Question

9 of 14 (1 point) View problem in a pop-up 10.3 Section Exerci Data for per capita state debt and per capita state tax for nine randomly selected states are shown. The correlation coefficient is r = 0.805. Compute the standard error of the estimate, if appropriate. Assume a = 0.05. 1209 5329 3691 2176 2526 2685 1962 6452 1294 Per capita debt x Per capita taxy 2353 3069 2069 1910 2203 2724 1640 3300 1905 Source: World Almanac. Download data Part 1 The standard error of the estimate should be calculated. Part 2 out of 2 Compute the standard error of the estimate. Round the intermediate calculations to three decimal places and the final answer to two decimal places. S est

Answer 1

X 1209.0 5329.0 3691.0 2176.0 2526.0 2685.0 1962.0 6452.0 1294.0 Y 2353.0 3069.0 2069.0 1910.0 2203.0 2724.0 1640.0 3300.0 1905.0 X*Y 2844777.0 16354701.0 7636679.0 4156160.0 5564778.0 7313940.0 3217680.0 21291600.0 2465070.0 X^2 1461681.0 28398241.0 13623481.0 4734976.0 6380676.0 7209225.0 3849444.0 41628304.0 1674436.0 Y^2 5536609.0 9418761.0 4280761.0 3648100.0 4853209.0 7420176.0 2689600.0 10890000.0 3629025.0 EX = 27324, EY = 21173, E(X*Y) = 70845385, E(X^2) = 108960464, E(Y^2) = 52366241 SSxx = {(x^2) - (1/n) (EX)^2 = 108960464 SSyy = {(Y^2) - (1/n) (EY)^2 = 52366241 Ssxy = E(X*Y) (1/n) (EX) (Y) = 70845385 - (1/9) (27324^2) = 26004800 (1/9) (21173^2) = 2555582.2222 (1/9) (27324) (21173) = 6564157 Total sum of square: SST = SSyy = 2555582.2222 Regression sum of square: SSR = slope Ssxy = (0.2524) * (512) = 1656793.2268 we know that SST = SSR + SSE Sum of squared error: SSE = SST SSR = 2555582.2222 - 1656793.2268 = 898788.9954 Mean squared error: MSE = SSE/(n-2) = 898788.9954/(9-2) = 128398.4279 Standard Error of estimate:o^ = VMSE = V128398.4279 = 358.3273 Ans. Sest = 358.93