Exam 16: Simple Linear Regression and Correlation

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

NARRBEGIN: Cost of TextBooks 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. $\begin{array} { | c | c | c | } \hline \text { Textbook } & \text { Number af Peges } & \text { Selling Price (\$) } \\\hline 1 & 844 & 55 \\2 & 727 & 50 \\3 & 360 & 35 \\4 & 915 & 60 \\5 & 295 & 30 \\6 & 706 & 50 \\7 & 410 & 40 \\8 & 905 & 53 \\9 & 1058 & 65 \\10 & 865 & 54 \\11 & 677 & 42 \\12 & 912 & 58 \\\hline\end{array}$ NARREND -{Cost of Textbooks Narrative} Determine the least squares regression line.

In simple linear regression, the denominator of the standard error of estimate s _{$\varepsilon$} is $\sqrt { n - 2 }$ .

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

If the standard error of estimate is ____________________, this implies that the model's fit is poor.

For a regression analysis to be valid, the error variable must have a mean of ____________________.

NARRBEGIN: Theatre Revenues 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. Play Cost of Two Highest Paid Performers ( \mil ) Gross Revenue () 1 5.3 48 2 7.2 65 3 1.3 18 4 1.8 20 5 3.5 31 6 2.6 26 7 8.0 73 8 2.4 23 9 4.5 39 10 0.7 58 NARREND -{Theatre Revenues Narrative} Estimate the gross revenue of a play if the two highest paid performers received 6 million dollars.

In the simple linear regression model, the y-intercept represents the:

NARRBEGIN: Rock Concert Revenues 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. Concert Cost of Twa Highest Paid Performers ( \mil ) Gross Revenue () 1 5.3 48 2 7.2 65 3 1.3 18 4 1.8 20 5 3.5 31 6 2.6 26 7 8.0 73 8 2.4 23 9 4.5 39 10 0.7 58 NARREND -{Rock Concert Revenues Narrative} Calculate the Pearson correlation coefficient. Interpret the results.

NARRBEGIN: Game Winnings & Ed.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. Contestant Years of Education Winnings 1 11 750 2 15 400 3 12 600 4 16 350 5 11 800 0 16 300 7 13 650 8 14 400 NARREND -{Game Winnings & Education Narrative} Use the regression equation $\hat { y } = 1735 - 89.1667 x$ to determine the predicted values of y.

The symbol for the sample coefficient of correlation is:

A confidence interval estimate for the expected value of y will always be wider than the prediction interval for the same given value of x and the same confidence level.

The residual r_i is defined as the difference between the actual value y_i and the estimated value $\hat { y } _ { i }$ .

NARRBEGIN: Theatre Revenues 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. Play Cost of Two Highest Paid Performers ( \mil ) Gross Revenue () 1 5.3 48 2 7.2 65 3 1.3 18 4 1.8 20 5 3.5 31 6 2.6 26 7 8.0 73 8 2.4 23 9 4.5 39 10 0.7 58 NARREND -{Theatre Revenues Narrative} Interpret the value of the slope of the regression line.

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

Which of the following statistics and procedures can be used to determine whether a linear model should be employed?

NARRBEGIN: Game Show Winnings & Ed.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. Contestant Years of Education Winnings 1 11 750 2 15 400 3 12 600 4 16 350 5 11 800 0 16 300 7 13 650 8 14 400 NARREND -{Game Show Winnings & Education Narrative} Conduct a test of the population slope to determine at the 5% significance level whether a negative linear relationship exists between years of education and TV game shows' winnings.

If the plot of the residuals vs. the predicted values resembles a straight line with non-zero slope, then the regression line fits well.

The least squares method for determining the best fit minimizes:

When the error variable does not have constant variance, this condition is called ____________________.