Exam 16: Simple Linear Regression and Correlation

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} Do the and $\beta$ ₁ tests in the previous two questions provide the same results? Explain.

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.

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

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 Textbooks Narrative} Determine the least squares regression line.

Trivia Games & 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. -{Trivia Games & Education Narrative} Determine the least squares regression line.

Accidents and Rain A statistician investigating the relationship between the amount of rain (in inches) and the number of automobile accidents gathered data on accidents in her city for 10 randomly selected days throughout the year.The results are shown below. -{Accidents and Rain Narrative} What other variables might be associated with accidents, besides or along with rain?

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?

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.

You use a(n) ____________________ interval whenever you want to estimate the mean of y when x is a given value.

The regression line has been fitted to the data points (4, 11), (2, 7), and (1, 5).The sum of squares for error will be 10.0.

Which of the following assumptions concerning the probability distribution of the random error term is stated incorrectly?

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: -{Oil Quality and Price Narrative} Conduct a test of the population slope to determine at the 5% significance level whether a linear relationship exists between the quality of oil and price per barrel.

A scatter diagram includes the following data points: Two regression models are proposed: (1) , and (2) .Using the least squares method, which of these regression models provides the better fit to the data? Why?

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

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 standard error of estimate and describe what this statistic tells you about the regression line.

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. -{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?

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.

One method of diagnosing heteroscedasticity is to plot the residuals against the predicted values of y, then look for a change in the spread of the plotted values.

A(n) ____________________ is an observation that is unusually small or large.

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} Use the regression equation to determine the predicted values of y.