Exam 16: Simple Linear Regression and Correlat

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.

Which of the following techniques is used to predict the value of one variable on the basis of other variables?

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?

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.

The probability distribution of the error variable e is normal, with mean E ( e )= 0, and standard deviation s _e =1.

Sunshine and Melanoma A medical researcher wanted to examine the relationship between the amount of sunshine ( x )in hours, and incidence of melanoma, a type of skin cancer ( y ). As an experiment he found the number of melanoma cases detected per 100,000 of population and the average daily sunshine in eight counties around the country. These data are shown below. {Sunshine and Melanoma Narrative} What does the value of the slope of the regression line tell you?

In a simple linear regression model, testing whether the slope b ₁ of the population regression line could be zero is the same as testing whether or not the population coefficient of correlation r equals zero.

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.

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

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.

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 does the slope of the least squares regression line tell you?

If the coefficient of correlation between x and y is close to 1.0, this indicates that:

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} Estimate the number of Allman Brothers concerts attended by a 64 year old person.

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.

In a simple linear regression problem, the least squares line is , and the coefficient of determination is 0.81. The coefficient of correlation must be - 0.90.

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.

The first-order linear model is sometimes called the simple linear regression model.

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

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

If the coefficient of determination is 1.0, then the coefficient of correlation must be 1.0.