SECTION 9.3 Measures of Regression and Prediction Intervals 501 Finding the Standard Error of Estimate The regression equation for the gross domestic products and carbon dioxide emissions data is ny = 187.660x + 44.663. See Example 1 in Section 9.2. Find the standard error of estimate. SOLUTION Use a table to calculate the sum of the squared differences of each observed y@value and the corresponding predicted y@value. xi yi nyi yi − nyi 1yi − nyi2 2 1.7 620.1 363.685 256.415 65,748.65223 2.4 475.2 495.047 -19.847 393.903409 3.0 457.6 607.643 -150.043 22,512.90185 1.2 389.7 269.855 119.845 14,362.82403 4.1 810.8 814.069 -3.269 10.686361 2.3 352.9 476.281 -123.381 15,222.87116 0.9 235.0 213.557 21.443 459.802249 1.8 297.8 382.451 -84.651 7165.791801 2.9 413.9 588.877 -174.977 30,616.95053 5.4 1216.5 1058.027 158.473 25,113.69173 Σ = 181,608.0754 Unexplained variation Because n = 10 and Σ1yi - nyi2 2 = 181,608.0754 are used, the standard error of estimate is se = CΣ1yi - nyi2 2 n - 2 = A181,608.0754 10 - 2 ≈ 150.669. Interpretation The standard error of estimate of the carbon dioxide emissions for a specific gross domestic product is about 150.669 million metric tons. TRY IT YOURSELF 2 A researcher collects the data shown below and concludes that there is a significant relationship between the amount of radio advertising time (in minutes per week) and the weekly sales of a product (in hundreds of dollars). Radio ad time, x 15 20 20 30 40 45 50 60 Weekly sales, y 26 32 38 56 54 78 80 88 Find the standard error of estimate. Use the regression equation ny = 1.405x + 7.311. Answer: Page A42 EXAMPLE 2
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