Exam 16: Simple Linear Regression and Correlation

Another name for the residual term in a regression equation is random error.

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. -Draw a scatter diagram of the data. Comment on whether it appears that a linear model might be appropriate.

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

A zero correlation coefficient between a pair of random variables means that there is no linear relationship between the random variables.

An inverse relationship between an independent variable x and a dependent variably y means that as x increases, y decreases, and vice versa.

Sale and Experience: The general manager of a chain of Designer 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. -Conduct a test of the population coefficient of correlation to determine at the 5% significance level whether more experience is related to higher sales, as the manager speculates.

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. -Conduct a test of the population coefficient of correlation to determine at the 5% significance level whether a negative linear relationship exists between years of education and TV game shows' winnings.

Statisticians have shown that sample y-intercept b₀ and sample slope coefficient b₁ are unbiased estimators of the population regression parameters $\beta$ ₀ and $\beta$ ₁, respectively.

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

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.

If cov(x, y) = 1260, , and , then the coefficient of determination is:

For a regression analysis to be valid, the error variable must have a(n) ____________________ distribution.

Calculate the Pearson correlation coefficient. What sign does it have? Why?

In a regression problem, if the coefficient of determination is 0.95, this means that:

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. -Calculate the residual corresponding to the pair (x, y) = (8, 15).

In order to predict with 98% confidence the expected value of y for a given value of x in a simple linear regression problem, a random sample of 15 observations is taken. Which of the following t-table values listed below would be used?

Graphically, a confidence interval for the mean of y is represented as two ____________________ lines.

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: -Predict with 95% confidence the number of concerts attended by a 45 years-old individual.

In a simple linear regression problem, the following statistics are calculated from a sample of 10 observations: . The least squares estimates of the slope and y-intercept are, respectively,

You cannot interpret the ____________________ of the simple linear regression line unless the value of x = 0 lies within the range of where data was collected.