Exam 16: Simple Linear Regression and Correlation

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

A zero population correlation coefficient for x and y means that there is no type of relationship whatsoever between x and y.

When the error variable does not have constant variance, this condition is called ____________________.

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. -{Trivia Games & Education Narrative} Estimate the game winnings for a contestant with 15 years of education.

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} Calculate the coefficient of determination and interpret its value.

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} Plot the residuals against the predicted values .What does the graph tell you?

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 least squares regression line on the scatter diagram.

The least squares method requires that the variance of the error variable is a constant no matter what the value of x is.When this requirement is violated, the condition is called:

U V'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. -{UV's and Skin Cancer Narrative} Calculate the Pearson coefficient.What sign does it have? Why?

If the sum of squared residuals is zero, then the:

Testing whether the slope of the population regression line could be zero is equivalent to testing whether the:

In a simple linear regression problem, r and b₀:

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 predicted values and the actual values of y to calculate the residuals.

In regression analysis, the coefficient of determination R² measures the amount of variation in y that is:

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

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. -{Income and Education Narrative} Draw a scatter diagram of the data.Comment on whether it appears that a linear model might be appropriate.

We check for normality by drawing a pie chart of the residuals.

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

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. -{Cost of Books Narrative} Predict with 90% confidence the selling price of a book with 900 pages.

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} Determine the standard error of estimate and describe what this statistic tells you about the regression line.