Multiple Linear Regressions (MLR) is best used when which of these are applicable? (Note: There are 3 correct answers).

Multiple Linear Regression (MLR) is a statistical method used to model the relationship between a single dependent variable (Y) and two or more independent variables (X's). Its application is appropriate when these conditions are met. A fundamental assumption for building a valid and interpretable MLR model is the absence of high correlation among the independent variables (X's), a condition known as multicollinearity. In the context of process improvement methodologies like Lean Six Sigma, MLR is a valuable tool in the Analyze phase. It uses historical data to identify significant relationships between inputs and outputs, which can sometimes provide enough information to make effective process changes, thereby avoiding the greater time and expense of conducting a Designed Experiment (DOE).

A. MLR is predicated on the assumption of linear relationships between the independent variables and the dependent variable; non-linear relationships require different techniques.
B. All regression analyses quantify uncertainty in coefficient estimates (slopes); this is a characteristic of the output, not a primary reason for choosing the MLR method.

1. Pennsylvania State University. (n.d.). STAT 501: Regression Methods, Lesson 5: Multiple Linear Regression. PennState Eberly College of Science. Retrieved from https://online.stat.psu.edu/stat501/lesson/5.

Section 5.1 explicitly defines the MLR model as relating a response Y to multiple predictor variables (X's), supporting option C.

Section 5.4 lists the assumption that "the predictor variables are not highly correlated with each other" (i.e., no multicollinearity), supporting option E.

2. Montgomery, D. C. (2019). Design and Analysis of Experiments (10th ed.). John Wiley & Sons.

Chapter 1, Section 1.3, p. 13 discusses the use of regression modeling on historical or observational data as a preliminary step. It notes that while powerful, these observational studies can have limitations, which leads to the use of DOE. This supports the practical application where a successful regression analysis may preclude the need for a DOE, as mentioned in option D.

3. Tjahjono, B., Ball, P., Vitanov, V. I., Scorzafave, C., Nogueira, J., Calleja, J., & Minguet, M. (2010). Six Sigma: a literature review. International Journal of Lean Six Sigma, 1(3), 216-233. https://doi.org/10.1108/20401461011075017

Page 225, Table II shows that Regression Analysis is a key tool in the "Analyze" phase of DMAIC for data analysis, while Design of Experiments (DOE) is primarily used in the "Improve" phase for solution implementation and optimization. This sequential placement supports the idea that regression on existing data is used first and can potentially prevent the need for a subsequent DOE, aligning with option D.