This relationship is described by the model below. We must eventually decide if the model is useful to us. The methodology below will generate the best fit linear equation for almost any set of data. Remember, this does not mean there is a linear relationship. We begin by assuming that there is a linear relationship between the age of the propellant and shear strength. x is the independent variable - in this case, the age of the propellant. In this example, y is the shear strength. In regression, y is the variable we want to predict (the dependent variable). We start by determining the best fit linear equation. This will also allow us to predict the shear strength based on the age of the propellant. We can use regression analysis to quantify that relationship. It appears that as the age of the propellant increases, the shear strength decreases. As can be seen from the scatter diagram, there does appear to be a relationship. The scatter diagram for this data is shown below. Someone asked the question, "Is the age of the propellant related to the shear strength?" To answer this question, twenty paired observations of shear strength and age of the propellant were collected. The shear strength of the bond between two types of propellant is important in the manufacturing of a rocket motor. This is an excellent book on regression for those of you who want to learn much more about regression. This example is from the book Introduction to Linear Regression Analysis (Montgomery, Peck and Vinning, 4th edition, Wiley & Sons, 2006). The following example demonstrates how linear regression works. Next month we will explore how to tell if the relationship is significant. This month we will explore how the best fit linear equation is developed. This is one method of decreasing process variation. Linear regression helps us build a model of the process. The major objective is to determine if one variable can be controlled by controlling another variable. Linear regression helps us define this relationship. There is sometimes a straight line relationship between two variables. We often want to know how the changes in one variable affect another variable. Linear regression can be used to mathematically define the relationship between two variables. Our February 2005 publication explores scatter diagrams in more detail. It may be that one variable increases as the other increases or decreases. A scatter diagram examines the relationship between two variables. Linear regression is closely related to one of the basic SPC tools: the scatter diagram. This month is the first part of a series on linear regression.
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