute the standardised residuals.

Accepted Answer

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

Question 18

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. $$\begin{array} { | c | c | c | } 
\hline \text { Contestant } & \begin{array} { c } 
\text { Years of } \
\text { education }
\end{array} & \text { Winnings } \
\hline 1 & 11 & 750 \
\hline 2 & 15 & 400 \
\hline 3 & 12 & 600 \
\hline 4 & 16 & 350 \
\hline 5 & 11 & 800 \
\hline 6 & 16 & 300 \
\hline 7 & 13 & 650 \
\hline 8 & 14 & 400 \
\hline
\end{array}$$ Conduct a test of the population slope to determine at the 5% significance level whether a linear relationship exists between TV game show contestants' years of education and their winnings.

Accepted Answer

The answer of An ardent fan of television game shows...

Question 19

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. $$\begin{array} { | l | c | c | c | c | c | c | c | c | c | c | } 
\hline \text { Age } & 62 & 57 & 40 & 49 & 67 & 54 & 43 & 65 & 54 & 41 \
\hline \text { Number of concerts } & 6 & 5 & 4 & 3 & 5 & 5 & 2 & 6 & 3 & 1 \
\hline
\end{array}$$ $$\begin{array} { | l | c | c | c | c | c | c | c | c | c | c | } 
\hline \text { Age } & 44 & 48 & 55 & 60 & 59 & 63 & 69 & 40 & 38 & 52 \
\hline \text { Number of Concerts } & 3 & 2 & 4 & 5 & 4 & 5 & 4 & 2 & 1 & 3 \
\hline
\end{array}$$  a. Predict with 95% confidence the number of concerts attended by a 45-year-old individual.
b. Predict with 95% confidence the average number of concerts attended by all 45-year-old individuals.

Accepted Answer

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

Question 20

Another name for the residual term in a regression equation is random error.

Accepted Answer

A) True 
 B)False

Exam 15: Simple Linear Regression and Correlation

The regression line Estimated y = 3 + 2x has been fitted to the data points (4,8) , (2,5) , and (1,2) . The sum of the squared residuals will be:

In simple linear regression, the coefficient of correlation r and the least squares estimate $\hat { \beta } _ { 1 }$ of the population slope $\beta _ { 1 }$ :

In developing a 95% confidence interval for the expected value of y from a simple linear regression problem involving a sample of size 10, the appropriate table value would be 2.306.

Correlation analysis is used to determine the strength of a non-linear relationship between an independent variable x and a dependent variable y.

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

The smallest value that the standard error of estimate $S _ { ? }$ can assume is:

On the least squares regression line Estimated y= 2 - 3x, the predicted value of y equals:

Another name for the residual term in a regression equation is random error.

Exam 15: Simple Linear Regression and Correlation

The regression line Estimated y = 3 + 2x has been fitted to the data points (4,8) , (2,5) , and (1,2) . The sum of the squared residuals will be:

In simple linear regression, the coefficient of correlation r and the least squares estimate β^1\hat { \beta } _ { 1 }β^​1​ of the population slope β1\beta _ { 1 }β1​ :

In developing a 95% confidence interval for the expected value of y from a simple linear regression problem involving a sample of size 10, the appropriate table value would be 2.306.

Correlation analysis is used to determine the strength of a non-linear relationship between an independent variable x and a dependent variable y.

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

The smallest value that the standard error of estimate S?S _ { ? }S?​ can assume is:

On the least squares regression line Estimated y= 2 - 3x, the predicted value of y equals:

Another name for the residual term in a regression equation is random error.

In simple linear regression, the coefficient of correlation r and the least squares estimate $\hat { \beta } _ { 1 }$ of the population slope $\beta _ { 1 }$ :

The smallest value that the standard error of estimate $S _ { ? }$ can assume is: