Question 1

Truck Speed and Gas Mileage
 An economist wanted to analyze the relationship between the speed of a truck (x)and its gas mileage (y).As an experiment a truck is operated at several different speeds and for each speed the gas mileage is measured.These data are shown below.  ​ ​
-{Truck Speed and Gas Mileage Narrative} Calculate the coefficient of determination and interpret its value.

Accepted Answer

The answer of Truck Speed and Gas Mileage
 An economist...

Question 2

The variance of the error variable  is required to be constant.When this requirement is satisfied,the condition is called homoscedasticity.

Accepted Answer

A) True 
 B)False

Question 3

The width of the confidence interval estimate for the predicted value of y depends on

Accepted Answer

A) the standard error of the estimate 
B) the value of x for which the prediction is being made 
C) the sample size 
D) All of these choices are true.

Question 4

In a simple linear regression model b₁ is the ____________________ of the straight line.

Accepted Answer

The answer of In a simple linear regression model b₁...

Question 5

A regression line using 25 observations produced SSR = 118.68 and SSE = 56.32.The standard error of estimate was:

Accepted Answer

A) 2.11 
B) 1.56 
C) 2.44 
D) None of these choices.

Question 6

Movie Revenues
 A financier whose specialty is investing in movie productions has observed that,in general,movies with "big-name" stars seem to generate more revenue than those movies whose stars are less well known.To examine his belief he records the gross revenue and the payment (in $ millions)given to the two highest-paid performers in the movie for ten recently released movies.  ​ ​
-{Movie Revenues Narrative} Predict with 95% confidence the gross revenue of a movie whose top two stars earn $5.0 million.

Accepted Answer

The answer of Movie Revenues
 A financier whose specialty is...

Question 7

Wayne Newton Concert 
At a recent Wayne Newton concert,a survey was conducted that asked a random sample of 20 people their age and how many concerts they have attended since the first of the year.The following data were collected:  An Excel output follows: 
-{Wayne Newton Concert Narrative} Which interval in the previous two questions is narrower: the confidence interval estimate of the expected value of y or the prediction interval for the same given value of x (10 years)and same confidence level? Why?

Accepted Answer

The answer of Wayne Newton Concert 
At a recent Wayne...

Question 8

Consider the following data values of variables x and y.  ​ 
a.Determine the least squares regression line.
b.Find the predicted value of y for x = 9.
c.What does the value of the slope of the regression line tell you?

Accepted Answer

The answer of Consider the following data values of variables...

Question 9

If the coefficient of correlation is −0.81,then the percentage of the variation in y that is explained by the regression line is 81%.

Accepted Answer

A) True 
 B)False

Question 10

Given the least squares regression line  ,and a coefficient of determination of 0.81,the coefficient of correlation is:

Accepted Answer

A) −0.66 
B) 0.81 
C) −0.90 
D) 0.90

Question 11

Truck Speed and Gas Mileage
 An economist wanted to analyze the relationship between the speed of a truck (x)and its gas mileage (y).As an experiment a truck is operated at several different speeds and for each speed the gas mileage is measured.These data are shown below.  ​ ​
-{Truck Speed and Gas Mileage Narrative} Calculate the standard error of estimate,and describe what this statistic tells you about the regression line.

Accepted Answer

The answer of Truck Speed and Gas Mileage
 An economist...

Question 12

Grateful Dead Concert 
At a recent Grateful Dead concert,a survey was conducted that asked a random sample of 20 people their age and how many concerts they have attended since the first of the year.It is suspected that older concert goers tend to go to more of his concerts in one year than younger concert goers.The data and analysis are shown below.  An Excel output follows: 
-{Grateful Dead Concert Narrative} Conduct a test of the population coefficient of correlation to determine at the 5% significance level whether a positive linear relationship exists between age and number of concerts attended.

Accepted Answer

The answer of Grateful Dead Concert 
At a recent Grateful...

Question 13

An outlier is an observation that is unusually small or unusually large.

Accepted Answer

A) True 
 B)False

Question 14

If the variance of the errors is constant for each predicted y value,the condition is called ____________________.

Accepted Answer

The answer of If the variance of the errors is...

Question 15

If the coefficient of correlation is 0.90,then the percentage of the variation in the dependent variable y that is explained by the variation in the independent variable x is:

Accepted Answer

A) 90% 
B) 81% 
C) 95% 
D) None of these choices.

Question 16

Rock Concert Revenues 
A financier whose specialty is investing in rock concerts has observed that,in general,concerts with "big-name" stars seem to generate more revenue than those concerts whose stars are less well known.To examine his belief he records the gross revenue and the payment (in $ millions)given to the two highest-paid performers in the concert for ten concert tours.  ​ ​
-{Rock Concert Revenues Narrative} Determine the coefficient of determination and discuss what its value tells you about the two variables.

Accepted Answer

The answer of Rock Concert Revenues 
A financier whose specialty...

Question 17

Oil Quality and Price
 Quality of oil is measured in API gravity degrees--the higher the degrees API,the higher the quality.The table shown below is produced by an expert in the field who believes that there is a relationship between quality and price per barrel.  A partial Minitab output follows:  ​  ​  ​ 
-{Oil Quality and Price Narrative} Determine the least squares regression line.

Accepted Answer

The answer of Oil Quality and Price
 Quality of oil...

Question 18

The value of the sum of squares for regression SSR can never be smaller than 1.

Accepted Answer

A) True 
 B)False

Question 19

Income and Education
A professor of economics wants to study the relationship between income (y in $1000s)and education (x in years).A random sample eight individuals is taken and the results are shown below.  ​ ​
-{Income and Education Narrative} Interpret the value of the slope of the regression line.

Accepted Answer

The answer of  Income and Education
A professor of economics...

Question 20

In a simple linear regression problem,r and b0:

Accepted Answer

A) must be equal to each other. 
B) must have the same sign. 
C) must have opposite signs. 
D) are not related.

Exam 16: Simple Linear Regression and Correlation

The variance of the error variable is required to be constant.When this requirement is satisfied,the condition is called homoscedasticity.

The width of the confidence interval estimate for the predicted value of y depends on

In a simple linear regression model b₁ is the ____________________ of the straight line.

A regression line using 25 observations produced SSR = 118.68 and SSE = 56.32.The standard error of estimate was:

Consider the following data values of variables x and y. a.Determine the least squares regression line. b.Find the predicted value of y for x = 9. c.What does the value of the slope of the regression line tell you?

If the coefficient of correlation is −0.81,then the percentage of the variation in y that is explained by the regression line is 81%.

Given the least squares regression line ,and a coefficient of determination of 0.81,the coefficient of correlation is:

An outlier is an observation that is unusually small or unusually large.

If the variance of the errors is constant for each predicted y value,the condition is called ____________________.

If the coefficient of correlation is 0.90,then the percentage of the variation in the dependent variable y that is explained by the variation in the independent variable x is:

The value of the sum of squares for regression SSR can never be smaller than 1.

Income and Education A professor of economics wants to study the relationship between income (y in $1000s)and education (x in years).A random sample eight individuals is taken and the results are shown below. -{Income and Education Narrative} Interpret the value of the slope of the regression line.

In a simple linear regression problem,r and b₀:

Exam 16: Simple Linear Regression and Correlation

The variance of the error variable is required to be constant.When this requirement is satisfied,the condition is called homoscedasticity.

The width of the confidence interval estimate for the predicted value of y depends on

In a simple linear regression model b1 is the ____________________ of the straight line.

A regression line using 25 observations produced SSR = 118.68 and SSE = 56.32.The standard error of estimate was:

Consider the following data values of variables x and y. ​ a.Determine the least squares regression line. b.Find the predicted value of y for x = 9. c.What does the value of the slope of the regression line tell you?

If the coefficient of correlation is −0.81,then the percentage of the variation in y that is explained by the regression line is 81%.

Given the least squares regression line ,and a coefficient of determination of 0.81,the coefficient of correlation is:

An outlier is an observation that is unusually small or unusually large.

If the variance of the errors is constant for each predicted y value,the condition is called ____________________.

If the coefficient of correlation is 0.90,then the percentage of the variation in the dependent variable y that is explained by the variation in the independent variable x is:

The value of the sum of squares for regression SSR can never be smaller than 1.

In a simple linear regression problem,r and b0:

In a simple linear regression model b₁ is the ____________________ of the straight line.

Consider the following data values of variables x and y. a.Determine the least squares regression line. b.Find the predicted value of y for x = 9. c.What does the value of the slope of the regression line tell you?

In a simple linear regression problem,r and b₀: