Question

Try It Yourself 3 Construct a 95% prediction interval for the carbon dioxide emissions when the gross domestic product is $4 trillion. What can you conclude? a. Specify n, d.f., le, se b. Calculate y when x = 4. c. Calculate the margin of error E. d. Construct the prediction interval. e. Interpret the results. Answer: Page A45 TION AND REGRESSION EXAMPLE 2 SC Report 42 Finding the Standard Error of Estimate The regression equation for the gross domestic products and carbon dioe emissions data as calculated in Example 1 in Section 9.2 is 190.1 52x + 102.289. У 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. ri 1.6 428.2 416.1322 3.6 828.8 808.4362 20.3638 4.9 1214.2 1063.4338 150.7662 22,730.44706244 1.1 444.6 318.0562 126.5438 16,013.33331844 09 264.0 278.8258 2.9 415.3 671.1298255.8298 65,448.88656804 2.7 571.8 631.899460.09943611.93788036 2.3 454.9 553.4386 98.5386 9709.85568996 1.6 358.7 416.1322 -57.4322 1.5 573.5 396.517176.983 31,322.982289 yi yi-yi 12.0678 145.63179684 414.68435044 -14.8258 219.80434564 3298.45759684 Σ 152916.020898 Unexplained variation When n 10 and E(y -)152,916.020898 are used, the standard error of estimate is n- 152,916.020898 STU 10 2 The E ust 138.255 Interpretation The standard error of estimate of the carbon dioxide emissions for a specific gross domestic product is about 138.255 million metric tons and to ca quar ION AND REGRESSION EXAMPLE 3 SC Report 43 Constructing a Prediction Interval Using the results of Example 2, construct a 95% prediction interval fr carbon dioxide emissions when the gross domestic product is $3.5 tri What can you conclude? Solution Because n 10, there are 10-2 8 196.152x +102.289 x-3.5, degrees of freedom. Using the regression equation and the point estimate is y-196.152x + 102.289 196.152(3.5) +102.289 - 788.821. From Table 5, the critical value is t 2.306, and from Example 138.255. Using these values, the margin of error is E-tesfri름.ntnr)-(S.. 110(35 2.31) 10 10(67.35) (23.1) (30)0138.255)1+ 10 1007.35)-(231 349.424. Using ý 788.821 and E 349424, the prediction interval is Right Endpoint Left Endpoint 788.821-349.424 439.397 788.821 + 349.424Ξ1138245 439.397

Answer 1

S. -138.2S5 y- 196, 152 x 4 + 102 9 88 6,89구 2 2.306メ139, 255 '0 (67.15) -(23y2 |364.088 ㄚ一E 886.897 365.088 ะ|(522.809, 1250.915