Exam 16: Simple Linear Regression and Correlation

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} Draw a scatter diagram of the data.Comment on whether it appears that a linear model might be appropriate to describe the relationship between the quality of oil and price per barrel.

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

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

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

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} Estimate the number of accidents in a day with 0.25 inches of rain.

The first-order linear model is sometimes called the simple linear regression model.

The graph of a confidence interval for the expected value of y is represented by two curved lines,one on either side 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: -{Oil Quality and Price Narrative} Estimate with 95% confidence the average oil price per barrel for an API degree of 35.

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} Does it appear that the errors are normally distributed? Explain.

The residual is defined as the difference between:

The deviations between the actual data points and the fitted values from the model are called ____________________.

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} Conduct a test of the population slope to determine at the 5% significance level whether a positive linear relationship exists between payment to the two highest-paid performers and gross revenue.

Theatre Revenues A financier whose specialty is investing in stage productions has observed that,in general,movies with "big-name" stars seem to generate more revenue than those plays 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 play for ten recently staged plays. ​ ​ -{Theatre Revenues Narrative} Draw a scatter diagram of the data.Comment on whether it appears that a linear model might be appropriate.

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} Predict with 95% confidence the oil price per barrel for an API degree of 35.

Cost of Books The editor of a major academic book publisher claims that a large part of the cost of books is the cost of paper.This implies that larger books 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 books.These data are listed below. ​ ​ -{Cost of Books Narrative} Can we infer at the 5% significance level that the editor is correct?

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

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} Predict with 95% confidence the winnings of a contestant who has 10 years of education.

When the actual values y of a dependent variable and the corresponding predicted values are the same,the standard error of the estimate will be 1.0.

The prediction interval for a particular value of y is always wider than the confidence interval for mean value of y,given the same data set,x value,and confidence level.

In order to estimate with 95% confidence the expected value of y for a given value of x in a simple linear regression problem,a random sample of 10 observations is taken.Which of the following t-table values listed below would be used?