Solution: Finding the Coefficient of Determination and the Standard Error of Estimate In

Graphical Analysis In Exercises 13, use the figure. (xi , y) (xi , yi ) xDescribe the total variation about a regression line in words and in symbols.

Graphical Analysis In Exercises 13, use the figure. (xi , y) (xi , yi ) xDescribe the explained variation about a regression line in words and in symbols.

Graphical Analysis In Exercises 13, use the figure. (xi , y) (xi , yi ) x Describe the unexplained variation about a regression line in words and in symbols.

The coefficient of determination r2 is the ratio of which two types of variations? What does r2 measure? What does 1 - r2 measure?

What is the coefficient of determination for two variables that have perfect positive linear correlation or perfect negative linear correlation? Interpret your answer.

Two variables have a bivariate normal distribution. Explain what this means.

In Exercises 710, use the value of the correlation coefficient r to calculate the coefficient of determination r2 . What does this tell you about the explained variation of the data about the regression line? About the unexplained variation?r = 0.465

In Exercises 710, use the value of the correlation coefficient r to calculate the coefficient of determination r2 . What does this tell you about the explained variation of the data about the regression line? About the unexplained variation?r = -0.328

In Exercises 710, use the value of the correlation coefficient r to calculate the coefficient of determination r2 . What does this tell you about the explained variation of the data about the regression line? About the unexplained variation?. r = -0.957

In Exercises 710, use the value of the correlation coefficient r to calculate the coefficient of determination r2 . What does this tell you about the explained variation of the data about the regression line? About the unexplained variation?r = 0.881

Finding the Coefficient of Determination and the Standard Error of Estimate In Exercises 1120, use the data to find (a) the coefficient of determination r2 and interpret the result, and (b) the standard error of estimate se and interpret the result Stock Offerings The numbers of initial public offerings of stock issued and the total proceeds of these offerings (in millions of dollars) for 12 years are shown in the table. The equation of the regression line is yn = 104.965x + 14,093.666. (Source: University of Florida) Number of issues, x 316 485 382 79 70 67 Proceeds, y 34,314 64,906 64,876 34,241 22,136 10,068 Number of issues, x 183 168 162 162 21 43 Proceeds, y 31,927 28,593 30,648 35,762 22,762 13,307

Finding the Coefficient of Determination and the Standard Error of Estimate In Exercises 1120, use the data to find (a) the coefficient of determination r2 and interpret the result, and (b) the standard error of estimate se and interpret the result Earnings of Men and Women The table shows the median annual earnings (in dollars) of male and female workers from 10 states in a recent year. The equation of the regression line is yn = 0.939x - 6745.842. (Source: U.S. Census Bureau) Median annual earnings of male workers, x 41,331 48,389 42,667 43,631 55,116 Median annual earnings of female workers, y 30,658 40,019 33,665 31,762 44,937 Median annual earnings of male workers, x 48,492 37,528 43,425 39,562 40,621 Median annual earnings of female workers, y 38,025 28,506 35,691 30,578 32,578

Finding the Coefficient of Determination and the Standard Error of Estimate In Exercises 1120, use the data to find (a) the coefficient of determination r2 and interpret the result, and (b) the standard error of estimate se and interpret the resultSquare Footage and Sales The table shows the total square footages (in billions) of retailing space at shopping centers and their sales (in billions of dollars) for 11 years. The equation of the regression line is yn = 445.257x - 1480.117. (Adapted from International Council for Shopping Centers) Total square footage, x 5.3 5.4 5.5 5.7 5.8 6.0 Sales, y 893.8 933.9 980.0 1032.4 1105.3 1181.1 Total square footage, x 6.1 6.2 6.4 6.5 6.7 Sales, y 1221.7 1277.2 1339.2 1432.6 1530.4

Finding the Coefficient of Determination and the Standard Error of Estimate In Exercises 1120, use the data to find (a) the coefficient of determination r2 and interpret the result, and (b) the standard error of estimate se and interpret the result Trees The table shows the heights (in feet) and trunk diameters (in inches) of eight trees. The equation of the regression line is yn = 0.479x - 24.086. Height, x 70 72 75 76 85 78 77 82 Trunk diameter, y 8.3 10.5 11.0 11.4 14.9 14.0 16.3 15.8

Finding the Coefficient of Determination and the Standard Error of Estimate In Exercises 1120, use the data to find (a) the coefficient of determination r2 and interpret the result, and (b) the standard error of estimate se and interpret the result State and Federal Government Wages The table shows the average weekly wages (in dollars) for state government employees and federal government employees for 10 years. The equation of the regression line is yn = 1.632x - 200.284. (Source: U.S. Bureau of Labor Statistics) Average weekly wages (state), x 754 770 791 812 844 Average weekly wages (federal), y 1001 1043 1111 1151 1198 Average weekly wages (state), x 883 923 937 942 966 Average weekly wages (federal), y 1248 1275 1303 1331 1404

Finding the Coefficient of Determination and the Standard Error of Estimate In Exercises 1120, use the data to find (a) the coefficient of determination r2 and interpret the result, and (b) the standard error of estimate se and interpret the result Voter Turnout The U.S. voting age populations (in millions) and the turnout of the voting age populations (in millions) for federal elections for nine nonpresidential election years are shown in the table. The equation of the regression line is yn = 0.369x + 0.994. (Adapted from Federal Election Commission) Voting age population, x 158.4 169.9 178.6 185.8 193.7 Turnout in federal elections, y 58.9 67.6 65.0 67.9 75.1 Voting age population, x 200.9 215.5 220.6 235.8 Turnout in federal elections, y 73.1 79.8 80.6 90.7

Finding the Coefficient of Determination and the Standard Error of Estimate In Exercises 1120, use the data to find (a) the coefficient of determination r2 and interpret the result, and (b) the standard error of estimate se and interpret the result Crude Oil The table shows the amounts of crude oil (in thousands of barrels per day) produced by the United States and the amounts of crude oil (in thousands of barrels per day) imported by the United States for seven years. The equation of the regression line is yn = -1.167x + 16,118.763. (Source: Energy Information Administration) Produced, x 5801 5744 5644 5435 5186 5089 5077 Imported, y 9328 9140 9665 10,088 10,126 10,118 10,031

Finding the Coefficient of Determination and the Standard Error of Estimate In Exercises 1120, use the data to find (a) the coefficient of determination r2 and interpret the result, and (b) the standard error of estimate se and interpret the result Fund Assets The table shows the total assets (in billions of dollars) of individual retirement accounts (IRAs) and federal pension plans for nine years. The equation of the regression line is yn = 0.177x + 450.146. (Adapted from Investment Company Institute) IRAs, x 2619 2533 2993 3299 3652 Federal pension plans, y 860 894 958 1023 1072 IRAs, x 4207 4784 3585 4251 Federal pension plans, y 1141 1197 1221 1324

Finding the Coefficient of Determination and the Standard Error of Estimate In Exercises 1120, use the data to find (a) the coefficient of determination r2 and interpret the result, and (b) the standard error of estimate se and interpret the result New-Vehicle Sales The table shows the numbers of new-vehicle sales (in thousands) in the United States for Ford and General Motors for 11 years. The equation of the regression line is yn = 1.200x + 433.900. (Data from NADA Industry Analysis Division) New-vehicle sales (Ford), x 4148 3916 3576 3438 3271 3107 New-vehicle sales (General Motors), y 4912 4853 4815 4716 4657 4457 New-vehicle sales (Ford), x 2848 2502 1942 1656 1905 New-vehicle sales (General Motors), y 4068 3825 2956 2072 2211

Finding the Coefficient of Determination and the Standard Error of Estimate In Exercises 1120, use the data to find (a) the coefficient of determination r2 and interpret the result, and (b) the standard error of estimate se and interpret the result New-Vehicle Sales The table shows the numbers of new-vehicle sales (in thousands) in the United States for Toyota and Honda for 11 years. The equation of the regression line is yn = 0.396x + 536.161. (Data from NADA Industry Analysis Division) New-vehicle sales (Toyota), x 1619 1741 1756 1866 2060 2260 New-vehicle sales (Honda), y 1159 1208 1248 1350 1394 1463 New-vehicle sales (Toyota), x 2543 2621 2218 1770 1764 New-vehicle sales (Honda), y 1509 1552 1429 1151 1231

Constructing and Interpreting Prediction Intervals In Exercises 2130, construct the indicated prediction interval and interpret the results.Proceeds Construct a 95% prediction interval for the proceeds from initial public offerings in Exercise 11 when the number of issues is 450.

Constructing and Interpreting Prediction Intervals In Exercises 2130, construct the indicated prediction interval and interpret the results.Earnings of Women Construct a 95% prediction interval for the median annual earnings of female workers in Exercise 12 when the median annual earnings of male workers is $45,637.

Retail Sales Construct a 90% prediction interval for shopping center sales in Exercise 13 when the total square footage of shopping centers is 5.75 billion.

Trees Construct a 90% prediction interval for the trunk diameter of a tree in Exercise 14 when the height is 80 feet.

Federal Government Wages Construct a 99% prediction interval for the average weekly wages of federal government employees in Exercise 15 when the average weekly wages of state government employees is $800.

Voter Turnout Construct a 99% prediction interval for voter turnout in Exercise 16 when the voting age population is 210 million.

Crude Oil Construct a 95% prediction interval for the amount of crude oil imported by the United States in Exercise 17 when the amount of crude oil produced by the United States is 5500 thousand barrels per day.

Total Assets Construct a 90% prediction interval for the total assets in federal pension plans in Exercise 18 when the total assets in IRAs is $3800 billion.

New-Vehicle Sales Construct a 95% prediction interval for new-vehicle sales for General Motors in Exercise 19 when the number of new vehicles sold by Ford is 2628 thousand.

New-Vehicle Sales Construct a 99% prediction interval for new-vehicle sales for Honda in Exercise 20 when the number of new vehicles sold by Toyota is 2359 thousand.

Old Vehicles In Exercises 3134, use the figure shown at the left.. Scatter Plot Construct a scatter plot of the data. Show y and x on the graph.

Old Vehicles In Exercises 3134, use the figure shown at the left.Regression Line Find and draw the regression line.

Old Vehicles In Exercises 3134, use the figure shown at the left.Coefficient of Determination Find the coefficient of determination r2 and interpret the results.

Old Vehicles In Exercises 3134, use the figure shown at the left.Error of Estimate Find the standard error of estimate se and interpret the results.

Hypothesis Testing for Slope In Exercises 35 and 36, use the following information The table shows the weights (in pounds) and the numbers of hours slept in a day by a random sample of infants. Test the claim that M 0. Use a = 0.01. Then interpret the results in the context of the problem. If convenient, use technology. Weight, x 8.1 10.2 9.9 7.2 6.9 11.2 11 15 Hours slept, y 14.8 14.6 14.1 14.2 13.8 13.2 13.9 12.5

Hypothesis Testing for Slope In Exercises 35 and 36, use the following information The table shows the ages (in years) and salaries (in thousands of dollars) of a random sample of engineers at a company. Test the claim that M 0. Use a = 0.05. Then interpret the results in the context of the problem. If convenient, use technology. Age, x 25 34 29 30 42 38 49 52 35 40 Salary, y 57.5 61.2 59.9 58.7 87.5 67.4 89.2 85.3 69.5 75.1

In Exercises 37 and 38, construct the indicated confidence intervals for B and M using the gross domestic products and carbon dioxide emissions data found in Example 2.95% confidence interval

In Exercises 37 and 38, construct the indicated confidence intervals for B and M using the gross domestic products and carbon dioxide emissions data found in Example 2.. 99% confidence interval