Exam 16: Simple Linear Regression and Correlation

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

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

A confidence interval (as opposed to a prediction interval) is used to estimate the long-run average value of y.

If cov(x, y) = 7.5075 and , then the sample slope coefficient is 2.145.

The following 10 observations of variables x and y were collected. a. Calculate the standard error of estimate. b. Test to determine if there is enough evidence at the 5% significance level to indicate that x and y are negatively linearly related. c. Calculate the coefficient of correlation, and describe what this statistic tells you about the regression line.

The residual is defined as the difference between:

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?

In a simple linear regression problem, the least squares line is , and the coefficient of determination is 0.81.The coefficient of correlation must be -0.90.

Another name for the residual term in a regression equation is random error.

Given the least squares regression line :

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 15 years of education.

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.

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. -{Cost of Books Narrative} Estimate with 90% confidence the average selling price of all books with 900 pages.

The residuals are observations of the error variable .Consequently, the minimized sum of squared deviations is called the sum of squares for error, denoted SSE.

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} For what values of API gravity degrees do we feel comfortable making predictions for oil price?

If the plot of the residuals is fan shaped, which assumption of regression analysis (if any) is violated?

Data that exhibit an autocorrelation effect violate the regression assumption of independence.

The point where confidence intervals and prediction intervals do best is .

If an estimated regression line has a y-intercept of 10 and a slope of 4, then when x = 2 the actual value of y is:

There is ____________________ error in estimating a mean than in predicting an individual value.