An Article In The Journal Of The Environmental Engineering Division Least Squares Estimates Of Bod Parameters Vol 1 1 (84.98 KiB) Viewed 16 times
An article in the Journal of the Environmental Engineering Division ("Least Squares Estimates of BOD Parameters," Vol. 106, 1980, pp. 1197-1202) describes the results of testing a sample from the Holston River below Kingport, TN, during August 1977. The biochemical oxygen demand (BOD) test is conducted over a period of time in days. The resulting data is shown below: Predictor Constant Time Source Regression Residual Error Coef Total 0.6578 0.17806 S=0.287281 R-Sq = 94.7% R-Sq(adj) = 94.1% Analysis of Variance DF 1 9 SE Coef 10 0.1657 0.01400 SS 13.344 Time (days) BOD (mg/liter) Minitab output resulting from fitting a simple linear regression model with time as the explanatory variable and BOD as the response follows. 0.743 14.087 1 2 4 6 8 10 12 14 16 18 20 T 3.97 12.72 MS 13.344 0.6 0.083 0.7 1.5 1.9 2.1 2.6 2.9 3.7 3.5 3.7 3.8 P 0.003 0.000 F 161.69 P 0.000
(a) Assuming that a simple linear regression model is appropriate, estimate the regression model relating BOD (y) to the time (x). Round your final answers to 4 decimal places. ŷ i What is the estimate of ²? Round your final answer to 3 decimal places. 2 (b) What is the estimate of expected BOD level when the time is 7 days? Round your final answer to 3 decimal places. (c) What change in mean BOD is expected when the time increases by 5 days? Round your final answer to 4 decimal places. +i ŷ (d) Suppose the time used is 6 days. Calculate the fitted value of y and the corresponding residual. Round your final answers to 4 decimal places. = i e= X i
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