Deck 13: Simple Linear Regression

Question 1

SCENARIO 13-2
A candy 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 6 small cities and offers the candy bar at
different prices. Using candy bar sales as the dependent variable, the company will conduct a simple
linear regression on the data below: $\begin{array}{ccc}\underline{\text { City }} &\underline{ \text { Price (\$)}} &\underline{\text { Sales }}\\\text { River Falls } & 1.30 & 100 \\\text { Hudson } & 1.60 & 90 \\\text { Ellsworth } & 1.80 & 90 \\\text { Prescott } & 2.00 & 40 \\\text { Rock Elm } & 2.40 & 38 \\\text { Stillwater } & 2.90 & 32\end{array}$


-Referring to Scenario 13-2, what is the standard error of the estimate, SYX, for the data?

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

Answer 1

16.299

Question 2

The slope (b1) represents

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

Answer 2

B

Question 3

SCENARIO 13-2
A candy 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 6 small cities and offers the candy bar at
different prices. Using candy bar sales as the dependent variable, the company will conduct a simple
linear regression on the data below: $\begin{array}{ccc}\underline{\text { City }} &\underline{ \text { Price (\$)}} &\underline{\text { Sales }}\\\text { River Falls } & 1.30 & 100 \\\text { Hudson } & 1.60 & 90 \\\text { Ellsworth } & 1.80 & 90 \\\text { Prescott } & 2.00 & 40 \\\text { Rock Elm } & 2.40 & 38 \\\text { Stillwater } & 2.90 & 32\end{array}$


-Referring to Scenario 13-2, what is the standard error of the regression slope estimate, Sb1 ?

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

Answer 3

12.650

Question 4

SCENARIO 13-1
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
charges 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: $$Y _ { i } = \beta _ { 0 } + \beta _ { 1 } X _ { i } + \varepsilon _ { i }$$
The results of the simple linear regression are provided below.
$$\hat { Y } = - 2,700 + 20 X , S _ { X X } = 65 , \text { two-tail } p \text { value } = 0.034 \left( \text { for testing } \beta _ { 1 } \right)$$

-Referring to Scenario 13-1, 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 $65 of the least squares line.
B) About 95% of the observed service charges equal their corresponding predicted values.
C) About 95% of the observed service charges fall within $130 of the least squares line.
D) For every $1 million increase in sales revenue, we expect a service charge to increase $65.

Question 5

SCENARIO 13-2
A candy 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 6 small cities and offers the candy bar at
different prices. Using candy bar sales as the dependent variable, the company will conduct a simple
linear regression on the data below: $\begin{array}{ccc}\underline{\text { City }} &\underline{ \text { Price (\$)}} &\underline{\text { Sales }}\\\text { River Falls } & 1.30 & 100 \\\text { Hudson } & 1.60 & 90 \\\text { Ellsworth } & 1.80 & 90 \\\text { Prescott } & 2.00 & 40 \\\text { Rock Elm } & 2.40 & 38 \\\text { Stillwater } & 2.90 & 32\end{array}$


-Referring to Scenario 13-2, what is the estimated mean change in the sales of the candy bar if price goes up by $1.00?

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

Question 6

SCENARIO 13-2
A candy 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 6 small cities and offers the candy bar at
different prices. Using candy bar sales as the dependent variable, the company will conduct a simple
linear regression on the data below: $\begin{array}{ccc}\underline{\text { City }} &\underline{ \text { Price (\$)}} &\underline{\text { Sales }}\\\text { River Falls } & 1.30 & 100 \\\text { Hudson } & 1.60 & 90 \\\text { Ellsworth } & 1.80 & 90 \\\text { Prescott } & 2.00 & 40 \\\text { Rock Elm } & 2.40 & 38 \\\text { Stillwater } & 2.90 & 32\end{array}$


-Referring to Scenario 13-2, what is $\Sigma ( X - \bar { X } ) ^ { 2 }$ for these data?

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

Question 7

The Y-intercept (b0) represents the

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

Question 8

The Y-intercept (b0) represents the

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

Question 9

SCENARIO 13-2
A candy 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 6 small cities and offers the candy bar at
different prices. Using candy bar sales as the dependent variable, the company will conduct a simple
linear regression on the data below: $\begin{array}{ccc}\underline{\text { City }} &\underline{ \text { Price (\$)}} &\underline{\text { Sales }}\\\text { River Falls } & 1.30 & 100 \\\text { Hudson } & 1.60 & 90 \\\text { Ellsworth } & 1.80 & 90 \\\text { Prescott } & 2.00 & 40 \\\text { Rock Elm } & 2.40 & 38 \\\text { Stillwater } & 2.90 & 32\end{array}$


-Referring to Scenario 13-2, what percentage of the total variation in candy bar sales is explained by prices?

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

Question 10

SCENARIO 13-2
A candy 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 6 small cities and offers the candy bar at
different prices. Using candy bar sales as the dependent variable, the company will conduct a simple
linear regression on the data below: $\begin{array}{ccc}\underline{\text { City }} &\underline{ \text { Price (\$)}} &\underline{\text { Sales }}\\\text { River Falls } & 1.30 & 100 \\\text { Hudson } & 1.60 & 90 \\\text { Ellsworth } & 1.80 & 90 \\\text { Prescott } & 2.00 & 40 \\\text { Rock Elm } & 2.40 & 38 \\\text { Stillwater } & 2.90 & 32\end{array}$


-Referring to Scenario 13-2, what is the coefficient of correlation for these data?

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

Question 11

SCENARIO 13-1
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
charges 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: $$Y _ { i } = \beta _ { 0 } + \beta _ { 1 } X _ { i } + \varepsilon _ { i }$$
The results of the simple linear regression are provided below.
$$\hat { Y } = - 2,700 + 20 X , S _ { X X } = 65 , \text { two-tail } p \text { value } = 0.034 \left( \text { for testing } \beta _ { 1 } \right)$$

-Referring to Scenario 13-1, interpret the p-value for testing whether $\beta _ { 1 }$ 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) There is insufficient evidence (at the ? = 0.10) to conclude that sales revenue (X) is a useful linear predictor of service charge (Y).
C) Sales revenue (X) is a poor predictor of service charge (Y).
D) For every $1 million increase in sales revenue, you expect a service charge to increase $0.034.

Question 12

SCENARIO 13-1
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
charges 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: $$Y _ { i } = \beta _ { 0 } + \beta _ { 1 } X _ { i } + \varepsilon _ { i }$$
The results of the simple linear regression are provided below.
$$\hat { Y } = - 2,700 + 20 X , S _ { X X } = 65 , \text { two-tail } p \text { value } = 0.034 \left( \text { for testing } \beta _ { 1 } \right)$$

-Referring to Scenario 13-1, interpret the estimate of $\beta _ { 0 }$ , the Y-intercept of the line.

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

Question 13

SCENARIO 13-2
A candy 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 6 small cities and offers the candy bar at
different prices. Using candy bar sales as the dependent variable, the company will conduct a simple
linear regression on the data below: $\begin{array}{ccc}\underline{\text { City }} &\underline{ \text { Price (\$)}} &\underline{\text { Sales }}\\\text { River Falls } & 1.30 & 100 \\\text { Hudson } & 1.60 & 90 \\\text { Ellsworth } & 1.80 & 90 \\\text { Prescott } & 2.00 & 40 \\\text { Rock Elm } & 2.40 & 38 \\\text { Stillwater } & 2.90 & 32\end{array}$


-Referring to Scenario 13-2, what is the estimated slope for the candy bar price and sales data?

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

Question 14

The least squares method minimizes which of the following?

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

Question 15

The Chancellor of a university has commissioned a team to collect data on
students' GPAs and the amount of time they spend bar hopping every week (measured in
minutes). He wants to know if imposing much tougher regulations on all campus bars to make it
more difficult for students to spend time in any campus bar will have a significant impact on
general students' GPAs. His team should use a t test on the slope of the population regression.

Question 16

SCENARIO 13-1
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
charges 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: $$Y _ { i } = \beta _ { 0 } + \beta _ { 1 } X _ { i } + \varepsilon _ { i }$$
The results of the simple linear regression are provided below.
$$\hat { Y } = - 2,700 + 20 X , S _ { X X } = 65 , \text { two-tail } p \text { value } = 0.034 \left( \text { for testing } \beta _ { 1 } \right)$$

-Referring to Scenario 13-1, a 95% confidence interval for $\beta _ { 1 }$ is (15, 30). Interpret the interval.

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

Question 17

SCENARIO 13-2
A candy 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 6 small cities and offers the candy bar at
different prices. Using candy bar sales as the dependent variable, the company will conduct a simple
linear regression on the data below: $\begin{array}{ccc}\underline{\text { City }} &\underline{ \text { Price (\$)}} &\underline{\text { Sales }}\\\text { River Falls } & 1.30 & 100 \\\text { Hudson } & 1.60 & 90 \\\text { Ellsworth } & 1.80 & 90 \\\text { Prescott } & 2.00 & 40 \\\text { Rock Elm } & 2.40 & 38 \\\text { Stillwater } & 2.90 & 32\end{array}$


-Referring to Scenario 13-2, if the price of the candy bar is set at $2, the predicted sales will be

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

Question 18

SCENARIO 13-2
A candy 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 6 small cities and offers the candy bar at
different prices. Using candy bar sales as the dependent variable, the company will conduct a simple
linear regression on the data below: $\begin{array}{ccc}\underline{\text { City }} &\underline{ \text { Price (\$)}} &\underline{\text { Sales }}\\\text { River Falls } & 1.30 & 100 \\\text { Hudson } & 1.60 & 90 \\\text { Ellsworth } & 1.80 & 90 \\\text { Prescott } & 2.00 & 40 \\\text { Rock Elm } & 2.40 & 38 \\\text { Stillwater } & 2.90 & 32\end{array}$


-Referring to Scenario 13-2, if the price of the candy bar is set at $2, the estimated mean sales will be

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

Question 19

The residual represents the discrepancy between the observed dependent variable and its
_______ value.

Question 20

SCENARIO 13-2
A candy 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 6 small cities and offers the candy bar at
different prices. Using candy bar sales as the dependent variable, the company will conduct a simple
linear regression on the data below: $\begin{array}{ccc}\underline{\text { City }} &\underline{ \text { Price (\$)}} &\underline{\text { Sales }}\\\text { River Falls } & 1.30 & 100 \\\text { Hudson } & 1.60 & 90 \\\text { Ellsworth } & 1.80 & 90 \\\text { Prescott } & 2.00 & 40 \\\text { Rock Elm } & 2.40 & 38 \\\text { Stillwater } & 2.90 & 32\end{array}$


-Referring to Scenario 13-2, what is the percentage of the total variation in candy bar sales explained by the regression model?

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

Question 21

SCENARIO 13-3
The director of cooperative education at a state college wants to examine the effect of cooperative
education job experience on marketability in the work place. She takes a random sample of 4
students. For these 4, 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.
Referring to Scenario 13-3, suppose the director of cooperative education wants to construct a
95% prediction interval for the number of job offers received by a student who has had exactly
two cooperative education jobs. The t critical value she would use is ________.

Question 22

SCENARIO 13-3
The director of cooperative education at a state college wants to examine the effect of cooperative
education job experience on marketability in the work place. She takes a random sample of 4
students. For these 4, 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.
Referring to Scenario 13-3, suppose the director of cooperative education wants to construct a
95% confidence interval estimate for the mean number of job offers received by students who
have had exactly one cooperative education job. The confidence interval is from ________ to
________.

Question 23

SCENARIO 13-3
The director of cooperative education at a state college wants to examine the effect of cooperative
education job experience on marketability in the work place. She takes a random sample of 4
students. For these 4, 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. $$\begin{array} { c c l } \text { Student } & \text { CoopJobs } & \text { JobOffer } \\1 & 1 & 4 \\2 & 2 & 6 \\3 & 1 & 3 \\4 & 0 & 1\end{array}$$

-Referring to Scenario 13-3, suppose the director of cooperative education wants to
construct both a 95% confidence interval estimate and a 95% prediction interval for X = 2. The
confidence interval estimate would be the wider of the two intervals.

Question 24

SCENARIO 13-3
The director of cooperative education at a state college wants to examine the effect of cooperative
education job experience on marketability in the work place. She takes a random sample of 4
students. For these 4, 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.
Referring to Scenario 13-3, the prediction for the number of job offers for a person with 2 coop
jobs is __________.

Question 25

SCENARIO 13-3
The director of cooperative education at a state college wants to examine the effect of cooperative
education job experience on marketability in the work place. She takes a random sample of 4
students. For these 4, 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.
Referring to Scenario 13-3, the standard error of estimate is __________.

Question 26

SCENARIO 13-3
The director of cooperative education at a state college wants to examine the effect of cooperative
education job experience on marketability in the work place. She takes a random sample of 4
students. For these 4, 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.
Referring to Scenario 13-3, the coefficient of correlation is __________.

Question 27

SCENARIO 13-3
The director of cooperative education at a state college wants to examine the effect of cooperative
education job experience on marketability in the work place. She takes a random sample of 4
students. For these 4, 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.
Referring to Scenario 13-3, the regression sum of squares (SSR) is __________.

Question 28

SCENARIO 13-3
The director of cooperative education at a state college wants to examine the effect of cooperative
education job experience on marketability in the work place. She takes a random sample of 4
students. For these 4, 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.
Referring to Scenario 13-3, the director of cooperative education wanted to test the hypothesis
that the population slope was equal to 0. The value of the test statistic is ________.

Question 29

SCENARIO 13-3
The director of cooperative education at a state college wants to examine the effect of cooperative
education job experience on marketability in the work place. She takes a random sample of 4
students. For these 4, 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.
Referring to Scenario 13-3, the error or residual sum of squares (SSE) is __________.

Question 30

SCENARIO 13-3
The director of cooperative education at a state college wants to examine the effect of cooperative
education job experience on marketability in the work place. She takes a random sample of 4
students. For these 4, 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.
Referring to Scenario 13-3, the least squares estimate of the slope is __________.

Question 31

SCENARIO 13-3
The director of cooperative education at a state college wants to examine the effect of cooperative
education job experience on marketability in the work place. She takes a random sample of 4
students. For these 4, 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.
Referring to Scenario 13-3, the director of cooperative education wanted to test the hypothesis
that the population slope was equal to 3.0. The value of the test statistic is ________.

Question 32

SCENARIO 13-3
The director of cooperative education at a state college wants to examine the effect of cooperative
education job experience on marketability in the work place. She takes a random sample of 4
students. For these 4, 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. $$\begin{array} { c c l } \text { Student } & \text { CoopJobs } & \text { JobOffer } \\1 & 1 & 4 \\2 & 2 & 6 \\3 & 1 & 3 \\4 & 0 & 1\end{array}$$

-Referring to Scenario 13-3, suppose the director of cooperative education wants to
construct two 95% confidence interval estimates. One is for the mean number of job offers
received by students who have had exactly one cooperative education job and one for students
who have had two. The confidence interval for students who have had one cooperative education
job would be the wider of the two intervals.

Question 33

SCENARIO 13-3
The director of cooperative education at a state college wants to examine the effect of cooperative
education job experience on marketability in the work place. She takes a random sample of 4
students. For these 4, 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.
Referring to Scenario 13-3, set up a scatter plot.

Question 34

SCENARIO 13-3
The director of cooperative education at a state college wants to examine the effect of cooperative
education job experience on marketability in the work place. She takes a random sample of 4
students. For these 4, 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.
Referring to Scenario 13-3, the total sum of squares (SST) is __________.

Question 35

SCENARIO 13-3
The director of cooperative education at a state college wants to examine the effect of cooperative
education job experience on marketability in the work place. She takes a random sample of 4
students. For these 4, 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.
Referring to Scenario 13-3, the least squares estimate of the Y-intercept is __________.

Question 36

SCENARIO 13-3
The director of cooperative education at a state college wants to examine the effect of cooperative
education job experience on marketability in the work place. She takes a random sample of 4
students. For these 4, 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.
Referring to Scenario 13-3, the coefficient of determination is __________.

Question 37

SCENARIO 13-3
The director of cooperative education at a state college wants to examine the effect of cooperative
education job experience on marketability in the work place. She takes a random sample of 4
students. For these 4, 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.
Referring to Scenario 13-3, suppose the director of cooperative education wants to construct a
95% confidence-interval estimate for the mean number of job offers received by students who
have had exactly one cooperative education job. The t critical value she would use is ________.

Question 38

SCENARIO 13-3
The director of cooperative education at a state college wants to examine the effect of cooperative
education job experience on marketability in the work place. She takes a random sample of 4
students. For these 4, 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.
Referring to Scenario 13-3, suppose the director of cooperative education wants to construct a
95% prediction interval for the number of job offers received by a student who has had exactly
two cooperative education jobs. The prediction interval is from ________ to ________.

Question 39

SCENARIO 13-3
The director of cooperative education at a state college wants to examine the effect of cooperative
education job experience on marketability in the work place. She takes a random sample of 4
students. For these 4, 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.
Referring to Scenario 13-3, the director of cooperative education wanted to test the hypothesis
that the population slope was equal to 0. The denominator of the test statistic is sb1 . The value of
sb1 in this sample is ________.

Question 40

SCENARIO 13-3
The director of cooperative education at a state college wants to examine the effect of cooperative
education job experience on marketability in the work place. She takes a random sample of 4
students. For these 4, 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.
Referring to Scenario 13-3, suppose the director of cooperative education wants to construct a
95% prediction interval estimate for the number of job offers received by students who have had
exactly one cooperative education job. The prediction interval is from ________ to ________.

Question 41

EXPLANATION: The t-test statistic is KEYWORDS: t test on slope, p-value, slope
SCENARIO 13-4
The managers of a brokerage firm are interested in finding out if the number of new clients a broker
brings into the firm affects the sales generated by the broker. They sample 12 brokers and determine
the number of new clients they have enrolled in the last year and their sales amounts in thousands of
dollars. These data are presented in the table that follows.
Referring to Scenario 13-4, the standard error of estimate is __________.

Question 42

EXPLANATION: The t-test statistic is KEYWORDS: t test on slope, p-value, slope
SCENARIO 13-4
The managers of a brokerage firm are interested in finding out if the number of new clients a broker
brings into the firm affects the sales generated by the broker. They sample 12 brokers and determine
the number of new clients they have enrolled in the last year and their sales amounts in thousands of
dollars. These data are presented in the table that follows.
Referring to Scenario 13-4, the standard error of the estimated slope coefficient is __________.

Question 43

SCENARIO 13-3
The director of cooperative education at a state college wants to examine the effect of cooperative
education job experience on marketability in the work place. She takes a random sample of 4
students. For these 4, 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.
Referring to Scenario 13-3, the director of cooperative education wanted to test the hypothesis
that the population slope was equal to 0. The p-value of the test is between ________ and
________.

Question 44

EXPLANATION: The t-test statistic is KEYWORDS: t test on slope, p-value, slope
SCENARIO 13-4
The managers of a brokerage firm are interested in finding out if the number of new clients a broker
brings into the firm affects the sales generated by the broker. They sample 12 brokers and determine
the number of new clients they have enrolled in the last year and their sales amounts in thousands of
dollars. These data are presented in the table that follows.
Referring to Scenario 13-4, the error or residual sum of squares (SSE) is __________.

Question 45

EXPLANATION: The t-test statistic is KEYWORDS: t test on slope, p-value, slope
SCENARIO 13-4
The managers of a brokerage firm are interested in finding out if the number of new clients a broker
brings into the firm affects the sales generated by the broker. They sample 12 brokers and determine
the number of new clients they have enrolled in the last year and their sales amounts in thousands of
dollars. These data are presented in the table that follows.
Referring to Scenario 13-4, the coefficient of correlation is __________.

Question 46

EXPLANATION: The t-test statistic is KEYWORDS: t test on slope, p-value, slope
SCENARIO 13-4
The managers of a brokerage firm are interested in finding out if the number of new clients a broker
brings into the firm affects the sales generated by the broker. They sample 12 brokers and determine
the number of new clients they have enrolled in the last year and their sales amounts in thousands of
dollars. These data are presented in the table that follows.
Referring to Scenario 13-4, suppose the managers of the brokerage firm want to construct a 99%
confidence interval estimate for the mean sales made by brokers who have brought into the firm
24 new clients. The t critical value they would use is ________.

Question 47

EXPLANATION: The t-test statistic is KEYWORDS: t test on slope, p-value, slope
SCENARIO 13-4
The managers of a brokerage firm are interested in finding out if the number of new clients a broker
brings into the firm affects the sales generated by the broker. They sample 12 brokers and determine
the number of new clients they have enrolled in the last year and their sales amounts in thousands of
dollars. These data are presented in the table that follows.
Referring to Scenario 13-4, ______% of the total variation in sales generated can be explained by
the number of new clients brought in.

Question 48

EXPLANATION: The t-test statistic is KEYWORDS: t test on slope, p-value, slope
SCENARIO 13-4
The managers of a brokerage firm are interested in finding out if the number of new clients a broker
brings into the firm affects the sales generated by the broker. They sample 12 brokers and determine
the number of new clients they have enrolled in the last year and their sales amounts in thousands of
dollars. These data are presented in the table that follows.
Referring to Scenario 13-4, the coefficient of determination is __________.

Question 49

SCENARIO 13-3
The director of cooperative education at a state college wants to examine the effect of cooperative
education job experience on marketability in the work place. She takes a random sample of 4
students. For these 4, 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.
Referring to Scenario 13-3, the director of cooperative education wanted to test the hypothesis
that the population slope was equal to 3.0. For a test with a level of significance of 0.05, the null
hypothesis should be rejected if the value of the test statistic is ________.

Question 50

EXPLANATION: The t-test statistic is KEYWORDS: t test on slope, p-value, slope
SCENARIO 13-4
The managers of a brokerage firm are interested in finding out if the number of new clients a broker
brings into the firm affects the sales generated by the broker. They sample 12 brokers and determine
the number of new clients they have enrolled in the last year and their sales amounts in thousands of
dollars. These data are presented in the table that follows.
Referring to Scenario 13-4, the regression sum of squares (SSR) is __________.

Question 51

EXPLANATION: The t-test statistic is KEYWORDS: t test on slope, p-value, slope
SCENARIO 13-4
The managers of a brokerage firm are interested in finding out if the number of new clients a broker
brings into the firm affects the sales generated by the broker. They sample 12 brokers and determine
the number of new clients they have enrolled in the last year and their sales amounts in thousands of
dollars. These data are presented in the table that follows.
Referring to Scenario 13-4, the least squares estimate of the Y-intercept is __________.

Question 52

EXPLANATION: The t-test statistic is KEYWORDS: t test on slope, p-value, slope
SCENARIO 13-4
The managers of a brokerage firm are interested in finding out if the number of new clients a broker
brings into the firm affects the sales generated by the broker. They sample 12 brokers and determine
the number of new clients they have enrolled in the last year and their sales amounts in thousands of
dollars. These data are presented in the table that follows.
Referring to Scenario 13-4, the least squares estimate of the slope is __________.

Question 53

SCENARIO 13-3
The director of cooperative education at a state college wants to examine the effect of cooperative
education job experience on marketability in the work place. She takes a random sample of 4
students. For these 4, 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.
Referring to Scenario 13-3, the director of cooperative education wanted to test the hypothesis
that the population slope was equal to 0. For a test with a level of significance of 0.05, the null
hypothesis should be rejected if the value of the test statistic is ________.

Question 54

EXPLANATION: The t-test statistic is KEYWORDS: t test on slope, p-value, slope
SCENARIO 13-4
The managers of a brokerage firm are interested in finding out if the number of new clients a broker
brings into the firm affects the sales generated by the broker. They sample 12 brokers and determine
the number of new clients they have enrolled in the last year and their sales amounts in thousands of
dollars. These data are presented in the table that follows.
Referring to Scenario 13-4, suppose the managers of the brokerage firm want to construct a 99%
prediction interval for the sales made by a broker who has brought into the firm 18 new clients.
The prediction interval is from ________ to ________.

Question 55

EXPLANATION: The t-test statistic is KEYWORDS: t test on slope, p-value, slope
SCENARIO 13-4
The managers of a brokerage firm are interested in finding out if the number of new clients a broker
brings into the firm affects the sales generated by the broker. They sample 12 brokers and determine
the number of new clients they have enrolled in the last year and their sales amounts in thousands of
dollars. These data are presented in the table that follows.
Referring to Scenario 13-4, suppose the managers of the brokerage firm want to construct n a
99% prediction interval for the sales made by a broker who has brought into the firm 18 new
clients. The t critical value they would use is ________.

Question 56

SCENARIO 13-3
The director of cooperative education at a state college wants to examine the effect of cooperative
education job experience on marketability in the work place. She takes a random sample of 4
students. For these 4, 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.
Referring to Scenario 13-3, the director of cooperative education wanted to test the hypothesis
that the population slope was equal to 3.0. The p-value of the test is between ________ and
________.

Question 57

EXPLANATION: The t-test statistic is KEYWORDS: t test on slope, p-value, slope
SCENARIO 13-4
The managers of a brokerage firm are interested in finding out if the number of new clients a broker
brings into the firm affects the sales generated by the broker. They sample 12 brokers and determine
the number of new clients they have enrolled in the last year and their sales amounts in thousands of
dollars. These data are presented in the table that follows.
Referring to Scenario 13-4, the total sum of squares (SST) is __________.

Question 58

EXPLANATION: The t-test statistic is KEYWORDS: t test on slope, p-value, slope
SCENARIO 13-4
The managers of a brokerage firm are interested in finding out if the number of new clients a broker
brings into the firm affects the sales generated by the broker. They sample 12 brokers and determine
the number of new clients they have enrolled in the last year and their sales amounts in thousands of
dollars. These data are presented in the table that follows.
Referring to Scenario 13-4, suppose the managers of the brokerage firm want to construct a 99%
confidence interval estimate for the mean sales made by brokers who have brought into the firm
24 new clients. The confidence interval is from ________ to ________.

Question 59

EXPLANATION: The t-test statistic is KEYWORDS: t test on slope, p-value, slope
SCENARIO 13-4
The managers of a brokerage firm are interested in finding out if the number of new clients a broker
brings into the firm affects the sales generated by the broker. They sample 12 brokers and determine
the number of new clients they have enrolled in the last year and their sales amounts in thousands of
dollars. These data are presented in the table that follows.
Referring to Scenario 13-4, set up a scatter plot.

Question 60

EXPLANATION: The t-test statistic is KEYWORDS: t test on slope, p-value, slope
SCENARIO 13-4
The managers of a brokerage firm are interested in finding out if the number of new clients a broker
brings into the firm affects the sales generated by the broker. They sample 12 brokers and determine
the number of new clients they have enrolled in the last year and their sales amounts in thousands of
dollars. These data are presented in the table that follows.
Referring to Scenario 13-4, the prediction for the amount of sales (in $1,000s) for a person who
brings 25 new clients into the firm is ________.

Question 61

SCENARIO 13-5
The managing partner of an advertising agency believes that his company's sales are related to the
industry sales. He uses Microsoft Excel to analyze the last 4 years of quarterly data with
the following results:
Referring to Scenario 13-5, the prediction for a quarter in which X = 120 is Y = ________.

Question 62

EXPLANATION: The t-test statistic is KEYWORDS: t test on slope, p-value, slope
SCENARIO 13-4
The managers of a brokerage firm are interested in finding out if the number of new clients a broker
brings into the firm affects the sales generated by the broker. They sample 12 brokers and determine
the number of new clients they have enrolled in the last year and their sales amounts in thousands of
dollars. These data are presented in the table that follows.
Referring to Scenario 13-4, the managers of the brokerage firm wanted to test the hypothesis that
the number of new clients brought in had a positive impact on the amount of sales generated. For
a test with a level of significance of 0.01, the null hypothesis should be rejected if the value of the
test statistic is ________.

Question 63

EXPLANATION: The t-test statistic is KEYWORDS: t test on slope, p-value, slope
SCENARIO 13-4
The managers of a brokerage firm are interested in finding out if the number of new clients a broker
brings into the firm affects the sales generated by the broker. They sample 12 brokers and determine
the number of new clients they have enrolled in the last year and their sales amounts in thousands of
dollars. These data are presented in the table that follows.
Referring to Scenario 13-4, the managers of the brokerage firm wanted to test the hypothesis that
the population slope was equal to 0. At a level of significance of 0.01, the decision that should be
made implies that _____ (there is a or there is no) linear dependent relationship between the
independent and dependent variables.

Question 64

SCENARIO 13-5
The managing partner of an advertising agency believes that his company's sales are related to the
industry sales. He uses Microsoft Excel to analyze the last 4 years of quarterly data with
the following results:
Referring to Scenario 13-5, the correlation coefficient is ________.

Question 65

EXPLANATION: The t-test statistic is KEYWORDS: t test on slope, p-value, slope
SCENARIO 13-4
The managers of a brokerage firm are interested in finding out if the number of new clients a broker
brings into the firm affects the sales generated by the broker. They sample 12 brokers and determine
the number of new clients they have enrolled in the last year and their sales amounts in thousands of
dollars. These data are presented in the table that follows.
Referring to Scenario 13-4, the managers of the brokerage firm wanted to test the hypothesis that
the population slope was equal to 0. At a level of significance of 0.01, the null hypothesis should
be _______ (rejected or not rejected).

Question 66

EXPLANATION: The t-test statistic is KEYWORDS: t test on slope, p-value, slope
SCENARIO 13-4
The managers of a brokerage firm are interested in finding out if the number of new clients a broker
brings into the firm affects the sales generated by the broker. They sample 12 brokers and determine
the number of new clients they have enrolled in the last year and their sales amounts in thousands of
dollars. These data are presented in the table that follows.
Referring to Scenario 13-4, the managers of the brokerage firm wanted to test the hypothesis that
the population slope was equal to 0. The p-value of the test is ________.

Question 67

EXPLANATION: The t-test statistic is KEYWORDS: t test on slope, p-value, slope
SCENARIO 13-4
The managers of a brokerage firm are interested in finding out if the number of new clients a broker
brings into the firm affects the sales generated by the broker. They sample 12 brokers and determine
the number of new clients they have enrolled in the last year and their sales amounts in thousands of
dollars. These data are presented in the table that follows.
Referring to Scenario 13-4, the managers of the brokerage firm wanted to test the hypothesis that
the number of new clients brought in had a positive impact on the amount of sales generated. The
value of the test statistic is _______.

Question 68

SCENARIO 13-5
The managing partner of an advertising agency believes that his company's sales are related to the
industry sales. He uses Microsoft Excel to analyze the last 4 years of quarterly data with
the following results:
Referring to Scenario 13-5, the standard error of the estimate is ________.

Question 69

SCENARIO 13-5
The managing partner of an advertising agency believes that his company's sales are related to the
industry sales. He uses Microsoft Excel to analyze the last 4 years of quarterly data with
the following results:
Referring to Scenario 13-5, the standard error of the estimated slope coefficient is ________.

Question 70

EXPLANATION: The t-test statistic is KEYWORDS: t test on slope, p-value, slope
SCENARIO 13-4
The managers of a brokerage firm are interested in finding out if the number of new clients a broker
brings into the firm affects the sales generated by the broker. They sample 12 brokers and determine
the number of new clients they have enrolled in the last year and their sales amounts in thousands of
dollars. These data are presented in the table that follows.
Referring to Scenario 13-4, the managers of the brokerage firm wanted to test the hypothesis that
the population slope was equal to 0. For a test with a level of significance of 0.01, the null
hypothesis should be rejected if the value of the test statistic is ________.

Question 71

EXPLANATION: The t-test statistic is KEYWORDS: t test on slope, p-value, slope
SCENARIO 13-4
The managers of a brokerage firm are interested in finding out if the number of new clients a broker
brings into the firm affects the sales generated by the broker. They sample 12 brokers and determine
the number of new clients they have enrolled in the last year and their sales amounts in thousands of
dollars. These data are presented in the table that follows.
Referring to Scenario 13-4, the managers of the brokerage firm wanted to test the hypothesis that
the population slope was equal to 0. The denominator of the test statistic is sb1 . The value of sb1
in this sample is ________.

Question 72

EXPLANATION: The t-test statistic is KEYWORDS: t test on slope, p-value, slope
SCENARIO 13-4
The managers of a brokerage firm are interested in finding out if the number of new clients a broker
brings into the firm affects the sales generated by the broker. They sample 12 brokers and determine
the number of new clients they have enrolled in the last year and their sales amounts in thousands of
dollars. These data are presented in the table that follows.
Referring to Scenario 13-4, the managers of the brokerage firm wanted to test the hypothesis that
the number of new clients brought in had a positive impact on the amount of sales generated. At a
level of significance of 0.01, the decision that should be made implies that the number of new
clients brought in _____ (had or did not have) a positive impact on the amount of sales
generated.

Question 73

EXPLANATION: The t-test statistic is KEYWORDS: t test on slope, p-value, slope
SCENARIO 13-4
The managers of a brokerage firm are interested in finding out if the number of new clients a broker
brings into the firm affects the sales generated by the broker. They sample 12 brokers and determine
the number of new clients they have enrolled in the last year and their sales amounts in thousands of
dollars. These data are presented in the table that follows.
Referring to Scenario 13-4, the managers of the brokerage firm wanted to test the hypothesis that
the number of new clients brought in had a positive impact on the amount of sales generated. At a
level of significance of 0.01, the null hypothesis should be _______ (rejected or not rejected).

Question 74

EXPLANATION: The t-test statistic is KEYWORDS: t test on slope, p-value, slope
SCENARIO 13-4
The managers of a brokerage firm are interested in finding out if the number of new clients a broker
brings into the firm affects the sales generated by the broker. They sample 12 brokers and determine
the number of new clients they have enrolled in the last year and their sales amounts in thousands of
dollars. These data are presented in the table that follows.
Referring to Scenario 13-4, the managers of the brokerage firm wanted to test the hypothesis that
the number of new clients brought in did not affect the amount of sales generated. The value of
the test statistic is _______.

Question 75

EXPLANATION: The t-test statistic is KEYWORDS: t test on slope, p-value, slope
SCENARIO 13-4
The managers of a brokerage firm are interested in finding out if the number of new clients a broker
brings into the firm affects the sales generated by the broker. They sample 12 brokers and determine
the number of new clients they have enrolled in the last year and their sales amounts in thousands of
dollars. These data are presented in the table that follows.
Referring to Scenario 13-4, the managers of the brokerage firm wanted to test the hypothesis that
the number of new clients brought in had a positive impact on the amount of sales generated. The
p-value of the test is ________.

Question 76

EXPLANATION: The t-test statistic is KEYWORDS: t test on slope, p-value, slope
SCENARIO 13-4
The managers of a brokerage firm are interested in finding out if the number of new clients a broker
brings into the firm affects the sales generated by the broker. They sample 12 brokers and determine
the number of new clients they have enrolled in the last year and their sales amounts in thousands of
dollars. These data are presented in the table that follows.
Referring to Scenario 13-4, suppose the managers of the brokerage firm want to construct both a
99% confidence interval estimate and a 99% prediction interval for X = 24. The confidence
interval estimate would be the __________ (wider or narrower) of the two intervals.

Question 77

SCENARIO 13-5
The managing partner of an advertising agency believes that his company's sales are related to the
industry sales. He uses Microsoft Excel to analyze the last 4 years of quarterly data with
the following results:
Referring to Scenario 13-5, the value of the quantity that the least squares regression line
minimizes is ________.

Question 78

SCENARIO 13-5
The managing partner of an advertising agency believes that his company's sales are related to the
industry sales. He uses Microsoft Excel to analyze the last 4 years of quarterly data with
the following results:
Referring to Scenario 13-5, the coefficient of determination is ________.

Question 79

EXPLANATION: The t-test statistic is KEYWORDS: t test on slope, p-value, slope
SCENARIO 13-4
The managers of a brokerage firm are interested in finding out if the number of new clients a broker
brings into the firm affects the sales generated by the broker. They sample 12 brokers and determine
the number of new clients they have enrolled in the last year and their sales amounts in thousands of
dollars. These data are presented in the table that follows.
Referring to Scenario 13-4, the managers of the brokerage firm wanted to test the hypothesis that
the population slope was equal to 0. The value of the test statistic is _______.

Question 80

SCENARIO 13-5
The managing partner of an advertising agency believes that his company's sales are related to the
industry sales. He uses Microsoft Excel to analyze the last 4 years of quarterly data with
the following results:
Referring to Scenario 13-5, the estimates of the Y-intercept and slope are ________ and
________, respectively.