Exam 16: Simple Linear Regression and Correlation

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 coefficient of determination and interpret it.

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} Use the regression equation to determine the predicted values of y.

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

A regression analysis between sales (in $1,000)and advertising (in $1,000)resulted in the following least squares line: .This implies that:

If an estimated regression line has a y-intercept of 10 and a slope of 4,then when x = 2 the actual value of y is:

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. -{Sales and Experience Narrative} Determine the standard error of estimate and describe what this statistic tells you about the regression line.

Which of the following statistics and procedures can be used to determine whether a linear model should be employed?

The value of the sum of squares for regression SSR can never be smaller than 0.0.

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.

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} Estimate the selling price for a 650 pages book.

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?

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} 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.

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,

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} Do the ρ and β₁ tests in the previous two questions provide the same results? Explain.

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} Find the least squares regression line.

If the standard error of estimate is ____________________,this implies that the model's fit is poor.

The following 10 observations of variables x and y were collected. Find the least squares regression line,and the estimated value of y when x = 3.

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. -{Sales and Experience Narrative} Calculate the Pearson correlation coefficient.Interpret this result.

The residual r_i is defined as the difference between the actual value y_i and the estimated value .

The coefficient of correlation is used to determine: