Exam 16: Simple Linear Regression and Correlation

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} Interpret the value of the slope of the regression line.

Telemarketing Sales and Experience The general manager of a telemarketing company believes that experience is the most important factor in determining the level of success of a telemarketer.To examine this belief she records last month's sales (in $1,000s)and the years of experience of 10 randomly selected telemarketers.These data are listed below. ​ ​ -{Telemarketer Sales and Experience Narrative} Use the regression equation to determine the predicted values of y.

A regression analysis between sales (in $)and advertising (in $)resulted in the following least squares line: .This implies that an increase of $1 in advertising is associated with an increase of $60 in sales.

Grateful Dead Concert At a recent Grateful Dead 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.It is suspected that older concert goers tend to go to more of his concerts in one year than younger concert goers.The data and analysis are shown below. An Excel output follows: -{Grateful Dead Concert Narrative} Calculate the Pearson correlation coefficient and interpret.

Grateful Dead Concert At a recent Grateful Dead 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.It is suspected that older concert goers tend to go to more of his concerts in one year than younger concert goers.The data and analysis are shown below. An Excel output follows: -{Grateful Dead Concert Narrative} Determine the coefficient of determination and discuss what its value tells you about the two variables.

One method of diagnosing heteroscedasticity is to plot the residuals against the predicted values of y,then look for a change in the spread of the plotted values.

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} Can we conclude at the 1% significance level that there is a linear relationship between sunshine and skin cancer?

Given the least squares regression line ,and a coefficient of determination of 0.81,the coefficient of correlation is:

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} Compute the standardized residuals.

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: -{Allman Brothers Concert Narrative} Interpret the value of the slope of the regression line.

The confidence interval estimate of the expected value of y will be wider than the prediction interval for the same given value of x and confidence level.This is because there is more error in estimating a mean value as opposed to predicting an individual value.

If the coefficient of determination is 0.95,this means that 95% of the variation in the independent variable x can be explained by the y variable.

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} What does the coefficient of correlation tell you about the direction and strength of the relationship between the two variables?

In a simple linear regression problem,the following sum of squares are produced: The percentage of the variation in y that is explained by the variation in x is:

A(n)____________________ is an observation that is unusually small or large.

The method of least squares requires that the sum of the squared deviations between actual y values in the scatter diagram and y values predicted by the regression line be minimized.

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 least squares regression line.

The value of the sum of squares for regression SSR can never be larger than the value of sum of squares for error SSE.

The confidence interval estimate of the expected value of y for a given value x,compared to the prediction interval of y for the same given value of x and confidence level,will be:

If all the points in a scatter diagram lie on the least squares regression line,then the coefficient of correlation must be 1.0.