Hydroxyethyl cellulose HEC is a gelling and thickening agent

Hydroxyethyl cellulose (HEC) is a gelling and thickening agent created from a molecular combination of cellulose, ethylene oxide (EO), and nitric acid. It is designed to mix with a water-based solution to increase the viscosity of the mixture. This added viscosity acts as a suspension polymer that, for example, allows the herbs in a salad dressing to stay in the solution and not settle to the bottom of the bottle. Gaston Moat is a manufacturing engineer for the Atlas Corporation which is one of the major manufacturers of HEC in the United States. He has collected the data given in file Dat9-20.xlsx from several production lots of HEC. For each production lot, he recorded the viscosity if the HEC (Y) produced along with the viscosity of the cellulose material used (X1), the square root of the viscosity of the cellulose material used (X2), the length of the cellulose fibers used (X3), the amount (in pounds) of cellulose used (X4), the amount (in pounds) of EO used (X5), the temperature of the nitric acid used (X6), and the ratio of cellulose to EO used (X7). Atlas\' customers often specify the average viscosity level needed for a particular HEC application. Gaston would like to build a multiple regression function to better understand how the various impacts in the production process relate to viscosity of the final HEC product.

a. Supppose a customer wants a batch of HEC with an average viscosity level of 7000. Gaston plans to fill this order using a batch of cellulose with a viscosity level of 20,300, an average fiber length of 30, and a nitric temperature of 50. How much EO should he plan to use in this batch to achieve the desired HEC average viscosity level?

Data table:

Solution

using minitab with respect to all the data given the multiple regression equation of Y on X1,X2,X3,X4,X5,X6,X7 is

Y = - 98901 - 5.44*X1 + 1582*X2 - 88.0*X3 + 0.143*X4 - 0.652*X5 - 19.8*X6
    - 1421*X7

now he want to estimate the EO that is he wants to find predicted value of X5

so the multiple regression of X5 on Y,X1,X2,X3,X4,X6,X7 is

X5 = - 28686 - 1.76*X1 + 515*X2 - 15.1*X3 + 0.707*X4 - 0.183*Y + 5.1*X6
     - 5314*X7

given that Y=7000   X1=20300 so X2=20300^0.5=142.4781 X3=50 but value of X4 is not given.

hence the prediction can not be done. hence the conclusion is that the given data at part a) is inconsistent.