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 of the HEC (Y) produced along with the viscosity of the 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 inputs in the production process relate to viscosity of the final HEC product.

a. Prepare scatter plots showing the relationship between HEC viscosity and each of the independent variables. What sort of relationship does each plot suggest?

b. Using the variables in this data set, what regression model has the highest R2 value? What is its R2 value?

c. Using the variables in this data set, what regression model has the highest adjusted R2 value? What is its adjusted R2 value?

d. Suppose 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 of 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?