An article in Technometrics (1974, Vol. 16, pp. 523-531) considered the followin
ID: 3155804 • Letter: A
Question
An article in Technometrics (1974, Vol. 16, pp. 523-531) considered the following stack-loss data from a plant oxidizing ammonia to nitric acid. Twenty-one daily responses of stack loss y (the amount of ammonia escaping) were measured with air flow x1, temperature x2, and acid concentration x3.
y = 42, 37, 37, 28, 18, 18, 19, 20, 15, 14, 14, 13, 11, 12, 8, 7, 8, 8, 9, 15, 16
x1 = 80, 80, 75, 62, 62, 62, 62, 62, 58, 58, 58, 58, 58, 58, 50, 50, 50, 50, 50, 56, 70
x2 = 27, 27, 25, 24, 22, 23, 24, 24, 23, 18, 18, 17, 18, 19, 18, 18, 19, 19, 20, 20, 20
x3 = 89, 88, 90, 87, 87, 87, 93, 93, 87, 80, 89, 88, 82, 93, 89, 86, 72, 79, 80, 82, 91
What proportion of total variability is explained by this model? Round your answer to three significant digits.
Explanation / Answer
From Excel
From Excel
Coefficient of determination is0.920
92% total variability is explained by this model
SUMMARY OUTPUT Regression Statistics Multiple R 0.959202 R Square 0.920068 Adjusted R Square 0.905963 Standard Error 3.116087 Observations 21 ANOVA df SS MS F Significance F Regression 3 1900.073 633.3576 65.22735 1.56E-09 Residual 17 165.07 9.71 Total 20 2065.143 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept -40.2938 11.42917 -3.52552 0.002596 -64.4072 -16.1803 -64.4072 -16.1803 X1 0.732788 0.129566 5.655709 2.85E-05 0.459427 1.006148 0.459427 1.006148 X2 1.247969 0.353582 3.529501 0.002574 0.501976 1.993962 0.501976 1.993962 X3 -0.14768 0.150161 -0.98345 0.339175 -0.46449 0.169135 -0.46449 0.169135Related Questions
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