Exam 16: Simple Linear Regression and Correlation

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

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: Descriptive Statistics Variable N Mean StDev SE Mean Degrees 13 34.60 4.613 1.280 Price 13 12.730 0.457 0.127 Covariances Degrees Price Degrees 21.281667 Price 2.026750 0.208833 Regression Analysis Predictor Coef StDev T P Constant 9.4349 0.2867 32.91 0.000 Degrees 0.095235 0.008220 11.59 0.000 S = 0.1314 R−Sq = 92.46% R−Sq(adj)= 91.7% Analysis of Variance Source DF SS MS F P Regression 1 2.3162 2.3162 134.24 0.000 Residual Error 11 0.1898 0.0173 Total 12 2.5060 -{Oil Quality and Price Narrative} Plot the residuals against the predicted values .

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} Are the two highest paid performers worth all the money paid for them? Comment using the statistical analyses you have done.

You use a(n)____________________ interval whenever you want to estimate a one-time occurrence for a particular value of y when x is a given value.

Error terms that are autocorrelated ____________________ (are/are not)independent.

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. ​ ​ -{Movie Revenues Narrative} Estimate with 95% confidence the average gross revenue of a movie whose top two stars earn $5.0 million.

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

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} Determine the coefficient of determination and discuss what its value tells you.

Given that and n = 6,the standard error of estimate is:

You use a(n)____________________ interval whenever you want to estimate the mean of y when x is a given value.

The value of the sum of squares for regression SSR can never be larger than the value of total sum of squares SST.

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

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: Descriptive Statistics Variable N Mean StDev SE Mean Degrees 13 34.60 4.613 1.280 Price 13 12.730 0.457 0.127 Covariances Degrees Price Degrees 21.281667 Price 2.026750 0.208833 Regression Analysis Predictor Coef StDev T P Constant 9.4349 0.2867 32.91 0.000 Degrees 0.095235 0.008220 11.59 0.000 S = 0.1314 R−Sq = 92.46% R−Sq(adj)= 91.7% Analysis of Variance Source DF SS MS F P Regression 1 2.3162 2.3162 134.24 0.000 Residual Error 11 0.1898 0.0173 Total 12 2.5060 -{Oil Quality and Price Narrative} Use the predicted values and the actual values of y to calculate the residuals.

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

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

We check for normality by drawing a(n)____________________ of the residuals.

A direct relationship between an independent variable x and a dependent variably y means that the variables x and y increase or decrease together.

If you take the residuals,subtract their mean and divide by their standard deviation,the result is called the ____________________ residuals.

The standard error of estimate sε is given by:

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: Descriptive Statistics Variable N Mean StDev SE Mean Degrees 13 34.60 4.613 1.280 Price 13 12.730 0.457 0.127 Covariances Degrees Price Degrees 21.281667 Price 2.026750 0.208833 Regression Analysis Predictor Coef StDev T P Constant 9.4349 0.2867 32.91 0.000 Degrees 0.095235 0.008220 11.59 0.000 S = 0.1314 R−Sq = 92.46% R−Sq(adj)= 91.7% Analysis of Variance Source DF SS MS F P Regression 1 2.3162 2.3162 134.24 0.000 Residual Error 11 0.1898 0.0173 Total 12 2.5060 -{Oil Quality and Price Narrative} Draw a histogram of the residuals.