Goldtone Chemical Company is developing a new stain-resistant liquid product that can be applied to different types of fabric. The product can be manufactured in different ways that result in different costs and differing levels of stability for application once the product is opened and exposed to air. The stability of the product (measured in minutes) (Y) depends on its acidity (measured by pH level) (X₁) and the ounces per gallon of product of two different raw materials (X₂ and X₃). Additionally, the company believes the total amount of raw material per gallon (X₄) and the ratio of raw material 1 to raw material 2 (X₅) might affect the stability of the product. The company ran a series of experiment with different levels of acidity and raw materials 1 and 2, and tested the stability of the resulting product. Data from these experiments may be found in the file FabricTreatment.xlsx.

a. Prepare a scatter plot of the stability variables against each of the potential independent variables. What do these plots suggest?

b. How many potential regression functions exist for this data set with five independent variables?

c. What regression function is identified if you employ the technique of forward stepwise regression? What is the adjusted-R² value for this model?

d. Regardless of your answer to the previous question, what regression function do you obtain using X₁, X₃, and X₄ as the independent variables in the model? What is the adjusted-R2 value for this model?

e. What do you learn from your answers to the previous two questions?

f. Using the previous model in part (e), develop an approximately 95% prediction interval for the stability of the product with a pH of 5, 1.5 ounces of raw material 1, and 6.5 ounces of raw material 2.

g. Referring to the previous question, suppose the company wants to adjust the amount of raw material 1 so that the lower limit of the 95% prediction interval is 15. How much raw material 1 is required?