Exam 16: Simple Linear Regression and Correlation

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

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. -Predict with 95% confidence the winnings of a contestant who has 15 years of education.

The standard error of estimate s _{$\varepsilon$} is a measure of the:

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. -Determine the least squares regression line.

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: -Estimate with 95% confidence the average oil price per barrel for an API degree of 35.

The unbiased estimator of the variance of the error variable is found by taking ____________________ divided by n - 2.

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. -Estimate with 95% confidence the average winnings of all contestants who have 15 years of education.

The graph of a confidence interval for the expected value of y is represented by two parallel lines, one on either side of the regression line.

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

If the value of the sum of squares for error SSE equals zero, then the coefficient of determination must equal zero.

Given the least squares regression line :

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. -What does the value of the slope of the regression line tell you?

In regression analysis, if the coefficient of determination is 1.0, then:

If the coefficient of correlation is -0.80, then the percentage of the variation in y that is explained by the variation in x is:

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: -Interpret the value of the slope of the regression line.

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: -Plot the least squares regression line on the scatter diagram.

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: -Interpret the value of the slope of the regression line.

Sales and Experience: The general manager of a chain of hardware 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. -Determine the standard error of estimate and describe what this statistic tells you about the regression line.

Truck Speed vs Gas Mileage: An economist wanted to analyze the relationship between the speed of a car (x) and its gas mileage (y). As an experiment a car is operated at several different speeds and for each speed the gas mileage is measured. These data are shown below. -Estimate the gas mileage of a car traveling 70 mph.

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. -Determine the coefficient of determination and discuss what its value tells you about the two variables.