Exam 16: Simple Linear Regression and Correlation

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 coefficient of determination and interpret its value.

The variance of the error variable is required to be constant.When this requirement is satisfied,the condition is called homoscedasticity.

The width of the confidence interval estimate for the predicted value of y depends on

In a simple linear regression model b₁ is the ____________________ of the straight line.

A regression line using 25 observations produced SSR = 118.68 and SSE = 56.32.The standard error of estimate was:

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} Predict with 95% confidence the gross revenue of a movie whose top two stars earn $5.0 million.

Wayne Newton Concert At a recent Wayne Newton 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: -{Wayne Newton Concert 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?

Consider the following data values of variables x and y. ​ a.Determine the least squares regression line. b.Find the predicted value of y for x = 9. c.What does the value of the slope of the regression line tell you?

If the coefficient of correlation is −0.81,then the percentage of the variation in y that is explained by the regression line is 81%.

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

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 standard error of estimate,and describe what this statistic tells you about the regression line.

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} Conduct a test of the population coefficient of correlation to determine at the 5% significance level whether a positive linear relationship exists between age and number of concerts attended.

An outlier is an observation that is unusually small or unusually large.

If the variance of the errors is constant for each predicted y value,the condition is called ____________________.

If the coefficient of correlation is 0.90,then the percentage of the variation in the dependent variable y that is explained by the variation in the independent variable x is:

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

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} Determine the least squares regression line.

The value of the sum of squares for regression SSR can never be smaller than 1.

Income and Education A professor of economics wants to study the relationship between income (y in $1000s)and education (x in years).A random sample eight individuals is taken and the results are shown below. ​ ​ -{Income and Education Narrative} Interpret the value of the slope of the regression line.

In a simple linear regression problem,r and b₀: