Question 1

In a regression problem the following pairs of (x,y)are given: (3,1),(3,−1),(3,0),(3,−2)and (3,2).That indicates that the:

Accepted Answer

A) correlation coefficient is −1/2. 
B) correlation coefficient is 0. 
C) correlation coefficient is 1. 
D) coefficient of determination is 3. 
A) correlation coefficient is −1/2. 
B) correlation coefficient is 0. 
C) correlation coefficient is 1. 
D) coefficient of determination is 3.

Question 2

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: Descriptive Statistics Variable N Mean StDev SE Mean Degrees 13 34.60 4.613 1.280 Price 13 12.730 0.457 0.127 Covariances Degrees Price Degrees 21.281667 Price 2.026750 0.208833 Regression Analysis Predictor Coef StDev T P Constant 9.4349 0.2867 32.91 0.000 Degrees 0.095235 0.008220 11.59 0.000 S = 0.1314 R−Sq = 92.46% R−Sq(adj)= 91.7% Analysis of Variance Source DF SS MS F P Regression 1 2.3162 2.3162 134.24 0.000 Residual Error 11 0.1898 0.0173 Total 12 2.5060
-{Oil Quality and Price Narrative} Use the residuals to compute the standardized residuals.

Accepted Answer

The standardized residuals r/s

Question 3

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} Conduct a test of the population coefficient of correlation to determine at the 5% significance level whether a positive linear relationship exists between payment to the two highest-paid performers and gross revenue.

Accepted Answer

H₀: ρ = 0 vs.H₁: ρ > 0 Rejection region: t

Question 4

In simple linear regression,the denominator of the standard error of estimate sε is   .

Accepted Answer

A) True 
 B)False

Question 5

Graphically,a prediction interval is represented as two ____________________ lines.

Accepted Answer

The answer of Graphically,a prediction interval is represented as two...

Question 6

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} Draw a scatter diagram of the data.Comment on whether it appears that a linear model might be appropriate.

Accepted Answer

@#IMG-DLM& It appears that a l

Question 7

Game Show Winnings & Education
 An ardent fan of television game shows has observed that,in general,the more educated the contestant,the less money he or she wins.To test her belief she gathers data about the last eight winners of her favorite game show.She records their winnings in dollars and the number of years of education.The results are as follows.   ​ ​
-{Game Show Winnings & Education Narrative} Do the tests ρ and β1 in the previous two questions provide the same results? Explain.

Accepted Answer

Yes.This is not a co

Question 8

Sales and Experience
The general manager of a chain of department stores believes that experience is the most important factor in determining the level of success of a salesperson. To examine this belief she records last month's sales (in $1,000s) and the years of experience of 10 randomly selected salespeople. These data are listed below.
 
-(Sales and Experience Narrative} Determine the coefficient of determination and discuss what its value tells you about the two variables.

Accepted Answer

R² = 0.9536,which means that 95

Question 9

Cost of Textbooks
The editor of a higher education book publisher claims that a large part of the cost of books is the cost of paper. This implies that larger textbooks will cost more money. As an experiment to analyze the claim, a university student visits the bookstore and records the number of pages and the selling price of twelve randomly selected textbooks. These data are listed below
 
-{Cost of Books Narrative} Which interval in the previous question 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 confidence interval estimate of the

Question 10

There is ____________________ error in estimating a mean than in predicting an individual value.

Accepted Answer

The answer of There is ____________________ error in estimating a...

Question 11

The residuals are observations of the error variable ε.Consequently,the minimized sum of squared deviations is called the sum of squares for error,denoted SSE.

Accepted Answer

A) True 
 B)False

Question 12

Game Winnings & Education 
An ardent fan of television game shows has observed that,in general,the more educated the contestant,the less money he or she wins.To test her belief she gathers data about the last eight winners of her favorite game show.She records their winnings in dollars and the number of years of education.The results are as follows.   ​ ​
-{Game Winnings & Education Narrative} Use the predicted and actual values of y to calculate the residuals.

Accepted Answer

r_i: −4.167,2.500,−65.

Question 13

In the simple linear regression model,the y-intercept represents the:

Accepted Answer

A) change in y per unit change in x. 
B) change in x per unit change in y. 
C) value of y when x = 0. 
D) value of x when y = 0. 
A) change in y per unit change in x. 
B) change in x per unit change in y. 
C) value of y when x = 0. 
D) value of x when y = 0.

Question 14

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} Predict with 99% confidence the gas mileage of a car traveling 55 mph.

Accepted Answer

31.234 ± 1.284.Thus,

Question 15

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: Descriptive Statistics Variable N Mean StDev SE Mean Degrees 13 34.60 4.613 1.280 Price 13 12.730 0.457 0.127 Covariances Degrees Price Degrees 21.281667 Price 2.026750 0.208833 Regression Analysis Predictor Coef StDev T P Constant 9.4349 0.2867 32.91 0.000 Degrees 0.095235 0.008220 11.59 0.000 S = 0.1314 R−Sq = 92.46% R−Sq(adj)= 91.7% Analysis of Variance Source DF SS MS F P Regression 1 2.3162 2.3162 134.24 0.000 Residual Error 11 0.1898 0.0173 Total 12 2.5060
-{Oil Quality and Price Narrative} Identify possible outliers.

Accepted Answer

There are no outliers since no

Question 16

A straight line regression model with only one independent variable is called a(n)____________________-order linear model.

Accepted Answer

The answer of A straight line regression model with only...

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 coefficient of determination and discuss what its value tells you about the two variables.

Accepted Answer

R² = 0.9242,which means that 92

Question 18

In a simple linear regression model,testing whether the slope β1 of the population regression line could be zero is the same as testing whether or not the population coefficient of correlation ρ equals zero.

Accepted Answer

A) True 
 B)False

Question 19

If the standard error of estimate is zero,then:

Accepted Answer

A) the coefficient of determination must be 1.0. 
B) all the points fall on the regression line. 
C) there is no unexplained variation left. 
D) All of these choices are true. 
A) the coefficient of determination must be 1.0. 
B) all the points fall on the regression line. 
C) there is no unexplained variation left. 
D) All of these choices are true.

Question 20

Game Winnings & Education 
An ardent fan of television game shows has observed that,in general,the more educated the contestant,the less money he or she wins.To test her belief she gathers data about the last eight winners of her favorite game show.She records their winnings in dollars and the number of years of education.The results are as follows.   ​ ​
-{Game Winnings & Education Narrative} Plot the residuals against the predicted values   .What does the graph tell you?

Accepted Answer

@#IMG-DLM& The residuals look randomly s

In a regression problem the following pairs of (x,y)are given: (3,1),(3,−1),(3,0),(3,−2)and (3,2).That indicates that the:

In simple linear regression,the denominator of the standard error of estimate sε is .

Graphically,a prediction interval is represented as two ____________________ lines.

There is ____________________ error in estimating a mean than in predicting an individual value.

The residuals are observations of the error variable ε.Consequently,the minimized sum of squared deviations is called the sum of squares for error,denoted SSE.

In the simple linear regression model,the y-intercept represents the:

A straight line regression model with only one independent variable is called a(n)____________________-order linear model.

In a simple linear regression model,testing whether the slope β₁ of the population regression line could be zero is the same as testing whether or not the population coefficient of correlation ρ equals zero.

If the standard error of estimate is zero,then:

What Is Statistics

Graphical Descriptive Techniques 1

Graphical Descriptive Techniques 2

Numerical Descriptive Techniques

Data Collection and Sampling

Probability

Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Sampling Distributions

Introduction to Estimation

Introduction to Hypothesis Testing

Inference About a Population

Inference About Comparing Two Populations

Analysis of Variance

Chi-Squared Tests

Multiple Regression

Model Building

Nonparametric Statistics

Time-Series Analytics and Forecasting

Statistical Process Control

Decision Analysis

Conclusion

Filters

Exam 16: Simple Linear Regression and Correlation

In a regression problem the following pairs of (x,y)are given: (3,1),(3,−1),(3,0),(3,−2)and (3,2).That indicates that the:

In simple linear regression,the denominator of the standard error of estimate sε is .

Graphically,a prediction interval is represented as two ____________________ lines.

There is ____________________ error in estimating a mean than in predicting an individual value.

The residuals are observations of the error variable ε.Consequently,the minimized sum of squared deviations is called the sum of squares for error,denoted SSE.

In the simple linear regression model,the y-intercept represents the:

A straight line regression model with only one independent variable is called a(n)____________________-order linear model.

In a simple linear regression model,testing whether the slope β1 of the population regression line could be zero is the same as testing whether or not the population coefficient of correlation ρ equals zero.

If the standard error of estimate is zero,then:

What Is Statistics

Graphical Descriptive Techniques 1

Graphical Descriptive Techniques 2

Numerical Descriptive Techniques

Data Collection and Sampling

Probability

Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Sampling Distributions

Introduction to Estimation

Introduction to Hypothesis Testing

Inference About a Population

Inference About Comparing Two Populations

Analysis of Variance

Chi-Squared Tests

Multiple Regression

Model Building

Nonparametric Statistics

Time-Series Analytics and Forecasting

Statistical Process Control

Decision Analysis

Conclusion

Filters

In a simple linear regression model,testing whether the slope β₁ of the population regression line could be zero is the same as testing whether or not the population coefficient of correlation ρ equals zero.