Exam 16: Simple Linear Regression and Correlation

Speed vs 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} Estimate the gas mileage of a car traveling 70 mph.

In a simple linear regression model b₀ is the ____________________ of the straight line.

Marc Anthony Concert At a recent Marc Anthony 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: -{Marc Anthony Concert Narrative} Use the regression equation to determine the predicted values of y.

If the standard error of estimate is zero, then:

The objective of a regression model is to analyze the relationship between two variables, x and y, both of which must be based on ____________________ data.

We check for normality by drawing a(n) ____________________ of the residuals.

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} Identify possible outliers.

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: -{Oil Quality and Price 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?

Marc Anthony Concert At a recent Marc Anthony 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: -{Marc Anthony Concert Narrative} Use the residuals to compute the standardized residuals.

A simple linear regression equation is given by .The point estimate of y when x = 4 is 20.45.

Allman Brothers Concert At a recent Allman Brothers 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: -{Allman Brothers Concert Narrative} Interpret the value of the slope of the regression line.

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 slope to determine at the 5% significance level whether a positive linear relationship exists between payment to the two highest-paid performers and gross revenue.

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} Calculate the Pearson correlation coefficient.What sign does it have? 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} Predict with 95% confidence the winnings of a contestant who has 10 years of education.

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.

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} Determine the coefficient of determination and discuss what its value tells you.

We standardize residuals by subtracting their mean and dividing by their variance.

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 testsand $\beta$ ₁ in the previous two questions provide the same results? Explain.

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} Does this data provide sufficient evidence at the 5% significance level to infer that a linear relationship exists between speed and gas mileage?

If the coefficient of correlation is -0.80, then the percentage of the variation in y that is explained by the variation in x is: