Deck 12: Simple Linear Regression

Question 1

Instruction 12.2
A chocolate bar manufacturer is interested in trying to estimate how sales are influenced by the price of their product. To do this, the company randomly chooses six country towns and cities and offers the chocolate bar at different prices. Using chocolate bar sales as the dependent variable, the company will conduct a simple linear regression on the data below:
$$\begin{array} { | l | l | l | } \hline \text { City } & \text { Price(\$) } & \text { Syles } \\\hline \text { Toowoomba } & 1.30 & 100 \\\hline \text { Broken Hill } & 1.60 & 50 \\\hline \text { Bendigo } & 1.80 & 50 \\\hline \text { Kalgoorlie } & 2.00 & 40 \\\hline \text { Launceston } & 2.40 & 38 \\\hline \text { Port Augusta } & 2.50 & 32 \\\hline\end{array}$$

-Referring to Instruction 12.2,what is the standard error of the regression slope estimate, $S _ { b _ { 1 } }$ ?

A) 0.885
B) 12.650
C) 16.299
D) 0.784

Answer 1

12.650

Question 2

A large national bank charges local companies for using their services. A bank official reported the results of a regression analysis designed to predict the bank's charges (Y) - measured in dollars per month - for services rendered to local companies. One independent variable used to predict service charge to a company is the company's sales revenue (X) - measured in millions of dollars. Data for 21 companies who use the bank's services were used to fit the model:
$$Y _ { 1 } = b _ { 0 } + b _ { 1 } x _ { 1 } + \varepsilon _ { j }$$
The results of the simple linear regression are provided below:
$$\hat { Y } = - 2,700 + 20 X , S _ { Y X } = 65 \text {, two-tailed } p \text {-value } = 0.034 \text { (for testing } \theta _ { 1 } \text { ) }$$

-Referring to Instruction 12.1,a 95% confidence interval for ?₁ is (15,30).Interpret the interval.

A) At the ? = 0.05 level, there is no evidence of a linear relationship between service charge (Y) and sales revenue (X).
B) We are 95% confident that average service charge (Y) will increase between $15 and $30 for every $1 million increase in sales revenue (X).
C) We are 95% confident that the mean service charge will fall between $15 and $30 per month.
D) We are 95% confident that the sales revenue (X) will increase between $15 and $30 million for every $1 increase in service charge (Y).

Answer 2

We are 95% confident that average service charge (Y) will increase between $15 and $30 for every $1 million increase in sales revenue (X).

Question 3

A large national bank charges local companies for using their services. A bank official reported the results of a regression analysis designed to predict the bank's charges (Y) - measured in dollars per month - for services rendered to local companies. One independent variable used to predict service charge to a company is the company's sales revenue (X) - measured in millions of dollars. Data for 21 companies who use the bank's services were used to fit the model:
$$Y _ { 1 } = b _ { 0 } + b _ { 1 } x _ { 1 } + \varepsilon _ { j }$$
The results of the simple linear regression are provided below:
$$\hat { Y } = - 2,700 + 20 X , S _ { Y X } = 65 \text {, two-tailed } p \text {-value } = 0.034 \text { (for testing } \theta _ { 1 } \text { ) }$$

-Referring to Instruction 12.1,interpret the p-value for testing whether ?₁ exceeds 0.

A) There is sufficient evidence (at the ? = 0.05) to conclude that sales revenue (X) is a useful linear predictor of service charge (Y).
B) Sales revenue (X) is a poor predictor of service charge (Y).
C) There is insufficient evidence (at the ? = 0.10) to conclude that sales revenue (X) is a useful linear predictor of service charge (Y).
D) For every $1 million increase in sales revenue, we expect a service charge to increase $0.034.

Answer 3

There is sufficient evidence (at the ? = 0.05) to conclude that sales revenue (X) is a useful linear predictor of service charge (Y).

Question 4

Instruction 12.2
A chocolate bar manufacturer is interested in trying to estimate how sales are influenced by the price of their product. To do this, the company randomly chooses six country towns and cities and offers the chocolate bar at different prices. Using chocolate bar sales as the dependent variable, the company will conduct a simple linear regression on the data below:
$$\begin{array} { | l | l | l | } \hline \text { City } & \text { Price(\$) } & \text { Syles } \\\hline \text { Toowoomba } & 1.30 & 100 \\\hline \text { Broken Hill } & 1.60 & 50 \\\hline \text { Bendigo } & 1.80 & 50 \\\hline \text { Kalgoorlie } & 2.00 & 40 \\\hline \text { Launceston } & 2.40 & 38 \\\hline \text { Port Augusta } & 2.50 & 32 \\\hline\end{array}$$

-Referring to Instruction 12.2,to test whether a change in price will have any impact on average sales,what would be the critical values? Use ? = 0.05.

A) ± 2.7765
B) ± 3.1634
C) ± 2.5706
D) ± 3.4954

Question 5

Instruction 12.2
A chocolate bar manufacturer is interested in trying to estimate how sales are influenced by the price of their product. To do this, the company randomly chooses six country towns and cities and offers the chocolate bar at different prices. Using chocolate bar sales as the dependent variable, the company will conduct a simple linear regression on the data below:
$$\begin{array} { | l | l | l | } \hline \text { City } & \text { Price(\$) } & \text { Syles } \\\hline \text { Toowoomba } & 1.30 & 100 \\\hline \text { Broken Hill } & 1.60 & 50 \\\hline \text { Bendigo } & 1.80 & 50 \\\hline \text { Kalgoorlie } & 2.00 & 40 \\\hline \text { Launceston } & 2.40 & 38 \\\hline \text { Port Augusta } & 2.50 & 32 \\\hline\end{array}$$

-Referring to Instruction 12.2,what is the coefficient of correlation for these data?

A) 0.8854
B) 0.7839
C) -0.7839
D) -0.8854

Question 6

Instruction 12.2
A chocolate bar manufacturer is interested in trying to estimate how sales are influenced by the price of their product. To do this, the company randomly chooses six country towns and cities and offers the chocolate bar at different prices. Using chocolate bar sales as the dependent variable, the company will conduct a simple linear regression on the data below:
$$\begin{array} { | l | l | l | } \hline \text { City } & \text { Price(\$) } & \text { Syles } \\\hline \text { Toowoomba } & 1.30 & 100 \\\hline \text { Broken Hill } & 1.60 & 50 \\\hline \text { Bendigo } & 1.80 & 50 \\\hline \text { Kalgoorlie } & 2.00 & 40 \\\hline \text { Launceston } & 2.40 & 38 \\\hline \text { Port Augusta } & 2.50 & 32 \\\hline\end{array}$$

-Referring to Instruction 12.2,if the price of the chocolate bar is set at $2,the predicted sales will be

A) 100.
B) 30.
C) 65.
D) 90.

Question 7

Instruction 12.3
The director of cooperative education at a university wants to examine the effect of cooperative education job experience on marketability in the workplace. She takes a random sample of four students. For these four, she finds out how many times each had a cooperative education job and how many job offers they received upon graduation. These data are presented in the table below.
$$\begin{array} { | l | l | l | } \hline \text { Student } & \text { Coop jobs } & \text { job Offer } \\\hline 1 & 1 & 4 \\\hline 2 & 2 & 6 \\\hline 3 & 1 & 3 \\\hline 4 & 0 & 1 \\\hline\end{array}$$

-Referring to Instruction 12.3,the prediction for the number of job offers for a person with two cooperative jobs is____________.

Question 8

Instruction 12.3
The director of cooperative education at a university wants to examine the effect of cooperative education job experience on marketability in the workplace. She takes a random sample of four students. For these four, she finds out how many times each had a cooperative education job and how many job offers they received upon graduation. These data are presented in the table below.
$$\begin{array} { | l | l | l | } \hline \text { Student } & \text { Coop jobs } & \text { job Offer } \\\hline 1 & 1 & 4 \\\hline 2 & 2 & 6 \\\hline 3 & 1 & 3 \\\hline 4 & 0 & 1 \\\hline\end{array}$$

-Referring to Instruction 12.3,the total sum of squares (SST)is ____________.

Question 9

A large national bank charges local companies for using their services. A bank official reported the results of a regression analysis designed to predict the bank's charges (Y) - measured in dollars per month - for services rendered to local companies. One independent variable used to predict service charge to a company is the company's sales revenue (X) - measured in millions of dollars. Data for 21 companies who use the bank's services were used to fit the model:
$$Y _ { 1 } = b _ { 0 } + b _ { 1 } x _ { 1 } + \varepsilon _ { j }$$
The results of the simple linear regression are provided below:
$$\hat { Y } = - 2,700 + 20 X , S _ { Y X } = 65 \text {, two-tailed } p \text {-value } = 0.034 \text { (for testing } \theta _ { 1 } \text { ) }$$

-Referring to Instruction 12.1,interpret the estimate of ?₀,the Y-intercept of the line.

A) About 95% of the observed service charges fall within $2,700 of the least squares line.
B) There is no practical interpretation since a sales revenue of $0 is a nonsensical value.
C) For every $1 million increase in sales revenue, we expect a service charge to decrease $2,700.
D) All companies will be charged at least $2,700 by the bank.

Question 10

Instruction 12.2
A chocolate bar manufacturer is interested in trying to estimate how sales are influenced by the price of their product. To do this, the company randomly chooses six country towns and cities and offers the chocolate bar at different prices. Using chocolate bar sales as the dependent variable, the company will conduct a simple linear regression on the data below:
$$\begin{array} { | l | l | l | } \hline \text { City } & \text { Price(\$) } & \text { Syles } \\\hline \text { Toowoomba } & 1.30 & 100 \\\hline \text { Broken Hill } & 1.60 & 50 \\\hline \text { Bendigo } & 1.80 & 50 \\\hline \text { Kalgoorlie } & 2.00 & 40 \\\hline \text { Launceston } & 2.40 & 38 \\\hline \text { Port Augusta } & 2.50 & 32 \\\hline\end{array}$$

-Referring to Instruction 12.2,what is the standard error of the estimate,S_YX,for the data?

A) 0.885
B) 0.784
C) 16.299
D) 12.650

Question 11

Instruction 12.2
A chocolate bar manufacturer is interested in trying to estimate how sales are influenced by the price of their product. To do this, the company randomly chooses six country towns and cities and offers the chocolate bar at different prices. Using chocolate bar sales as the dependent variable, the company will conduct a simple linear regression on the data below:
$$\begin{array} { | l | l | l | } \hline \text { City } & \text { Price(\$) } & \text { Syles } \\\hline \text { Toowoomba } & 1.30 & 100 \\\hline \text { Broken Hill } & 1.60 & 50 \\\hline \text { Bendigo } & 1.80 & 50 \\\hline \text { Kalgoorlie } & 2.00 & 40 \\\hline \text { Launceston } & 2.40 & 38 \\\hline \text { Port Augusta } & 2.50 & 32 \\\hline\end{array}$$

-Referring to Instruction 12.2,what percentage of the total variation in chocolate bar sales is explained by prices?

A) 78.39%
B) 88.54%
C) 48.19%
D) 100%

Question 12

Instruction 12.2
A chocolate bar manufacturer is interested in trying to estimate how sales are influenced by the price of their product. To do this, the company randomly chooses six country towns and cities and offers the chocolate bar at different prices. Using chocolate bar sales as the dependent variable, the company will conduct a simple linear regression on the data below:
$$\begin{array} { | l | l | l | } \hline \text { City } & \text { Price(\$) } & \text { Syles } \\\hline \text { Toowoomba } & 1.30 & 100 \\\hline \text { Broken Hill } & 1.60 & 50 \\\hline \text { Bendigo } & 1.80 & 50 \\\hline \text { Kalgoorlie } & 2.00 & 40 \\\hline \text { Launceston } & 2.40 & 38 \\\hline \text { Port Augusta } & 2.50 & 32 \\\hline\end{array}$$

-Referring to Instruction 12.2,what is ?(X * $\bar { X }$ )² for these data?

A) 25.66
B) 0
C) 2.54
D) 1.66

Question 13

Instruction 12.2
A chocolate bar manufacturer is interested in trying to estimate how sales are influenced by the price of their product. To do this, the company randomly chooses six country towns and cities and offers the chocolate bar at different prices. Using chocolate bar sales as the dependent variable, the company will conduct a simple linear regression on the data below:
$$\begin{array} { | l | l | l | } \hline \text { City } & \text { Price(\$) } & \text { Syles } \\\hline \text { Toowoomba } & 1.30 & 100 \\\hline \text { Broken Hill } & 1.60 & 50 \\\hline \text { Bendigo } & 1.80 & 50 \\\hline \text { Kalgoorlie } & 2.00 & 40 \\\hline \text { Launceston } & 2.40 & 38 \\\hline \text { Port Augusta } & 2.50 & 32 \\\hline\end{array}$$

-Referring to Instruction 12.2,what is the percentage of the total variation in chocolate bar sales explained by the regression model?

A) 48.19%
B) 100%
C) 88.54%
D) 78.39%

Question 14

Instruction 12.3
The director of cooperative education at a university wants to examine the effect of cooperative education job experience on marketability in the workplace. She takes a random sample of four students. For these four, she finds out how many times each had a cooperative education job and how many job offers they received upon graduation. These data are presented in the table below.
$$\begin{array} { | l | l | l | } \hline \text { Student } & \text { Coop jobs } & \text { job Offer } \\\hline 1 & 1 & 4 \\\hline 2 & 2 & 6 \\\hline 3 & 1 & 3 \\\hline 4 & 0 & 1 \\\hline\end{array}$$

-Referring to Instruction 12.3,the least squares estimate of the Y-intercept is____________.

Question 15

Instruction 12.2
A chocolate bar manufacturer is interested in trying to estimate how sales are influenced by the price of their product. To do this, the company randomly chooses six country towns and cities and offers the chocolate bar at different prices. Using chocolate bar sales as the dependent variable, the company will conduct a simple linear regression on the data below:
$$\begin{array} { | l | l | l | } \hline \text { City } & \text { Price(\$) } & \text { Syles } \\\hline \text { Toowoomba } & 1.30 & 100 \\\hline \text { Broken Hill } & 1.60 & 50 \\\hline \text { Bendigo } & 1.80 & 50 \\\hline \text { Kalgoorlie } & 2.00 & 40 \\\hline \text { Launceston } & 2.40 & 38 \\\hline \text { Port Augusta } & 2.50 & 32 \\\hline\end{array}$$

-Referring to Instruction 12.2,what is the estimated average change in the sales of the chocolate bar if price goes up by $1.00?

A) 0.784
B) -3.810
C) 161.386
D) -48.193

Question 16

Instruction 12.2
A chocolate bar manufacturer is interested in trying to estimate how sales are influenced by the price of their product. To do this, the company randomly chooses six country towns and cities and offers the chocolate bar at different prices. Using chocolate bar sales as the dependent variable, the company will conduct a simple linear regression on the data below:
$$\begin{array} { | l | l | l | } \hline \text { City } & \text { Price(\$) } & \text { Syles } \\\hline \text { Toowoomba } & 1.30 & 100 \\\hline \text { Broken Hill } & 1.60 & 50 \\\hline \text { Bendigo } & 1.80 & 50 \\\hline \text { Kalgoorlie } & 2.00 & 40 \\\hline \text { Launceston } & 2.40 & 38 \\\hline \text { Port Augusta } & 2.50 & 32 \\\hline\end{array}$$

-Referring to Instruction 12.2,to test that the regression coefficient,?₁ is not equal to 0,what would be the critical values? Use ? = 0.05.

A) ± 2.7765
B) ± 3.1634
C) ± 2.5706
D) ± 3.4954

Question 17

Instruction 12.3
The director of cooperative education at a university wants to examine the effect of cooperative education job experience on marketability in the workplace. She takes a random sample of four students. For these four, she finds out how many times each had a cooperative education job and how many job offers they received upon graduation. These data are presented in the table below.
$$\begin{array} { | l | l | l | } \hline \text { Student } & \text { Coop jobs } & \text { job Offer } \\\hline 1 & 1 & 4 \\\hline 2 & 2 & 6 \\\hline 3 & 1 & 3 \\\hline 4 & 0 & 1 \\\hline\end{array}$$

-Referring to Instruction 12.3,the least squares estimate of the slope is_____________.

Question 18

Instruction 12.2
A chocolate bar manufacturer is interested in trying to estimate how sales are influenced by the price of their product. To do this, the company randomly chooses six country towns and cities and offers the chocolate bar at different prices. Using chocolate bar sales as the dependent variable, the company will conduct a simple linear regression on the data below:
$$\begin{array} { | l | l | l | } \hline \text { City } & \text { Price(\$) } & \text { Syles } \\\hline \text { Toowoomba } & 1.30 & 100 \\\hline \text { Broken Hill } & 1.60 & 50 \\\hline \text { Bendigo } & 1.80 & 50 \\\hline \text { Kalgoorlie } & 2.00 & 40 \\\hline \text { Launceston } & 2.40 & 38 \\\hline \text { Port Augusta } & 2.50 & 32 \\\hline\end{array}$$

-Referring to Instruction 12.2,what is the estimated slope parameter for the chocolate bar price and sales data?

A) -48.193
B) -3.810
C) 161.386
D) 0.784

Question 19

A large national bank charges local companies for using their services. A bank official reported the results of a regression analysis designed to predict the bank's charges (Y) - measured in dollars per month - for services rendered to local companies. One independent variable used to predict service charge to a company is the company's sales revenue (X) - measured in millions of dollars. Data for 21 companies who use the bank's services were used to fit the model:
$$Y _ { 1 } = b _ { 0 } + b _ { 1 } x _ { 1 } + \varepsilon _ { j }$$
The results of the simple linear regression are provided below:
$$\hat { Y } = - 2,700 + 20 X , S _ { Y X } = 65 \text {, two-tailed } p \text {-value } = 0.034 \text { (for testing } \theta _ { 1 } \text { ) }$$

-Referring to Instruction 12.1,interpret the estimate of ?,the standard deviation of the random error term (standard error of the estimate)in the model.

A) About 95% of the observed service charges fall within $130 of the least squares line.
B) About 95% of the observed service charges fall within $65 of the least squares line.
C) About 95% of the observed service charges equal their corresponding predicted values.
D) For every $1 million increase in sales revenue, we expect a service charge to increase $65.

Question 20

Instruction 12.3
The director of cooperative education at a university wants to examine the effect of cooperative education job experience on marketability in the workplace. She takes a random sample of four students. For these four, she finds out how many times each had a cooperative education job and how many job offers they received upon graduation. These data are presented in the table below.
$$\begin{array} { | l | l | l | } \hline \text { Student } & \text { Coop jobs } & \text { job Offer } \\\hline 1 & 1 & 4 \\\hline 2 & 2 & 6 \\\hline 3 & 1 & 3 \\\hline 4 & 0 & 1 \\\hline\end{array}$$

-Referring to Instruction 12.3,the regression sum of squares (SSR)is____________.

Question 21

Instruction 12.4
The managers of a brokerage firm are interested in finding out if the number of new customers a broker brings into the firm affects the sales generated by the broker. They sample 12 brokers and determine the number of new customers they have enrolled in the last year and their sales amounts in thousands of dollars. These data are presented in the table that follows.
$$\begin{array} { | l | l | l | } \hline \text { Broker } & \text { Clients } & \text { Sales } \\\hline 1 & 27 & 52 \\\hline 2 & 11 & 37 \\\hline 3 & 42 & 64 \\\hline 4 & 33 & 55 \\\hline 5 & 15 & 29 \\\hline 6 & 15 & 34 \\\hline 7 & 25 & 58 \\\hline 8 & 36 & 59 \\\hline 9 & 28 & 44 \\\hline 10 & 30 & 48 \\\hline 11 & 17 & 31 \\\hline 12 & 22 & 38 \\\hline\end{array}$$

-Referring to Instruction 12.4,the regression sum of squares (SSR)is____________

Question 22

Instruction 12.9
The management of a chain electronic store would like to develop a model for predicting the weekly sales (in thousands of dollars) for individual stores based on the number of customers who made purchases. A random sample of 12 stores yields the following results:
$$\begin{array} { | c | c | } \hline \text { Customers } & \text { Sales (Thousands of Dollars) } \\\hline 907 & 11.20 \\\hline 926 & 11.05 \\\hline 713 & 8.21 \\\hline 741 & 9.21 \\\hline 780 & 9.42 \\\hline 898 & 10.08 \\\hline 510 & 6.73 \\\hline 529 & 7.02 \\\hline 460 & 6.12 \\\hline 872 & 9.52 \\\hline 650 & 7.53 \\\hline 603 & 7.25 \\\hline\end{array}$$

-Referring to Instruction 12.9,93.98% of the total variation in weekly sales can be explained by the variation in the number of customers who make purchases.

Question 23

Instruction 12.8
It is believed that the average numbers of hours spent studying per day (HOURS) during undergraduate education should have a positive linear relationship with the starting salary (SALARY, measured in thousands of dollars per month) after graduation. Given below is the Microsoft Excel output for predicting starting salary (Y) using number of hours spent studying per day (X) for a sample of 51 students. NOTE: Only partial output is shown.
$\text { Regression statistics }$
$\begin{array}{|l|l|}\hline\text { MultipleR } & 0.8857 \\\hline \text { R Square } & 0.7845 \\\hline \begin{array}{l}\text { Adjusted R } \\\text { Square }\end{array} & 0.7801 \\\hline \text { Standard Error } & 1.3704 \\\hline \text { Observations } & 51\\\hline\end{array}$

$\begin{array}{l}\text { ANOVA }\\\begin{array}{|l|l|l|l|l|l|l|}\hline & d f & 55 & \text { MS } & F & \begin{array}{l}\text { Significance } \\F\end{array} & \\\hline \text { Regression } & 1 & 335.0472 & 335.0473 & 178.3859 & & \\\hline \text { Residual } & & & 1.8782 & & & \\\hline \text { Total } & 50 & 427.0798 & & & & \\\hline\end{array}\end{array}$

$\begin{array}{|l|l|l|l|l|l|l|}\hline & \text { Coefficients } & \begin{array}{l}\text { Standard } \\\text { Error }\end{array} & \text { tStat } & \text { p-value } & \text { Lower 95\% } & \text { Upper 95\% } \\\hline \text { Intercept } & -1.8940 & 0.4018 & -4.7134 & 2.051 \mathrm{E}-05 & -2.7015 & -1.0865 \\\hline \text { Hours } & 0.9795 & 0.0733 & 13.3561 & 5.944 \mathrm{E}-18 & 0.8321 & 1.1269 \\\hline\end{array}$ Note: 2.051E-05 = 2.051 * 10S1^-0.5 and 5.944E-18 = 5.944 * 10S1^-18.

-Referring to Instruction 12.8,the estimated average change in salary (in thousands of dollars)as a result of spending an extra hour per day studying is

A) 0.9795.
B) 0.7845.
C) 335.0473.
D) -1.8940.

Question 24

Instruction 12.9
The management of a chain electronic store would like to develop a model for predicting the weekly sales (in thousands of dollars) for individual stores based on the number of customers who made purchases. A random sample of 12 stores yields the following results:
$$\begin{array} { | c | c | } \hline \text { Customers } & \text { Sales (Thousands of Dollars) } \\\hline 907 & 11.20 \\\hline 926 & 11.05 \\\hline 713 & 8.21 \\\hline 741 & 9.21 \\\hline 780 & 9.42 \\\hline 898 & 10.08 \\\hline 510 & 6.73 \\\hline 529 & 7.02 \\\hline 460 & 6.12 \\\hline 872 & 9.52 \\\hline 650 & 7.53 \\\hline 603 & 7.25 \\\hline\end{array}$$

-Referring to Instruction 12.9,generate the scatter plot.

Question 25

Instruction 12.9
The management of a chain electronic store would like to develop a model for predicting the weekly sales (in thousands of dollars) for individual stores based on the number of customers who made purchases. A random sample of 12 stores yields the following results:
$$\begin{array} { | c | c | } \hline \text { Customers } & \text { Sales (Thousands of Dollars) } \\\hline 907 & 11.20 \\\hline 926 & 11.05 \\\hline 713 & 8.21 \\\hline 741 & 9.21 \\\hline 780 & 9.42 \\\hline 898 & 10.08 \\\hline 510 & 6.73 \\\hline 529 & 7.02 \\\hline 460 & 6.12 \\\hline 872 & 9.52 \\\hline 650 & 7.53 \\\hline 603 & 7.25 \\\hline\end{array}$$

-Referring to Instruction 12.9,what are the values of the estimated intercept and slope?

Question 26

Instruction 12.4
The managers of a brokerage firm are interested in finding out if the number of new customers a broker brings into the firm affects the sales generated by the broker. They sample 12 brokers and determine the number of new customers they have enrolled in the last year and their sales amounts in thousands of dollars. These data are presented in the table that follows.
$$\begin{array} { | l | l | l | } \hline \text { Broker } & \text { Clients } & \text { Sales } \\\hline 1 & 27 & 52 \\\hline 2 & 11 & 37 \\\hline 3 & 42 & 64 \\\hline 4 & 33 & 55 \\\hline 5 & 15 & 29 \\\hline 6 & 15 & 34 \\\hline 7 & 25 & 58 \\\hline 8 & 36 & 59 \\\hline 9 & 28 & 44 \\\hline 10 & 30 & 48 \\\hline 11 & 17 & 31 \\\hline 12 & 22 & 38 \\\hline\end{array}$$

-Referring to Instruction 12.4,the total sum of squares (SST)is ____________.

Question 27

Instruction 12.4
The managers of a brokerage firm are interested in finding out if the number of new customers a broker brings into the firm affects the sales generated by the broker. They sample 12 brokers and determine the number of new customers they have enrolled in the last year and their sales amounts in thousands of dollars. These data are presented in the table that follows.
$$\begin{array} { | l | l | l | } \hline \text { Broker } & \text { Clients } & \text { Sales } \\\hline 1 & 27 & 52 \\\hline 2 & 11 & 37 \\\hline 3 & 42 & 64 \\\hline 4 & 33 & 55 \\\hline 5 & 15 & 29 \\\hline 6 & 15 & 34 \\\hline 7 & 25 & 58 \\\hline 8 & 36 & 59 \\\hline 9 & 28 & 44 \\\hline 10 & 30 & 48 \\\hline 11 & 17 & 31 \\\hline 12 & 22 & 38 \\\hline\end{array}$$

-Referring to Instruction 12.4,the prediction for the amount of sales (in $1,000s)for a person who brings 25 new customers into the firm is ____________.

Question 28

Instruction 12.5
The managing partner of an advertising agency believes that his company's sales are related to the industry sales. He uses Microsoft Excel's Data Analysis tool to analyse the last four years of quarterly data with the following results:


-Referring to Instruction 12.5,the prediction for a quarter in which X = 120 is Y = ____________.

Question 29

Instruction 12.3
The director of cooperative education at a university wants to examine the effect of cooperative education job experience on marketability in the workplace. She takes a random sample of four students. For these four, she finds out how many times each had a cooperative education job and how many job offers they received upon graduation. These data are presented in the table below.
$$\begin{array} { | l | l | l | } \hline \text { Student } & \text { Coop jobs } & \text { job Offer } \\\hline 1 & 1 & 4 \\\hline 2 & 2 & 6 \\\hline 3 & 1 & 3 \\\hline 4 & 0 & 1 \\\hline\end{array}$$

-Referring to Instruction 12.3,set up a scatter diagram.

Question 30

Instruction 12.3
The director of cooperative education at a university wants to examine the effect of cooperative education job experience on marketability in the workplace. She takes a random sample of four students. For these four, she finds out how many times each had a cooperative education job and how many job offers they received upon graduation. These data are presented in the table below.
$$\begin{array} { | l | l | l | } \hline \text { Student } & \text { Coop jobs } & \text { job Offer } \\\hline 1 & 1 & 4 \\\hline 2 & 2 & 6 \\\hline 3 & 1 & 3 \\\hline 4 & 0 & 1 \\\hline\end{array}$$

-Referring to Instruction 12.3,the coefficient of determination is____________.

Question 31

Instruction 12.4
The managers of a brokerage firm are interested in finding out if the number of new customers a broker brings into the firm affects the sales generated by the broker. They sample 12 brokers and determine the number of new customers they have enrolled in the last year and their sales amounts in thousands of dollars. These data are presented in the table that follows.
$$\begin{array} { | l | l | l | } \hline \text { Broker } & \text { Clients } & \text { Sales } \\\hline 1 & 27 & 52 \\\hline 2 & 11 & 37 \\\hline 3 & 42 & 64 \\\hline 4 & 33 & 55 \\\hline 5 & 15 & 29 \\\hline 6 & 15 & 34 \\\hline 7 & 25 & 58 \\\hline 8 & 36 & 59 \\\hline 9 & 28 & 44 \\\hline 10 & 30 & 48 \\\hline 11 & 17 & 31 \\\hline 12 & 22 & 38 \\\hline\end{array}$$

-Referring to Instruction 12.4,the least squares estimate of the Y-intercept is ____________.

Question 32

Instruction 12.4
The managers of a brokerage firm are interested in finding out if the number of new customers a broker brings into the firm affects the sales generated by the broker. They sample 12 brokers and determine the number of new customers they have enrolled in the last year and their sales amounts in thousands of dollars. These data are presented in the table that follows.
$$\begin{array} { | l | l | l | } \hline \text { Broker } & \text { Clients } & \text { Sales } \\\hline 1 & 27 & 52 \\\hline 2 & 11 & 37 \\\hline 3 & 42 & 64 \\\hline 4 & 33 & 55 \\\hline 5 & 15 & 29 \\\hline 6 & 15 & 34 \\\hline 7 & 25 & 58 \\\hline 8 & 36 & 59 \\\hline 9 & 28 & 44 \\\hline 10 & 30 & 48 \\\hline 11 & 17 & 31 \\\hline 12 & 22 & 38 \\\hline\end{array}$$

-Referring to Instruction 12.4,the error or residual sum of squares (SSE)is____________.

Question 33

Instruction 12.7
It is believed that average grade (based on a four-point scale) should have a positive linear relationship with university entrance exam scores. Given below is the Microsoft Excel output from regressing average grade on university entrance exam scores using a data set of eight randomly chosen students from a large university.


-Referring to Instruction 12.7,the interpretation of the coefficient of determination in this regression is

A) average grade accounts for 57.74% of the variability of university entrance exam scores.
B) university entrance exam scores account for 57.74% of the total fluctuation in average grade.
C) 57.74% of the total variation of university entrance exam scores can be explained by average grade.
D) None of the above.

Question 34

Instruction 12.4
The managers of a brokerage firm are interested in finding out if the number of new customers a broker brings into the firm affects the sales generated by the broker. They sample 12 brokers and determine the number of new customers they have enrolled in the last year and their sales amounts in thousands of dollars. These data are presented in the table that follows.
$$\begin{array} { | l | l | l | } \hline \text { Broker } & \text { Clients } & \text { Sales } \\\hline 1 & 27 & 52 \\\hline 2 & 11 & 37 \\\hline 3 & 42 & 64 \\\hline 4 & 33 & 55 \\\hline 5 & 15 & 29 \\\hline 6 & 15 & 34 \\\hline 7 & 25 & 58 \\\hline 8 & 36 & 59 \\\hline 9 & 28 & 44 \\\hline 10 & 30 & 48 \\\hline 11 & 17 & 31 \\\hline 12 & 22 & 38 \\\hline\end{array}$$

-Referring to Instruction 12.4,set up a scatter diagram.

Question 35

Instruction 12.4
The managers of a brokerage firm are interested in finding out if the number of new customers a broker brings into the firm affects the sales generated by the broker. They sample 12 brokers and determine the number of new customers they have enrolled in the last year and their sales amounts in thousands of dollars. These data are presented in the table that follows.
$$\begin{array} { | l | l | l | } \hline \text { Broker } & \text { Clients } & \text { Sales } \\\hline 1 & 27 & 52 \\\hline 2 & 11 & 37 \\\hline 3 & 42 & 64 \\\hline 4 & 33 & 55 \\\hline 5 & 15 & 29 \\\hline 6 & 15 & 34 \\\hline 7 & 25 & 58 \\\hline 8 & 36 & 59 \\\hline 9 & 28 & 44 \\\hline 10 & 30 & 48 \\\hline 11 & 17 & 31 \\\hline 12 & 22 & 38 \\\hline\end{array}$$

-Referring to Instruction 12.4,____% of the total variation in sales generated can be explained by the number of new customers brought in.

Question 36

Instruction 12.6
The following Microsoft Excel tables are obtained when 'Score received on an exam (measured in percentage points)' (Y) is regressed on 'percentage attendance' (X) for 22 students in a Statistics for Business and Economics course.
$\text { Regression Statistics }$
$\begin{array}{|l|l|}\hline \text { MultipleR } & 0.142620229 \\\hline \text { R Square } & 0.02034053 \\\hline \begin{array}{l}\text { Adjusted R } \\\text { Square }\end{array} & -0.028642444 \\\hline \text { Standard Error } & 20.25979924 \\\hline \text { Observations } & 22 \\\hline\end{array}$

$\begin{array}{|l|l|l|l|l|}\hline & \text { Coefficients } & \begin{array}{l}\text { Standard } \\\text { Error }\end{array} & t \text { Stat } & p \text {-value } \\\hline \text { Intercept } & 39.39027309 & 37.24347659 & 1.057642216 & 0.302826622 \\\hline \text { Attendance } & 0.340583573 & 0.52852452 & 0.644404489 & 0.526635689 \\\hline\end{array}$

-Referring to Instruction 12.6,which of the following statements is true?

A) If attendance increases by 1%, the estimated mean score received will increase by 39.39 percentage points.
B) If attendance increases by 0.341%, the estimated mean score received will increase by 1 percentage point.
C) If the score received increases by 39.39%, the estimated mean attendance will go up by 1%.
D) If attendance increases by 1%, the estimated mean score received will increase by 0.341 percentage points.

Question 37

Instruction 12.8
It is believed that the average numbers of hours spent studying per day (HOURS) during undergraduate education should have a positive linear relationship with the starting salary (SALARY, measured in thousands of dollars per month) after graduation. Given below is the Microsoft Excel output for predicting starting salary (Y) using number of hours spent studying per day (X) for a sample of 51 students. NOTE: Only partial output is shown.
$\text { Regression statistics }$
$\begin{array}{|l|l|}\hline\text { MultipleR } & 0.8857 \\\hline \text { R Square } & 0.7845 \\\hline \begin{array}{l}\text { Adjusted R } \\\text { Square }\end{array} & 0.7801 \\\hline \text { Standard Error } & 1.3704 \\\hline \text { Observations } & 51\\\hline\end{array}$

$\begin{array}{l}\text { ANOVA }\\\begin{array}{|l|l|l|l|l|l|l|}\hline & d f & 55 & \text { MS } & F & \begin{array}{l}\text { Significance } \\F\end{array} & \\\hline \text { Regression } & 1 & 335.0472 & 335.0473 & 178.3859 & & \\\hline \text { Residual } & & & 1.8782 & & & \\\hline \text { Total } & 50 & 427.0798 & & & & \\\hline\end{array}\end{array}$

$\begin{array}{|l|l|l|l|l|l|l|}\hline & \text { Coefficients } & \begin{array}{l}\text { Standard } \\\text { Error }\end{array} & \text { tStat } & \text { p-value } & \text { Lower 95\% } & \text { Upper 95\% } \\\hline \text { Intercept } & -1.8940 & 0.4018 & -4.7134 & 2.051 \mathrm{E}-05 & -2.7015 & -1.0865 \\\hline \text { Hours } & 0.9795 & 0.0733 & 13.3561 & 5.944 \mathrm{E}-18 & 0.8321 & 1.1269 \\\hline\end{array}$ Note: 2.051E-05 = 2.051 * 10S1^-0.5 and 5.944E-18 = 5.944 * 10S1^-18.

-Referring to Instruction 12.8,the error sum of squares (SSE)of the above regression is

A) 427.079804.
B) 92.0325465.
C) 1.878215.
D) 335.047257.

Question 38

Instruction 12.7
It is believed that average grade (based on a four-point scale) should have a positive linear relationship with university entrance exam scores. Given below is the Microsoft Excel output from regressing average grade on university entrance exam scores using a data set of eight randomly chosen students from a large university.


-Referring to Instruction 12.7,what is the predicted average value of average grade when university entrance exam score = 20?

A) 2.80
B) 2.61
C) 2.66
D) 3.12

Question 39

Instruction 12.3
The director of cooperative education at a university wants to examine the effect of cooperative education job experience on marketability in the workplace. She takes a random sample of four students. For these four, she finds out how many times each had a cooperative education job and how many job offers they received upon graduation. These data are presented in the table below.
$$\begin{array} { | l | l | l | } \hline \text { Student } & \text { Coop jobs } & \text { job Offer } \\\hline 1 & 1 & 4 \\\hline 2 & 2 & 6 \\\hline 3 & 1 & 3 \\\hline 4 & 0 & 1 \\\hline\end{array}$$

-Referring to Instruction 12.3,the error or residual sum of squares (SSE)is____________.

Question 40

Instruction 12.5
The managing partner of an advertising agency believes that his company's sales are related to the industry sales. He uses Microsoft Excel's Data Analysis tool to analyse the last four years of quarterly data with the following results:


-Referring to Instruction 12.5,the estimates of the Y-intercept and slope are ____________ and ____________,respectively.

Question 41

When using a regression model to make predictions,the term 'relevant range' refers to____________.

Question 42

The standard error of the estimate is a measure of

A) total variation of the Y variable.
B) explained variation.
C) the variation of the X variable.
D) the variation around the sample regression line.

Question 43

What do we mean when we say that a simple linear regression model is 'statistically' useful?

A) The model is 'practically' useful for predicting Y.
B) The model is an excellent predictor of Y.
C) All the statistics computed from the sample make sense.
D) The model is a better predictor of Y than the sample mean, $\bar { Y }$ .

Question 44

A simple regression has a b₀ value of 5 and a b₁ value of 3.5.What is the predicted Y for an X value of -2?

A) 13.5
B) 12.0
C) -6.0
D) -2.0

Question 45

Instruction 12.10
A computer software developer would like to use the number of downloads (in thousands) for the trial version of his new shareware to predict the amount of revenue (in thousands of dollars) he can make on the full version of the new shareware. Following is the output from a simple linear regression along with the residual plot and normal probability plot obtained from a data set of 30 different sharewares that he has developed:
$\text { Regression statistics }$
$\begin{array}{|l|l|}\hline \text { MultipleR } & 0.8691 \\\hline \text { R Square } & 0.7554 \\\hline \begin{array}{l}\text { Adjusted R } \\\text { Square }\end{array} & 0.7467 \\\hline \text { Standard Error } & 44.4765 \\\hline \text { Observations } & 30.0000\\\hline \end{array}$

$\text { ANOVA }$
$\begin{array}{|l|l|l|l|l|l|}\hline & d f & S S & M S & F & \begin{array}{l}\text { Significance } \\F\end{array} \\\hline \text { Regression } & 1 & 171062.9193 & 171062.9193 & 86.4759 & 0.0000 \\\hline \text { Residual } & 28 & 55388.4309 & 1978.1582 & & \\\hline \text { Total } & 29 & 226451.3503 & & & \\\hline\end{array}$

$\begin{array}{|l|l|l|l|l|l|l|}\hline & \text { Coefficients } & \begin{array}{l}\text { Standard } \\\text { Error }\end{array} & \text { t Stat } & p \text {-value } & \text { Lower 95\% } & \text { Upper 95\% } \\\hline \text { Intercept } & -95.0614 & 26.9183 & -3.5315 & 0.0015 & -150.2009 & -39.9218 \\\hline \text { Download } & 3.7297 & 0.4011 & 9.2992 & 0.0000 & 2.9082 & 4.5513 \\\hline\end{array}$

-Referring to Instruction 12.10,which of the following is the correct interpretation for the slope coefficient?

A) For each increase of 1,000 downloads, the expected revenue is estimated to increase by $3.7297 thousands.
B) For each increase of 1,000 dollars in expected revenue, the expected number of downloads is estimated to increase by 3.7297 thousands.
C) For each decrease of 1,000 dollars in expected revenue, the expected number of downloads is estimated to increase by 3.7297 thousands.
D) For each decrease of 1,000 downloads, the expected revenue is estimated to increase by $3.7297 thousands.

Question 46

The slope (b₁)represents

A) the estimated average change in Y per unit change in X.
B) predicted value of Y when X = 0.
C) variation around the line of regression.
D) the predicted value of Y.

Question 47

The regression sum of squares (SSR)can never be greater than the total sum of squares (SST).

Question 48

When using a regression model to make predictions,you should not predict Y for values of X larger or smaller than the values used to develop the model.

Question 49

A simple regression has a b₀ value of 1.3 and a b₁ value of 2.6.What is the predicted Y for an X value of 0?

A) 2.6
B) 3.9
C) 1.3
D) 3.4

Question 50

Instruction 12.10
A computer software developer would like to use the number of downloads (in thousands) for the trial version of his new shareware to predict the amount of revenue (in thousands of dollars) he can make on the full version of the new shareware. Following is the output from a simple linear regression along with the residual plot and normal probability plot obtained from a data set of 30 different sharewares that he has developed:
$\text { Regression statistics }$
$\begin{array}{|l|l|}\hline \text { MultipleR } & 0.8691 \\\hline \text { R Square } & 0.7554 \\\hline \begin{array}{l}\text { Adjusted R } \\\text { Square }\end{array} & 0.7467 \\\hline \text { Standard Error } & 44.4765 \\\hline \text { Observations } & 30.0000\\\hline \end{array}$

$\text { ANOVA }$
$\begin{array}{|l|l|l|l|l|l|}\hline & d f & S S & M S & F & \begin{array}{l}\text { Significance } \\F\end{array} \\\hline \text { Regression } & 1 & 171062.9193 & 171062.9193 & 86.4759 & 0.0000 \\\hline \text { Residual } & 28 & 55388.4309 & 1978.1582 & & \\\hline \text { Total } & 29 & 226451.3503 & & & \\\hline\end{array}$

$\begin{array}{|l|l|l|l|l|l|l|}\hline & \text { Coefficients } & \begin{array}{l}\text { Standard } \\\text { Error }\end{array} & \text { t Stat } & p \text {-value } & \text { Lower 95\% } & \text { Upper 95\% } \\\hline \text { Intercept } & -95.0614 & 26.9183 & -3.5315 & 0.0015 & -150.2009 & -39.9218 \\\hline \text { Download } & 3.7297 & 0.4011 & 9.2992 & 0.0000 & 2.9082 & 4.5513 \\\hline\end{array}$

-Referring to Instruction 12.10,predict the revenue when the number of downloads is 30,000.

Question 51

The coefficient of determination (r²)tells you

A) the proportion of variation in Y that is explained by the independent variable X in the model.
B) whether r has any significance.
C) that you should not partition the total variation.
D) that the coefficient of correlation (r) is larger than 1.

Question 52

The least squares method minimises which of the following?

A) SST
B) SSR
C) SSE
D) All of the above.

Question 53

Instruction 12.12
The director of cooperative education at a university wants to examine the effect of cooperative education job experience on marketability in the workplace. She takes a random sample of four students. For these four, she finds out how many times each had a cooperative education job and how many job offers they received upon graduation. These data are presented in the table below.
$$\begin{array} { | l | l | l | } \hline \text { Student } & \text { Coop jobs } & \text { job Offer } \\\hline 1 & 1 & 4 \\\hline 2 & 2 & 6 \\\hline 3 & 1 & 3 \\\hline 4 & 0 & 1 \\\hline\end{array}$$

-Referring to Instruction 12.12,the standard error of estimate is ____________.

Question 54

Instruction 12.13
The managers of a brokerage firm are interested in finding out if the number of new customers a broker brings into the firm affects the sales generated by the broker. They sample 12 brokers and determine the number of new customers they have enrolled in the last year and their sales amounts in thousands of dollars. These data are presented in the table that follows.
$$\begin{array} { | l | l | l | } \hline \text { Broker } & \text { Clients } & \text { Sales } \\\hline 1 & 27 & 52 \\\hline 2 & 11 & 37 \\\hline 3 & 42 & 64 \\\hline 4 & 33 & 55 \\\hline 5 & 15 & 29 \\\hline 6 & 15 & 34 \\\hline 7 & 25 & 58 \\\hline 8 & 36 & 59 \\\hline 9 & 28 & 44 \\\hline 10 & 30 & 48 \\\hline 11 & 17 & 31 \\\hline 12 & 22 & 38 \\\hline\end{array}$$

-Referring to Instruction 12.13,the coefficient of determination is ____________.

Question 55

The coefficient of determination represents the ratio of SSR to SST.

Question 56

Instruction 12.11
The manager of the purchasing department of a large savings and loan organization would like to develop a model to predict the amount of time (measured in hours) it takes to record a loan application. Data are collected from a sample of 30 days, and the number of applications recorded and completion time in hours is recorded. Below is the regression output:
$\text { Regression statistics }$
$\begin{array}{|l|l|}\hline\text { MultipleR } & 0.9447 \\\hline \text { R Square } & 0.8924 \\\hline \begin{array}{l}\text { Adjusted R } \\\text { Square }\end{array} & 0.8886 \\\hline \text { Standard Error } & 0.3342 \\\hline \text { Observations } & 30 \\\hline\end{array}$

$\text { ANOVA }$
$\begin{array}{|l|l|l|l|l|l|}\hline & d f & S 5 & M S & F & \begin{array}{l}\text { Significance } \\F\end{array} \\\hline \text { Regression } & 1 & 25.9438 & 25.9438 & 232.2200 & 4.3946 \mathrm{E}-15 \\\hline \text { Residual } & 28 & 3.1282 & 0.1117 & & \\\hline \text { Total } & 29 & 29.072 & & & \\\hline\end{array}$

$\begin{array}{|l|l|l|l|l|l|l|}\hline & \text { Coefficients } & \begin{array}{l}\text { Standard } \\\text { Error }\end{array} & \text { tStat } & \text { p-value } & \text { Lower 95\% } & \text { Upper 95\% } \\\hline \text { Intercept } & 0.4024 & 0.1236 & 3.2559 & 0.0030 & 0.1492 & 0.6555 \\\hline \begin{array}{l}\text { Applications } \\\text { Recorded }\end{array} & 0.0126 & 0.0008 & 15.2388 & \begin{array}{l}4.3946 \mathrm{E}- \\15\end{array} & 0.0109 & 0.0143 \\\hline\end{array}$
Note: 4.3946E-15 is 4.3946 × 10^-15.

-Referring to Instruction 12.11,the estimated mean amount of time it takes to record one additional loan application is

A) 0.4024 more hours.
B) 0.0126 more hours.
C) 0.0126 fewer hours.
D) 0.4024 fewer hours.

Question 57

The Y-intercept (b₀)represents the

A) predicted value of Y.
B) change in estimated average Y per unit change in X.
C) estimated average Y when X = 0.
D) variation around the sample regression line.

Question 58

Instruction 12.12
The director of cooperative education at a university wants to examine the effect of cooperative education job experience on marketability in the workplace. She takes a random sample of four students. For these four, she finds out how many times each had a cooperative education job and how many job offers they received upon graduation. These data are presented in the table below.
$$\begin{array} { | l | l | l | } \hline \text { Student } & \text { Coop jobs } & \text { job Offer } \\\hline 1 & 1 & 4 \\\hline 2 & 2 & 6 \\\hline 3 & 1 & 3 \\\hline 4 & 0 & 1 \\\hline\end{array}$$

-Referring to Instruction 12.12,the coefficient of correlation is ____________.

Question 59

Instruction 12.13
The managers of a brokerage firm are interested in finding out if the number of new customers a broker brings into the firm affects the sales generated by the broker. They sample 12 brokers and determine the number of new customers they have enrolled in the last year and their sales amounts in thousands of dollars. These data are presented in the table that follows.
$$\begin{array} { | l | l | l | } \hline \text { Broker } & \text { Clients } & \text { Sales } \\\hline 1 & 27 & 52 \\\hline 2 & 11 & 37 \\\hline 3 & 42 & 64 \\\hline 4 & 33 & 55 \\\hline 5 & 15 & 29 \\\hline 6 & 15 & 34 \\\hline 7 & 25 & 58 \\\hline 8 & 36 & 59 \\\hline 9 & 28 & 44 \\\hline 10 & 30 & 48 \\\hline 11 & 17 & 31 \\\hline 12 & 22 & 38 \\\hline\end{array}$$

-Referring to Instruction 12.13,the standard error of the estimated slope coefficient is ____________.

Question 60

Instruction 12.10
A computer software developer would like to use the number of downloads (in thousands) for the trial version of his new shareware to predict the amount of revenue (in thousands of dollars) he can make on the full version of the new shareware. Following is the output from a simple linear regression along with the residual plot and normal probability plot obtained from a data set of 30 different sharewares that he has developed:
$\text { Regression statistics }$
$\begin{array}{|l|l|}\hline \text { MultipleR } & 0.8691 \\\hline \text { R Square } & 0.7554 \\\hline \begin{array}{l}\text { Adjusted R } \\\text { Square }\end{array} & 0.7467 \\\hline \text { Standard Error } & 44.4765 \\\hline \text { Observations } & 30.0000\\\hline \end{array}$

$\text { ANOVA }$
$\begin{array}{|l|l|l|l|l|l|}\hline & d f & S S & M S & F & \begin{array}{l}\text { Significance } \\F\end{array} \\\hline \text { Regression } & 1 & 171062.9193 & 171062.9193 & 86.4759 & 0.0000 \\\hline \text { Residual } & 28 & 55388.4309 & 1978.1582 & & \\\hline \text { Total } & 29 & 226451.3503 & & & \\\hline\end{array}$

$\begin{array}{|l|l|l|l|l|l|l|}\hline & \text { Coefficients } & \begin{array}{l}\text { Standard } \\\text { Error }\end{array} & \text { t Stat } & p \text {-value } & \text { Lower 95\% } & \text { Upper 95\% } \\\hline \text { Intercept } & -95.0614 & 26.9183 & -3.5315 & 0.0015 & -150.2009 & -39.9218 \\\hline \text { Download } & 3.7297 & 0.4011 & 9.2992 & 0.0000 & 2.9082 & 4.5513 \\\hline\end{array}$

-Referring to Instruction 12.10,which of the following is the correct interpretation for the slope coefficient?

A) For each incsrease of 1 million dollars in box office gross, expected home video units sold are estimated to increase by 4.3331 thousand units.
B) For each increase of 1 dollar in box office gross, expected home video units sold are estimated to increase by 4.3331 units.
C) For each increase of 1 million dollars in box office gross, expected home video units sold are estimated to increase by 4.3331 units.
D) For each increase of 1 dollar in box office gross, expected home video units sold are estimated to increase by 4.3331 thousand units.

Question 61

Instruction 12.16
The management of a chain electronic store would like to develop a model for predicting the weekly sales (in thousands of dollars) for individual stores based on the number of customers who made purchases. A random sample of 12 stores yields the following results:
$$\begin{array} { | l | c | } \hline \text { Customers } & \text { Sales (Thousands of Dollars) } \\\hline 907 & 11.20 \\\hline 926 & 11.05 \\\hline 713 & 8.21 \\\hline 741 & 9.21 \\\hline 780 & 9.42 \\\hline 898 & 10.08 \\\hline 510 & 6.73 \\\hline 529 & 7.02 \\\hline 460 & 6.12 \\\hline 872 & 9.52 \\\hline 650 & 7.53 \\\hline 603 & 7.25 \\\hline\end{array}$$

-Referring to Instruction 12.16,what is the value of the standard error of the estimate?

Question 62

Instruction 12.14
The managing partner of an advertising agency believes that his company's sales are related to the industry sales. He uses Microsoft Excel's Data Analysis tool to analyse the last four years of quarterly data with the following results:
$\text { Regression statistics }$
$\begin{array}{|l|l|}\hline \text { Multiple R } & 0.802 \\\hline \text { R Square } & 0.643 \\\hline \begin{array}{l}\text { Adjusted R } \\\text { Square }\end{array} & 0.618 \\\hline \begin{array}{l}\text { Standard Error } \\\text { SYX }\end{array} & 0.9224 \\\hline \text { Observations } & 16 \\\hline\end{array}$

$\text { ANOVA }$
$\begin{array}{|l|l|l|l|l|l|}\hline & \text { df } & \text { SS } & \text { MS } & \text { F } & \text { Sig.F } \\\hline \text { Regression } & 1 & 21.497 & 21.497 & 25.27 & 0.000 \\\hline \text { Error } & 14 & 11.912 & 0.851 & & \\\hline \text { Total } & 15 & 33.409 & & & \\\hline\end{array}$

$\begin{array}{|l|l|l|l|l|}\hline\text { Predictor } & \text { Coef } & \text { StdError } & \text { t Stat } & \text { p-value } \\\hline \text { Intercept } & 3.962 & 1.440 & 2.75 & 0.016 \\\hline \text { Industry } & 0.040451 & 0.008048 & 5.03 & 0.000\\\hline\end{array}$


$\begin{array}{|l|l|}\hline\text { Durbin-Watson } & 1.59 \\\text { Statistic } &\\\hline\end{array}$

-Referring to Instruction 12.14,the standard error of the estimated slope coefficient is ____________.

Question 63

Instruction 12.13
The managers of a brokerage firm are interested in finding out if the number of new customers a broker brings into the firm affects the sales generated by the broker. They sample 12 brokers and determine the number of new customers they have enrolled in the last year and their sales amounts in thousands of dollars. These data are presented in the table that follows.
$$\begin{array} { | l | l | l | } \hline \text { Broker } & \text { Clients } & \text { Sales } \\\hline 1 & 27 & 52 \\\hline 2 & 11 & 37 \\\hline 3 & 42 & 64 \\\hline 4 & 33 & 55 \\\hline 5 & 15 & 29 \\\hline 6 & 15 & 34 \\\hline 7 & 25 & 58 \\\hline 8 & 36 & 59 \\\hline 9 & 28 & 44 \\\hline 10 & 30 & 48 \\\hline 11 & 17 & 31 \\\hline 12 & 22 & 38 \\\hline\end{array}$$

-Referring to Instruction 12.13,the coefficient of correlation is____________.

Question 64

Instruction 12.18
The manager of the purchasing department of a large savings and loan organization would like to develop a model to predict the amount of time (measured in hours) it takes to record a loan application. Data are collected from a sample of 30 days, and the number of applications recorded and completion time in hours is recorded. Below is the regression output:
$\text { Regression statistics }$
$\begin{array}{|l|l|}\hline\text { MultipleR } & 0.9447 \\\hline \text { R Square } & 0.8924 \\\hline \begin{array}{l}\text { Adjusted R } \\\text { Square }\end{array} & 0.8886 \\\hline \text { Standard Error } & 0.3342 \\\hline \text { Observations } & 30 \\\hline\end{array}$

$\text { ANOVA }$
$\begin{array}{|l|l|l|l|l|l|}\hline & d f & S 5 & M S & F & \begin{array}{l}\text { Significance } \\F\end{array} \\\hline \text { Regression } & 1 & 25.9438 & 25.9438 & 232.2200 & 4.3946 \mathrm{E}-15 \\\hline \text { Residual } & 28 & 3.1282 & 0.1117 & & \\\hline \text { Total } & 29 & 29.072 & & & \\\hline\end{array}$

$\begin{array}{|l|l|l|l|l|l|l|}\hline & \text { Coefficients } & \begin{array}{l}\text { Standard } \\\text { Error }\end{array} & \text { tStat } & \text { p-value } & \text { Lower 95\% } & \text { Upper 95\% } \\\hline \text { Intercept } & 0.4024 & 0.1236 & 3.2559 & 0.0030 & 0.1492 & 0.6555 \\\hline \begin{array}{l}\text { Applications } \\\text { Recorded }\end{array} & 0.0126 & 0.0008 & 15.2388 & \begin{array}{l}4.3946 \mathrm{E}- \\15\end{array} & 0.0109 & 0.0143 \\\hline\end{array}$

Note: 4.3946E-15 is 4.3946 x 10^-15. Note: 4.3946E-15 is 4.3946 × 10^-15.

-Referring to Instruction 12.18,the error sum of squares (SSE)of the above regression is

A) 0.1117.
B) 29.0720.
C) 25.9438.
D) 3.1282.

Question 65

Instruction 12.17
A computer software developer would like to use the number of downloads (in thousands) for the trial version of his new shareware to predict the amount of revenue (in thousands of dollars) he can make on the full version of the new shareware. Following is the output from a simple linear regression along with the residual plot and normal probability plot obtained from a data set of 30 different sharewares that he has developed:
$\text { Regression statistics }$
$\begin{array}{|l|l|}\hline \text { MultipleR } & 0.8691 \\\hline \text { R Square } & 0.7554 \\\hline \begin{array}{l}\text { Adjusted R } \\\text { Square }\end{array} & 0.7467 \\\hline \text { Standard Error } & 44.4765 \\\hline \text { Observations } & 30.0000\\\hline \end{array}$

$\text { ANOVA }$
$\begin{array}{|l|l|l|l|l|l|}\hline & d f & S S & M S & F & \begin{array}{l}\text { Significance } \\F\end{array} \\\hline \text { Regression } & 1 & 171062.9193 & 171062.9193 & 86.4759 & 0.0000 \\\hline \text { Residual } & 28 & 55388.4309 & 1978.1582 & & \\\hline \text { Total } & 29 & 226451.3503 & & & \\\hline\end{array}$

$\begin{array}{|l|l|l|l|l|l|l|}\hline & \text { Coefficients } & \begin{array}{l}\text { Standard } \\\text { Error }\end{array} & \text { t Stat } & p \text {-value } & \text { Lower 95\% } & \text { Upper 95\% } \\\hline \text { Intercept } & -95.0614 & 26.9183 & -3.5315 & 0.0015 & -150.2009 & -39.9218 \\\hline \text { Download } & 3.7297 & 0.4011 & 9.2992 & 0.0000 & 2.9082 & 4.5513 \\\hline\end{array}$


-Referring to Instruction 12.17,which of the following is the correct interpretation for the coefficient of determination?

A) 72.8% of the variation in the video unit sales can be explained by the variation in the box office gross.
B) 71.8% of the variation in the video unit sales can be explained by the variation in the box office gross.
C) 71.8% of the variation in the box office gross can be explained by the variation in the video unit sales.
D) 72.8% of the variation in the box office gross can be explained by the variation in the video unit sales.

Question 66

Instruction 12.13
The managers of a brokerage firm are interested in finding out if the number of new customers a broker brings into the firm affects the sales generated by the broker. They sample 12 brokers and determine the number of new customers they have enrolled in the last year and their sales amounts in thousands of dollars. These data are presented in the table that follows.
$$\begin{array} { | l | l | l | } \hline \text { Broker } & \text { Clients } & \text { Sales } \\\hline 1 & 27 & 52 \\\hline 2 & 11 & 37 \\\hline 3 & 42 & 64 \\\hline 4 & 33 & 55 \\\hline 5 & 15 & 29 \\\hline 6 & 15 & 34 \\\hline 7 & 25 & 58 \\\hline 8 & 36 & 59 \\\hline 9 & 28 & 44 \\\hline 10 & 30 & 48 \\\hline 11 & 17 & 31 \\\hline 12 & 22 & 38 \\\hline\end{array}$$

-Referring to Instruction 12.13,the standard error of estimate is ____________.

Question 67

If the plot of the residuals is fan shaped,which assumption is violated?

A) Homoscedasticity
B) Independence of errors
C) Normality
D) No assumptions are violated, the graph should resemble a fan

Question 68

Instruction 12.14
The managing partner of an advertising agency believes that his company's sales are related to the industry sales. He uses Microsoft Excel's Data Analysis tool to analyse the last four years of quarterly data with the following results:
$\text { Regression statistics }$
$\begin{array}{|l|l|}\hline \text { Multiple R } & 0.802 \\\hline \text { R Square } & 0.643 \\\hline \begin{array}{l}\text { Adjusted R } \\\text { Square }\end{array} & 0.618 \\\hline \begin{array}{l}\text { Standard Error } \\\text { SYX }\end{array} & 0.9224 \\\hline \text { Observations } & 16 \\\hline\end{array}$

$\text { ANOVA }$
$\begin{array}{|l|l|l|l|l|l|}\hline & \text { df } & \text { SS } & \text { MS } & \text { F } & \text { Sig.F } \\\hline \text { Regression } & 1 & 21.497 & 21.497 & 25.27 & 0.000 \\\hline \text { Error } & 14 & 11.912 & 0.851 & & \\\hline \text { Total } & 15 & 33.409 & & & \\\hline\end{array}$

$\begin{array}{|l|l|l|l|l|}\hline\text { Predictor } & \text { Coef } & \text { StdError } & \text { t Stat } & \text { p-value } \\\hline \text { Intercept } & 3.962 & 1.440 & 2.75 & 0.016 \\\hline \text { Industry } & 0.040451 & 0.008048 & 5.03 & 0.000\\\hline\end{array}$


$\begin{array}{|l|l|}\hline\text { Durbin-Watson } & 1.59 \\\text { Statistic } &\\\hline\end{array}$

-Referring to Instruction 12.14,the correlation coefficient is ____________.

Question 69

Instruction 12.17
A computer software developer would like to use the number of downloads (in thousands) for the trial version of his new shareware to predict the amount of revenue (in thousands of dollars) he can make on the full version of the new shareware. Following is the output from a simple linear regression along with the residual plot and normal probability plot obtained from a data set of 30 different sharewares that he has developed:
$\text { Regression statistics }$
$\begin{array}{|l|l|}\hline \text { MultipleR } & 0.8691 \\\hline \text { R Square } & 0.7554 \\\hline \begin{array}{l}\text { Adjusted R } \\\text { Square }\end{array} & 0.7467 \\\hline \text { Standard Error } & 44.4765 \\\hline \text { Observations } & 30.0000\\\hline \end{array}$

$\text { ANOVA }$
$\begin{array}{|l|l|l|l|l|l|}\hline & d f & S S & M S & F & \begin{array}{l}\text { Significance } \\F\end{array} \\\hline \text { Regression } & 1 & 171062.9193 & 171062.9193 & 86.4759 & 0.0000 \\\hline \text { Residual } & 28 & 55388.4309 & 1978.1582 & & \\\hline \text { Total } & 29 & 226451.3503 & & & \\\hline\end{array}$

$\begin{array}{|l|l|l|l|l|l|l|}\hline & \text { Coefficients } & \begin{array}{l}\text { Standard } \\\text { Error }\end{array} & \text { t Stat } & p \text {-value } & \text { Lower 95\% } & \text { Upper 95\% } \\\hline \text { Intercept } & -95.0614 & 26.9183 & -3.5315 & 0.0015 & -150.2009 & -39.9218 \\\hline \text { Download } & 3.7297 & 0.4011 & 9.2992 & 0.0000 & 2.9082 & 4.5513 \\\hline\end{array}$


-Referring to Instruction 12.17,what is the standard deviation around the regression line?

Question 70

Instruction 12.17
A computer software developer would like to use the number of downloads (in thousands) for the trial version of his new shareware to predict the amount of revenue (in thousands of dollars) he can make on the full version of the new shareware. Following is the output from a simple linear regression along with the residual plot and normal probability plot obtained from a data set of 30 different sharewares that he has developed:
$\text { Regression statistics }$
$\begin{array}{|l|l|}\hline \text { MultipleR } & 0.8691 \\\hline \text { R Square } & 0.7554 \\\hline \begin{array}{l}\text { Adjusted R } \\\text { Square }\end{array} & 0.7467 \\\hline \text { Standard Error } & 44.4765 \\\hline \text { Observations } & 30.0000\\\hline \end{array}$

$\text { ANOVA }$
$\begin{array}{|l|l|l|l|l|l|}\hline & d f & S S & M S & F & \begin{array}{l}\text { Significance } \\F\end{array} \\\hline \text { Regression } & 1 & 171062.9193 & 171062.9193 & 86.4759 & 0.0000 \\\hline \text { Residual } & 28 & 55388.4309 & 1978.1582 & & \\\hline \text { Total } & 29 & 226451.3503 & & & \\\hline\end{array}$

$\begin{array}{|l|l|l|l|l|l|l|}\hline & \text { Coefficients } & \begin{array}{l}\text { Standard } \\\text { Error }\end{array} & \text { t Stat } & p \text {-value } & \text { Lower 95\% } & \text { Upper 95\% } \\\hline \text { Intercept } & -95.0614 & 26.9183 & -3.5315 & 0.0015 & -150.2009 & -39.9218 \\\hline \text { Download } & 3.7297 & 0.4011 & 9.2992 & 0.0000 & 2.9082 & 4.5513 \\\hline\end{array}$


-Referring to Instruction 12.17,which of the following is the correct interpretation for the coefficient of determination?

A) 74.67% of the variation in revenue can be explained by the variation in the number of downloads.
B) 75.54% of the variation in revenue can be explained by the variation in the number of downloads.
C) 75.54% of the variation in the number of downloads can be explained by the variation in revenue.
D) 74.67% of the variation in the number of downloads can be explained by the variation in revenue.

Question 71

Which of the following assumptions concerning the probability distribution of the random error term is stated incorrectly?

A) The variance of the distribution increases as X increases.
B) The mean of the distribution is 0.
C) The errors are independent.
D) The distribution is normal.

Question 72

Instruction 12.15
The following Microsoft Excel tables are obtained when 'Score received on an exam (measured in percentage points)' (Y) is regressed on 'percentage attendance' (X) for 22 students in a Statistics for Business and Economics course.
$\text { Regression Statistics }$
$\begin{array}{|l|l|}\hline\text { MultipleR } & 0.142620229 \\\hline \text { R Square } & 0.02034053 \\\hline \begin{array}{l}\text { Adjusted R } \\\text { Square }\end{array} & -0.028642444 \\\hline \text { Standard Error } & 20.25979924 \\\hline \text { Observations } & 22\\\hline\end{array}$

$\begin{array}{|l|l|l|l|l|}\hline & \text { Coefficients } & \begin{array}{l}\text { Standard } \\\text { Error }\end{array} & t \text { Stat } & p \text {-value } \\\hline \text { Intercept } & 39.39027309 & 37.24347659 & 1.057642216 & 0.302826622 \\\hline \text { Attendance } & 0.340583573 & 0.52852452 & 0.644404489 & 0.526635689 \\\hline\end{array}$



-Referring to Instruction 12.15,which of the following statements is true?

A) 14.2% of the total variability in percentage attendance can be explained by score received.
B) 2% of the total variability in score received can be explained by percentage attendance.
C) 2% of the total variability in percentage attendance can be explained by score received.
D) 14.26% of the total variability in score received can be explained by percentage attendance.

Question 73

Instruction 12.14
The managing partner of an advertising agency believes that his company's sales are related to the industry sales. He uses Microsoft Excel's Data Analysis tool to analyse the last four years of quarterly data with the following results:
$\text { Regression statistics }$
$\begin{array}{|l|l|}\hline \text { Multiple R } & 0.802 \\\hline \text { R Square } & 0.643 \\\hline \begin{array}{l}\text { Adjusted R } \\\text { Square }\end{array} & 0.618 \\\hline \begin{array}{l}\text { Standard Error } \\\text { SYX }\end{array} & 0.9224 \\\hline \text { Observations } & 16 \\\hline\end{array}$

$\text { ANOVA }$
$\begin{array}{|l|l|l|l|l|l|}\hline & \text { df } & \text { SS } & \text { MS } & \text { F } & \text { Sig.F } \\\hline \text { Regression } & 1 & 21.497 & 21.497 & 25.27 & 0.000 \\\hline \text { Error } & 14 & 11.912 & 0.851 & & \\\hline \text { Total } & 15 & 33.409 & & & \\\hline\end{array}$

$\begin{array}{|l|l|l|l|l|}\hline\text { Predictor } & \text { Coef } & \text { StdError } & \text { t Stat } & \text { p-value } \\\hline \text { Intercept } & 3.962 & 1.440 & 2.75 & 0.016 \\\hline \text { Industry } & 0.040451 & 0.008048 & 5.03 & 0.000\\\hline\end{array}$


$\begin{array}{|l|l|}\hline\text { Durbin-Watson } & 1.59 \\\text { Statistic } &\\\hline\end{array}$

-Referring to Instruction 12.14,the standard error of the estimate is____________.

Question 74

Instruction 12.14
The managing partner of an advertising agency believes that his company's sales are related to the industry sales. He uses Microsoft Excel's Data Analysis tool to analyse the last four years of quarterly data with the following results:
$\text { Regression statistics }$
$\begin{array}{|l|l|}\hline \text { Multiple R } & 0.802 \\\hline \text { R Square } & 0.643 \\\hline \begin{array}{l}\text { Adjusted R } \\\text { Square }\end{array} & 0.618 \\\hline \begin{array}{l}\text { Standard Error } \\\text { SYX }\end{array} & 0.9224 \\\hline \text { Observations } & 16 \\\hline\end{array}$

$\text { ANOVA }$
$\begin{array}{|l|l|l|l|l|l|}\hline & \text { df } & \text { SS } & \text { MS } & \text { F } & \text { Sig.F } \\\hline \text { Regression } & 1 & 21.497 & 21.497 & 25.27 & 0.000 \\\hline \text { Error } & 14 & 11.912 & 0.851 & & \\\hline \text { Total } & 15 & 33.409 & & & \\\hline\end{array}$

$\begin{array}{|l|l|l|l|l|}\hline\text { Predictor } & \text { Coef } & \text { StdError } & \text { t Stat } & \text { p-value } \\\hline \text { Intercept } & 3.962 & 1.440 & 2.75 & 0.016 \\\hline \text { Industry } & 0.040451 & 0.008048 & 5.03 & 0.000\\\hline\end{array}$


$\begin{array}{|l|l|}\hline\text { Durbin-Watson } & 1.59 \\\text { Statistic } &\\\hline\end{array}$

-Referring to Instruction 12.14,the coefficient of determination is ____________.

Question 75

The residuals represent

A) the square root of the slope.
B) the difference between the actual Y values and the predicted Y values.
C) the difference between the actual Y values and the mean of Y.
D) the predicted value of Y for the average X value.

Question 76

Based on the residual plot below,you will conclude that there might be a violation of which of the following assumptions?

A) Homoscedasticity
B) Independence of errors
C) Linearity of the relationship
D) Normality of errors

Question 77

Instruction 12.17
A computer software developer would like to use the number of downloads (in thousands) for the trial version of his new shareware to predict the amount of revenue (in thousands of dollars) he can make on the full version of the new shareware. Following is the output from a simple linear regression along with the residual plot and normal probability plot obtained from a data set of 30 different sharewares that he has developed:
$\text { Regression statistics }$
$\begin{array}{|l|l|}\hline \text { MultipleR } & 0.8691 \\\hline \text { R Square } & 0.7554 \\\hline \begin{array}{l}\text { Adjusted R } \\\text { Square }\end{array} & 0.7467 \\\hline \text { Standard Error } & 44.4765 \\\hline \text { Observations } & 30.0000\\\hline \end{array}$

$\text { ANOVA }$
$\begin{array}{|l|l|l|l|l|l|}\hline & d f & S S & M S & F & \begin{array}{l}\text { Significance } \\F\end{array} \\\hline \text { Regression } & 1 & 171062.9193 & 171062.9193 & 86.4759 & 0.0000 \\\hline \text { Residual } & 28 & 55388.4309 & 1978.1582 & & \\\hline \text { Total } & 29 & 226451.3503 & & & \\\hline\end{array}$

$\begin{array}{|l|l|l|l|l|l|l|}\hline & \text { Coefficients } & \begin{array}{l}\text { Standard } \\\text { Error }\end{array} & \text { t Stat } & p \text {-value } & \text { Lower 95\% } & \text { Upper 95\% } \\\hline \text { Intercept } & -95.0614 & 26.9183 & -3.5315 & 0.0015 & -150.2009 & -39.9218 \\\hline \text { Download } & 3.7297 & 0.4011 & 9.2992 & 0.0000 & 2.9082 & 4.5513 \\\hline\end{array}$


-Referring to Instruction 12.17,what is the standard error of estimate?

Question 78

In performing a regression analysis involving two numerical variables,you are assuming

A) the variances of X and Y are equal.
B) that X and Y are independent.
C) the variation around the line of regression is the same for each X value.
D) All of the above.

Question 79

Instruction 12.16
The management of a chain electronic store would like to develop a model for predicting the weekly sales (in thousands of dollars) for individual stores based on the number of customers who made purchases. A random sample of 12 stores yields the following results:
$$\begin{array} { | l | c | } \hline \text { Customers } & \text { Sales (Thousands of Dollars) } \\\hline 907 & 11.20 \\\hline 926 & 11.05 \\\hline 713 & 8.21 \\\hline 741 & 9.21 \\\hline 780 & 9.42 \\\hline 898 & 10.08 \\\hline 510 & 6.73 \\\hline 529 & 7.02 \\\hline 460 & 6.12 \\\hline 872 & 9.52 \\\hline 650 & 7.53 \\\hline 603 & 7.25 \\\hline\end{array}$$

-Referring to Instruction 12.16,what is the value of the coefficient of correlation?

Question 80

Instruction 12.16
The management of a chain electronic store would like to develop a model for predicting the weekly sales (in thousands of dollars) for individual stores based on the number of customers who made purchases. A random sample of 12 stores yields the following results:
$$\begin{array} { | l | c | } \hline \text { Customers } & \text { Sales (Thousands of Dollars) } \\\hline 907 & 11.20 \\\hline 926 & 11.05 \\\hline 713 & 8.21 \\\hline 741 & 9.21 \\\hline 780 & 9.42 \\\hline 898 & 10.08 \\\hline 510 & 6.73 \\\hline 529 & 7.02 \\\hline 460 & 6.12 \\\hline 872 & 9.52 \\\hline 650 & 7.53 \\\hline 603 & 7.25 \\\hline\end{array}$$

-Referring to Instruction 12.16,what is the value of the coefficient of determination?