3. In the oil industry, water that mixes with crude oil during production and tr

Question

3. In the oil industry, water that mixes with crude oil during production and transportation must be removed. Chemists have found that oil can be extracted from the wateroil mix electrically. Researchers conducted a series ofexperiments to study the factors that influence the voltage required to separate the water from the oil (y). One study is on the effect of the disperse phase volume (X1), the salinity O2) and the surface concentration CX3). A first-orderlinear) model is fitted to the data and the computer output is shown below. (0 points) ANOVA MS Df SS p value Regression 2 7.11562 3.55 8.9628 0.0022 Residual 12 3.18 0.2646 Total 15 10.2912 Standard Error Coefficients Stat p-value Intercept 0.385 0.6002 0.6415 .256 0.0064 X1 -0.02 0056 3.1880 0.0857 0.17 1.9828 0456 0.46 0.1286 3.5768 0025 a. Based on the output, write down the estimated model. b. Interpret the estimated slope for predictor X2,the salinity.

Explanation / Answer

a) The estimated model is

Y = 0.385  - 0.021 X1 + 0.17X2 + 0.46X3

b) The oil decreases 2.1% when the effect of the disperse phase volume (X1) has one unit increases

c) P-value 0.0022 < alpha 0.01, we rejct H0.

Thus we conclude that the model is significant

The estimated equation is best fit to the given data

d)

H0: Slope of coefficient salinity (X2) is equal to zero

H1: Slope of coefficient salinity (X2) is not equal to zero

P-value of salinity X2 is 0.0456 which is > alpha 0.01, we accept H0

Thus we conclude that Slope of coefficient salinity (X2) is equal to zero

i.e. the increase of the salinity (X2) is not accompanied by an increase in the voltage required to separate the water from the oil (y)

e)

H0: Slope of coefficient surface concentration (X3) is equal to zero

H1: Slope of coefficient surface concentration (X3) is not equal to zero

P-value of surface concentration X3 is 0.0071 which is < alpha 0.01, we do not accept H0

Thus we conclude that Slope of coefficient surface concentration (X3) is not equal to zero

i.e. there is sufficient evidence to indicate this interaction

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