Exam 16: Simple Linear Regression and Correlation

Error terms that are autocorrelated ____________________ (are/are not) independent.

In the least squares regression line , the predicted value of y equals:

If the coefficient of correlation is -0.81, then the percentage of the variation in y that is explained by the regression line is 81%.

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} Plot the residuals against the predicted values .

If there is no linear relationship between two variables x and y, the coefficient of determination must be-1.0.

The Pearson coefficient of correlation r equals one when there is no:

A medical statistician wanted to examine the relationship between the amount of sunshine (x) and incidence of skin discolorations (y).As an experiment he found the number of skin discolorations detected per 100,000 of population and the average daily sunshine in eight counties around the country.These data are shown below. Predict with 95% confidence the skin discolorations per 100,000 in a county with a daily average of 6.5 hours of sunshine.

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

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.

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} Interpret the value of the slope of 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?

The plot of residuals vs.predicted values should show no patterns if the conditions of a regression analysis are met.

The value of the sum of squares for regression SSR can never be smaller than 1.

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} Draw a histogram of the residuals.

Telemarketing Sales and Experience The general manager of a telemarketing company believes that experience is the most important factor in determining the level of success of a telemarketer.To examine this belief she records last month's sales (in $1,000s) and the years of experience of 10 randomly selected telemarketers.These data are listed below. -{Telemarketer Sales and Experience Narrative} Compute the standardized residuals.

The confidence interval estimate of the expected value of y will be wider than the prediction interval for the same given value of x and confidence level.This is because there is more error in estimating a mean value as opposed to predicting an individual value.

Comedy Shows Revenues A financier whose specialty is investing in comedy shows has observed that, in general, shows with "big-name" stars seem to generate more revenue than those shows 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 comedians in the show for ten recently staged shows. -{Comedy Shows Revenues Narrative} Use the regression equation to determine the predicted values of y.

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 coefficient of correlation to determine at the 5% significance level whether a positive linear relationship exists between the quality of oil and price per barrel.

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

In simple linear regression, the coefficient of correlation r and the least squares estimate b₁ of the population slope $\beta$ ₁: