Exam 16: Simple Linear Regression and Correlation

The regression line has been fitted to the data points (4, 8), (2, 5), and (1, 2). The sum of the squared residuals will be:

In the first order linear regression model, the population parameters of the y-intercept and the slope are estimated, respectively, by:

The method statisticians use to produce a straight line that minimizes the SSE is called the ____________________ method.

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. -Estimate the selling price for a 650 pages book.

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. -Predict with 95% confidence the gross revenue of a movie whose top two stars earn $5.0 million.

UV's and Skin Cancer: A medical statistician wanted to examine the relationship between the amount of UV's (x) and incidence of skin cancer (y). As an experiment he found the number of skin cancers detected per 100,000 of population and the average daily sunshine in eight states around the country. These data are shown below. -Calculate the coefficient of determination and interpret it.

A straight line regression model with only one independent variable is called a(n) ____________________-order linear model.

The probability distribution of the error variable $\varepsilon$ is normal, with mean E( $\varepsilon$ ) = 0, and standard deviation $\sigma$ _{$\varepsilon$} =1.

Sales and Experience: The general manager of a chain of department 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. -Estimate the monthly sales for a salesperson with 16 years of experience.

Income and Education: A professor of economics wants to study the relationship between income (y in $1000s) and education (x in years). A random sample eight individuals is taken and the results are shown below. -Estimate the income of an individual with 15 years of education.

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. -Determine the least squares regression line.