An experiment carried out to study the effect of the mole contents of cobalt (x1

Question

An experiment carried out to study the effect of the mole contents of cobalt (x1) and the calcination temperature (x2) on the surface area of an iron-cobalt hydroxide catalyst (y) resulted in the accompanying data. You can use Excel or Minitab to find the regression model.

(a) What is your estimator of the regression line?

(b) Predict the value of surface area when cobalt content is 2.6 and temperature is 250, and calculate the value of the corresponding residual.

?

(d) Calculate the residuals, SST, SSE, and SSR.

x1 x2 y 0.6 200 90.6 0.6 250 82.7 0.6 400 58.7 0.6 500 43.2 0.6 600 25.0 1 200 127.1 1 250 112.3 1 400 19.6 1 500 17.8 1 600 9.1 2.6 200 53.1 2.6 250 52.0 2.6 400 43.4 2.6 500 42.4 2.6 600 31.6 2.8 200 40.9 2.8 250 37.9 2.8 400 27.5 2.8 500 27.3 2.8 600 19.0

Explanation / Answer

a) From Excel

The fitted model is

y=124.9 - 11.34x1 -0.15 x2

b) when x1=2.6 and x2=250

y=124.9 - 11.34*(2.6) -0.15*(250)

y=57.916

d)

SUMMARY OUTPUT Regression Statistics Multiple R 0.782444 R Square 0.612218 Adjusted R Square 0.566597 Standard Error 21.09809 Observations 20 ANOVA df SS MS F Significance F Regression 2 11946.87 5973.434 13.41955 0.000318 Residual 17 7567.2 445.1294 Total 19 19514.07 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 124.8788 15.7121 7.947936 3.99E-07 91.72915 158.0284 91.72915 158.0284 x1 -11.3369 4.898591 -2.31432 0.033417 -21.6721 -1.0018 -21.6721 -1.0018 x2 -0.1461 0.031521 -4.63498 0.000237 -0.2126 -0.0796 -0.2126 -0.0796

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