Data relating green liquor Na2S concentration (in grams per liter) and paper mac

Question

Data relating green liquor Na2S concentration (in grams per liter) and paper machine production (in tons per day) are collected at a paper manufacturing plant as follows: Production 915 910 1012 895 890 890 990 830 1030 1010 825 960 1050 Concentration 46 48 54 46 49 44 53 42 57 52 40 43 58 Fit a simple linear regression model with y = green liquor Na2S concentration and production. (a) The regression equation is y (b) Estimate 2 which is the variance of the errors, i. (c) Estimate the mean concentration for a production level of 1050. (d) Find the value of the associated residual for the data point with a production level of 1050 (data point number 13). e) What proportion of the variability is explained by regression? (f) Determine the test statistic for a Model Utility Test: (g) Determine the critical value of the test statistic for a Model Utility Test at the 5% level. (h) The conclusion of the model utility test is O A. the model has utility. x. B. the model does not have utility.

Explanation / Answer

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Analysis of Variance

Source DF Adj SS Adj MS F-Value P-Value
Regression 1 322.50 322.502 44.03 0.000
Production 1 322.50 322.502 44.03 0.000
Error 11 80.57 7.325
Lack-of-Fit 10 68.07 6.807 0.54 0.795
Pure Error 1 12.50 12.500
Total 12 403.08

__________________________________________________________________________________________

a)
The Regression equation is,
y^ = -16.5093 + 0.069355 * x
b)
variance of the error 7.325
c)
at x=1050
y^ = -16.5093 + 0.069355 * 1050
the estimated mean concentration is 56.31383
d)
The value of the associated residual for the data point with a production level of 1050 is 1.68617
e)
Proportion of variability explained by regression is 80.01%

SUMMARY OUTPUT Regression Statistics Multiple R 0.894484 R Square 0.800102 Adjusted R Square 0.781929 Standard Error 2.706465 Observations 13 ANOVA df SS MS F Significance F Regression 1 322.5025 322.5025 44.02793 3.68E-05 Residual 11 80.57446 7.324951 Total 12 403.0769 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept -16.5093 9.843464 -1.67718 0.121661 -38.1746 5.156013 -38.1746 5.156013 X Variable 1 0.069355 0.010452 6.635355 3.68E-05 0.04635 0.092361 0.04635 0.092361 RESIDUAL OUTPUT Observation Predicted Y Residuals 1 46.95086 -0.95086 2 46.60408 1.395921 3 53.67833 0.321674 4 45.56375 0.436252 5 45.21697 3.783028 6 45.21697 -1.21697 7 52.15251 0.847492 8 41.05565 0.94435 9 54.92672 2.073277 10 53.53962 -1.53962 11 40.70887 -0.70887 12 50.07185 -7.07185 13 56.31383 1.68617

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