The use of high-strength steels (HSS) rather than aluminum and magnesium alloys in autom...

The use of high-strength steels (HSS) rather than aluminum and magnesium alloys in automotive body structures reduces vehicle weight. However, HSS use is still problematic because of difficulties with limited formability, increased springback, difficulties in joining, and reduced die life. The article “Experimental Investigation of Springback Variation in Forming of High Strength Steels” (J. of Manuf. Sci. and Engr., 2008: 1–9) included data on y = springbackfrom the wall opening angle and x₁ = blank holder pressure. Three different material suppliers and three different lubrication regimens (no lubrication, lubricant #1, and lubricant #2) were also utilized.

a. What predictors would you use in a model to incorporate supplier and lubrication information in addition to BHP?

b. The accompanying Minitab output resulted from fitting the model of (a) (the article’s authors also used Minitab; amusingly, they employed a significance level of .06 in various tests of hypotheses). Does there appear to be a useful relationship between the response variable and at least one of the predictors? Carry out a formal test of hypotheses.

c. When BHP is 1000, material is from supplier 1, and nolubrication is used, . Calculate a 95% PI for the spingback that would result from making an additional observation under these conditions.

d. From the output, it appears that lubrication regimen may not be providing useful information. A regression with the corresponding predictors removed resulted in SSE = 48.426 . What is the coefficient of multiple determination for this model, and what would you conclude about the importance of the lubrication regimen?

e. A model with predictors for BHP, supplier, and lubrication regimen, as well as predictors for interactions between BHP and both supplier and lubrication regiment, resulted in SSE = 28.216 and R² = .849. Does this model appear to improve on the model with just BHP and predictors for supplier?