Deck 11: Simple Linear Regression

Question 1

Answer 1

Question 2

Consider the data set shown below. Find the estimate of the slope of the least squares regression line.

A)0.94643
B)0.9003
C)1.49045
D)1.5

Answer 2

A

Question 3

Plot the line y = 4 - 2x. Then give the slope and y-intercept of the line.

Answer 3

Question 4

In a comprehensive road test for new car models, one variable measured is the time it
takes the car to accelerate from 0 to 60 miles per hour. To model acceleration time, a
regression analysis is conducted on a random sample of 129 new cars.

Question 5

The probabilistic model allows the E(y)values to fall around the regression line while the actual
values of y must fall on the line.

Question 6

(4, 3)and (6, 9)

Question 7

To investigate the relationship between yield of potatoes, y, and level of fertilizer
application, x, a researcher divides a field into eight plots of equal size and applies
differing amounts of fertilizer to each. The yield of potatoes (in pounds)and the fertilizer
application (in pounds)are recorded for each plot. The data are as follows:

Question 8

Consider the following pairs of measurements:

Question 9

Consider the data set shown below. Find the estimate of the y-intercept of the least squares regression line.

A)0.9003
B)0.94643
C)1.49045
D)1.5

Question 10

a. Complete the table.

Question 11

Plot the line y = 3x. Then give the slope and y-intercept of the line.

Question 12

A county real estate appraiser wants to develop a statistical model to predict the appraised value of houses in a section of the county called East Meadow. One of the many variables thought to be
An important predictor of appraised value is the number of rooms in the house. Consequently, the
Appraiser decided to fit the linear regression model:

Question 13

Is there a relationship between the raises administrators at County University receive and their performance on the job?

Question 14

(0, 3)and (3, 0)

Question 15

Is the number of games won by a major league baseball team in a season related to the
teamʹs batting average? Data from 14 teams were collected and the summary statistics
yield: Find the least squares prediction equation for predicting the number of games won, y,
using a straight-line relationship with the teamʹs batting average, x.

Question 16

Plot the line y = 1.5 + .5x. Then give the slope and y-intercept of the line.

Question 17

(2, -6)and (-1, 3)

Question 18

In a study of feeding behavior, zoologists recorded the number of grunts of a warthog
feeding by a lake in the 15 minute period following the addition of food. The data showing
the number of grunts and and the age of the warthog (in days)are listed below:

Question 19

(-9, 0)and (-4, -1)

Question 20

(-6, -6)and (3, 3)

Question 21

What is the relationship between diamond price and carat size? 307 diamonds were sampled and a straight-line relationship was hypothesized between y = diamond price (in dollars)and x = size of
The diamond (in carats). The simple linear regression for the analysis is shown below:

Question 22

A county real estate appraiser wants to develop a statistical model to predict the appraised value of houses in a section of the county called East Meadow. One of the many variables thought to be
An important predictor of appraised value is the number of rooms in the house. Consequently, the
Appraiser decided to fit the simple linear regression model:

Question 23

The Method of Least Squares specifies that the regression line has an average error of 0 and has an
SSE that is minimized.

Question 24

If a least squares line were determined for the data set in each scattergram, which would have the smallest variance?

Question 25

Question 26

A county real estate appraiser wants to develop a statistical model to predict the appraised value of houses in a section of the county called East Meadow. One of the many variables thought to be
An important predictor of appraised value is the number of rooms in the house. Consequently, the
Appraiser decided to fit the simple linear regression model:

Question 27

Suppose you fit a least squares line to 20 data points and the calculated value of SSE is
0.476.

Question 28

A large national bank charges local companies for using its services. A bank official reported the results of a regression analysis designed to predict the bankʹs charges (y), measured in dollars per
Month, for services rendered to local companies. One independent variable used to predict the
Service charge to a company is the companyʹs sales revenue (x), measured in $ million. Data for 21
Companies who use the bankʹs services were used to fit the model

Question 29

An academic advisor wants to predict the typical starting salary of a graduate at a top business school using the GMAT score of the school as a predictor variable. A simple linear regression of
SALARY versus GMAT was created from a set of 25 data points.
Which of the following is not an assumption required for the simple linear regression analysis to
Be valid?

A)The errors of predicting SALARY are normally distributed.
B)SALARY is independent of GMAT.
C)The errors of predicting SALARY have a mean of 0.
D)The errors of predicting SALARY have a variance that is constant for any given value of GMAT.

Question 30

State the four basic assumptions about the general form of the probability distribution of
the random error ε.

Question 31

Is there a relationship between the raises administrators at State University receive and their performance on the job?

Question 32

A study of the top 75 MBA programs attempted to predict the average starting salary (in $1000's) of graduates of the program based on the amount of tuition (in $1000's)charged by the program.
The results of a simple linear regression analysis are shown below:

Question 33

Is there a relationship between the raises administrators at State University receive and their performance on the job?

Question 34

What is the relationship between diamond price and carat size? 307 diamonds were sampled and a straight-line relationship was hypothesized between y = diamond price (in dollars)and x = size of
The diamond (in carats). The simple linear regression for the analysis is shown below:

Question 35

A county real estate appraiser wants to develop a statistical model to predict the appraised value of houses in a section of the county called East Meadow. One of the many variables thought to be
An important predictor of appraised value is the number of rooms in the house. Consequently, the
Appraiser decided to fit the simple linear regression model:

Question 36

Consider the data set shown below. Find the standard deviation of the least squares regression line.

Question 37

Question 38

Suppose you fit a least squares line to 22 data points and the calculated value of SSE is
.678.

Question 39

What is the relationship between diamond price and carat size? 307 diamonds were sampled (ranging in size from 0.18 to 1.1 carats)and a straight-line relationship was hypothesized between
Y = diamond price (in dollars)and x = size of the diamond (in carats). The simple linear regression
For the analysis is shown below:

Question 40

A company keeps extensive records on its new salespeople on the premise that sales
should increase with experience. A random sample of seven new salespeople produced
the data on experience and sales shown in the table.

Question 41

The data for n = 25 points were subjected to a simple linear regression with the results:

Question 42

An academic advisor wants to predict the typical starting salary of a graduate at a top business school using the GMAT score of the school as a predictor variable. A simple linear regression of
SALARY versus GMAT using 25 data points is shown below.

Question 43

What is the relationship between diamond price and carat size? 307 diamonds were sampled and a straight-line relationship was hypothesized between y = diamond price (in dollars)and x = size of
The diamond (in carats). The simple linear regression for the analysis is shown below:

Question 44

Consider the following pairs of measurements:

Question 45

A county real estate appraiser wants to develop a statistical model to predict the appraised value of houses in a section of the county called East Meadow. One of the many variables thought to be
An important predictor of appraised value is the number of rooms in the house. Consequently, the
Appraiser decided to fit the simple linear regression model:

Question 46

Question 47

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 bankʹs 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 companyʹs sales revenue (x), measured in $ million. Data for 21
Companies who use the bankʹs services were used to fit the model

Question 48

The dean of the Business School at a small Florida college wishes to determine whether the grade-point average (GPA)of a graduating student can be used to predict the graduateʹs starting
Salary. More specifically, the dean wants to know whether higher GPAs lead to higher starting
Salaries. Records for 23 of last yearʹs Business School graduates are selected at random, and data
On GPA (x)and starting salary (y, in $thousands)for each graduate were used to fit the model

Question 49

A manufacturer of boiler drums wants to use regression to predict the number of man-hours needed to erect drums in the future. The manufacturer collected a random sample of 35 boilers
And measured the following two variables:

Question 50

Is the number of games won by a major league baseball team in a season related to the
teamʹs batting average? Data from 14 teams were collected and the summary statistics
yield:

Question 51

Question 52

In a comprehensive road test on new car models, one variable measured is the time it takes a car to accelerate from 0 to 60 miles per hour. To model acceleration time, a regression analysis is
Conducted on a random sample of 129 new cars.

Question 53

Question 54

A breeder of Thoroughbred horses wishes to model the relationship between the gestation
period and the length of life of a horse. The breeder believes that the two variables may
follow a linear trend. The information in the table was supplied to the breeder from
various thoroughbred stables across the state.

Question 55

Consider the data set shown below. Find the 95% confidence interval for the slope of the regression line.

Question 56

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 bankʹs 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 companyʹs sales revenue (x), measured in $ million. Data for 21
Companies who use the bankʹs services were used to fit the model

Question 57

In a study of feeding behavior, zoologists recorded the number of grunts of a warthog
feeding by a lake in the 15 minute period following the addition of food. The data showing
the number of grunts and the age of the warthog (in days)are listed below:

Question 58

A county real estate appraiser wants to develop a statistical model to predict the appraised value of houses in a section of the county called East Meadow. One of the many variables thought to be
An important predictor of appraised value is the number of rooms in the house. Consequently, the
Appraiser decided to fit the simple linear regression model:

Question 59

Question 60

The dean of the Business School at a small Florida college wishes to determine whether the grade-point average (GPA)of a graduating student can be used to predict the graduateʹs starting
Salary. More specifically, the dean wants to know whether higher GPAs lead to higher starting
Salaries. Records for 23 of last yearʹs Business School graduates are selected at random, and data
On GPA (x)and starting salary (y, in $thousands)for each graduate were used to fit the model

Question 61

To investigate the relationship between yield of potatoes, y, and level of fertilizer
application, x, a researcher divides a field into eight plots of equal size and applies
differing amounts of fertilizer to each. The yield of potatoes (in pounds)and the fertilizer
application (in pounds)are recorded for each plot. The data are as follows:

Question 62

Question 63

In team-teaching, two or more teachers lead a class. An researcher tested the use of
team-teaching in mathematics education. Two of the variables measured on each sample
of 165 mathematics teachers were years of teaching experience x and reported success rate
y (measured as a percentage)of team-teaching mathematics classes.
a. The researcher hypothesized that mathematics teachers with more years of experience
will report higher perceived success rates in team-taught classes.
State this hypothesis in terms of the parameter of a linear model relating x to y.
b. The correlation coefficient for the sample data was reported as r = -0.31.
Interpret this result.
c. Does the value of r support the hypothesis? Test using α = .05.

Question 64

The coefficient of correlation is a useful measure of the linear relationship between two variables.

Question 65

Consider the data set shown below. Find the coefficient of correlation for between the variables x and y.

A)0.9003
B)0.9383
C)0.8804
D)0.9489

Question 66

A low value of the correlation coefficient r implies that x and y are unrelated.

Question 67

A study of the top 75 MBA programs attempted to predict the average starting salary (in $1000's) of graduates of the program based on the amount of tuition (in $1000's)charged by the program.
The results of a simple linear regression analysis are shown below:

Question 68

Consider the following pairs of observations: Find and interpret the value of the coefficient of correlation.

Question 69

A high value of the correlation coefficient r implies that a causal relationship exists between x and
y.

Question 70

In a study of feeding behavior, zoologists recorded the number of grunts of a warthog
feeding by a lake in the 15 minute period following the addition of food. The data showing
the number of grunts and and the age of the warthog (in days)are listed below: Find and interpret the value of r.

Question 71

A breeder of Thoroughbred horses wishes to model the relationship between the gestation
period and the length of life of a horse. The breeder believes that the two variables may
follow a linear trend. The information in the table was supplied to the breeder from
various thoroughbred stables across the state.

Question 72

In team-teaching, two or more teachers lead a class. A researcher tested the use of 74)
team-teaching in mathematics education. Two of the variables measured on each teacher
in a sample of 159 mathematics teachers were years of teaching experience x and reported
success rate y (measured as a percentage)of team-teaching mathematics classes.
The correlation coefficient for the sample data was reported as r = -0.3. Interpret this
result.

Question 73

A study of the top 75 MBA programs attempted to predict the average starting salary (in $1000's) of graduates of the program based on the amount of tuition (in $1000's)charged by the program.
The results of a simple linear regression analysis are shown below:

Question 74

Operations managers often use work sampling to estimate how much time workers spend
on each operation. Work samplingwhich involves observing workers at random points
in timewas applied to the staff of the catalog sales department of a clothing
manufacturer. The department applied regression to data collected for 40 randomly
selected working days.

Question 75

Consider the following pairs of observations:

Question 76

Is the number of games won by a major league baseball team in a season related to the
teamʹs batting average? Data from 14 teams were collected and the summary statistics
yield:

Question 77

An academic advisor wants to predict the typical starting salary of a graduate at a top business school using the GMAT score of the school as a predictor variable. A simple linear regression of
SALARY versus GMAT using 25 data points is shown below.

Question 78

A realtor collected the following data for a random sample of ten homes that recently sold
in her area. a. Construct a scattergram for the data.
b. Find the least squares line for the data and plot the line on your scattergram.
c. Test whether the number of days on the market, y, is positively linearly related to the

Question 79

A study of the top 75 MBA programs attempted to predict the average starting salary (in $1000's) of graduates of the program based on the amount of tuition (in $1000's)charged by the program.
We are told that the coefficient of correlation was calculated to be r = 0.7763. Use this information
To calculate the test statistic that would be used to determine if a positive linear relationship exists
Between the two variables.

A)t = 0.6027
B)t = 10.52
C)t = 1.475
D)t = 1.760

Question 80

What is the relationship between diamond price and carat size? 307 diamonds were sampled and a straight-line relationship was hypothesized between y = diamond price (in dollars)and x = size of
The diamond (in carats). The simple linear regression for the analysis is shown below: