Regression Analysis in Plain Language
Simply stated, regression analysis is a statistical method that determines the extent to which a relationship exists between two variables. If the relationship is strong enough, one can then accurately predict the values of one variable based on the values of another using a simple linear formula.
There are many different types of relationships that can be identified, such as a curvilinear, u-shaped, or exponential relationship. However, the more common relationship, and the relationship that enables one to easily predict the value of a dependent variable, is the straight-line linear relationship.
To determine whether a relationship exists between two variables, one must plot the values on a graph, in which the independent variable is on the X-axis and the dependent variable is on the Y-axis. Since the dependent variable is what one is hoping to predict, the simple linear formula is Y = bo + b1X, in which:
- Y is the value of the dependent variable
- b0 is the Y-intercept, which is the value of Y when X=0
- b1 is the slope, which is the change in Y per one unit change in X
- X is the value of the independent variable
Using a regression analysis, one can accurately identify the best-fit line to minimize the variance between the sample data values and the imposed line. Once the best-fit line can be identified, the variables on the right-hand side of the simple linear formula can be calculated, enabling one to accurately predict the value of Y.