Stats 2

One of the more challenging problems confronting the water pollution control les is presented by the tanning industry. Tannery wastes are chemically complex. Theu are characterized by high values of chemical oxygen, volatile solids, and other pollution measures. Consider the experimental data below. which were obtained from 33 samples of chemically treated waste in a study conducted t Virginia Tech. Readings on x, the percent reduction in total solids, and y. the percent reduction in chemical oxygen demand were recorded. Measures of Reduction in Solids and Oxygen Demand Solid Reduction Oxygen Demand (96) Reduction (56) (9G) Reduction (96) 3 5 7 11 11 21 15 15 18 15 27 28 29 27 30 25 30 35 31 30 31 40 32. 32 33 34 33 32 34 34 36 37 36 38 a. Present a scatter diagram 50 45 40 35 30 25 20 15 10 b. Use Least Square method to identify the Regression Line X yi x 1 - x yi- y ( x , - * ) ( V1 - V ) ( x 1 - X ) 2 3 5 : 3 : 4 decimal 4 decimals 4 deicmals decimal places places places : places 50 51 sum sum Sum Sum (4 decimals (4 decimals places) places (3 decimals places) y = (3 decimals places) y = bot bix Least square estimates of the slope (bj ) = (4 decimal places) Intercept (bo) = (4 decimals places) Linear regression model (with the coefficient reported to the 3 decimal places) is D= D = bo(2 decimals places) + b1 (2 decimals places)x E(x1-x)2 (4 decimals places) bo = y - bix = (4 decimal places) Practical Interpretation: what is the predicted oxygen purity assume x = 1.00 y = 2 decimal places + 2 decimal places(x) D= COEFFICIENT OF DETERMINATION Xi Vi Vi - Vi (vi - D1)2 yi - y (Vi - y)2 3 5 2 decimal places 2 decimals 2 decimal 2 decimal 2 decimal places places places places 50 51 Sum Sum sum sum (2 decimal (2 decimal places) places) For our coefficient of determination r2 = . SSR ? SST SSR = SST - SSE SSR=SSR = r2 = : SSR = SST ( 2 decimal places) r = percent of variability in y can be expalined by x =_ % Correlation Coefficient: Txy = (sign of b,) Vrz Txy = We can conclude, in +0.9367, indicates there is a very strong positive linear relationship between x and y Hypothesis Test of Significance or the slope, t - test Ho(null hypothesis): B1 = 0 (State your statement) Ha(alternative hypothesis): B1 # 0 (State your statement) Test statistics: t - test = t = ~ where sb, = Jy(xi-2)2 and s = SSE =t= _(2 decimal places0 Sb1 Use level of significance = 0.01 b1 + ta sb, ta = find the value from the t distribution table: 2' ttable = 2.88 tta + 99% Confidence Interval Estimate for the Slope, B1 3 decimals places s B1 S 3 decimal places SBIS Hypothesis Test of significance for the slope, t - test: Ho(null hypothesis): B1 = 0 (State your statement) Ha(alternative hypothesis): B1 # 0 (State your statement) =t = D1 = = 14.947 sbi 1.31645408 = 11.353985 = 11.35 Critical value: ttable : Rejection rule: If tcomputed value 2 ttable, reject the null hypothesis, Accept the alternative hypothesis Conclusion: Recommendation