Exam 16: Simple Linear Regression and Correlation

The regression line has been fitted to the data points (4,8),(2,5),and (1,2).The sum of the squared residuals will be:

The method statisticians use to produce a straight line that minimizes the SSE is called the ____________________ method.

Statisticians have shown that sample y-intercept b₀ and sample slope coefficient b₁ are unbiased estimators of the population regression parameters β₀ and β₁,respectively.

Error terms that are correlated over time are said to be ____________________.

A simple linear regression equation is given by .The point estimate of y when x = 4 is 20.45.

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} Determine the least squares regression line.

For a regression analysis to be valid,the error variable must have a(n)____________________ distribution.

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

A medical statistician wanted to examine the relationship between the amount of sunshine (x)and incidence of skin discolorations (y).As an experiment he found the number of skin discolorations detected per 100,000 of population and the average daily sunshine in eight counties around the country.These data are shown below. Predict with 95% confidence the skin discolorations per 100,000 in a county with a daily average of 6.5 hours of sunshine.

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} Calculate the Pearson coefficient of correlation.

Testing whether the slope of the population regression line could be zero is equivalent to testing whether the:

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} Estimate with 95% confidence the average winnings of all contestants who have 10 years of education.

Suppose the slope of a simple linear regression line between hours studying and exam score is 5.That means as ____________________ increases by one,____________________ increases by 5.

The Pearson coefficient of correlation r equals one when there is no:

A regression analysis between weight (y in pounds)and height (x in inches)resulted in the following least squares line: .This implies that if the height is increased by 1 inch,the weight,on average,is expected to:

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

In regression analysis,the residuals represent the:

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} Does it appear that heteroscedasticity is a problem? Explain.

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} Which interval in the previous two questions is narrower: the confidence interval estimate of the expected value of y or the prediction interval for the same given value of x (10 years)and same confidence level? Why?

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} Does this data provide sufficient evidence at the 5% significance level to infer that a linear relationship exists between speed and gas mileage?