Question 1

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

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Question 2

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

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Question 3

Car Speed and Gas Mileage An economist wanted to analyze the relationship between the speed of a car ( x )and its gas mileage ( y ). As an experiment a car is operated at several different speeds and for each speed the gas mileage is measured. These data are shown below. 
  
 {Car Speed and Gas Mileage Narrative} What does the coefficient of correlation tell you about the direction and strength of the relationship between the two variables?

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Question 4

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} Estimate with 95% confidence the average winnings of all contestants who have 10 years of education.

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Question 5

Cost of Books The editor of a major academic book publisher claims that a large part of the cost of books is the cost of paper. This implies that larger books 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 books. These data are listed below.  {Cost of Books Narrative} Predict with 90% confidence the selling price of a book with 900 pages.

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Question 6

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} Predict with 95% confidence the winnings of a contestant who has 15 years of education.

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Question 7

Sale and Experience The general manager of a chain of Designer 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} Conduct a test of the population coefficient of correlation to determine at the 5% significance level whether more experience is related to higher sales, as the manager speculates.

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Question 8

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} Estimate with 95% confidence the average number of concerts attended by all 45 year-old individuals.

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Question 9

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} Predict with 95% confidence the number of concerts attended by a 45 years-old individual.

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Question 10

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} Predict with 95% confidence the winnings of a contestant who has 10 years of education.

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Question 11

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} Estimate with 95% confidence the average winnings of all contestants who have 15 years of education.

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Question 12

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

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Question 13

Car Speed and Gas Mileage An economist wanted to analyze the relationship between the speed of a car ( x )and its gas mileage ( y ). As an experiment a car is operated at several different speeds and for each speed the gas mileage is measured. These data are shown below.  {Car Speed and Gas Mileage Narrative} Does this data provide sufficient evidence at the 5% significance level to infer that a linear relationship exists between speed and gas mileage?

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Question 14

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?

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Question 15

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.

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Question 16

Car Speed and Gas Mileage An economist wanted to analyze the relationship between the speed of a car ( x )and its gas mileage ( y ). As an experiment a car is operated at several different speeds and for each speed the gas mileage is measured. These data are shown below.  {Car Speed and Gas Mileage Narrative} Predict with 99% confidence the gas mileage of a car traveling 55 mph.

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Question 17

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} 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?

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Question 18

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} Estimate with 95% confidence the average gross revenue of a movie whose top two stars earn $5.0 million.

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Quiz 16: Simple Linear Regression and Correlat