## What is Simple Linear Regression Analysis

Simple linear regression analysis is a statistical tool for quantifying the relationship between *one *independent variable (hence "simple") and one dependent variable based on past experience (observations).

Based on entering a reasonable number of observations of the independent and dependent variables, regression software will compute the best fitting *straight line* (hence "linear") that expresses the average relationship between the dependent and independent variable.

Simple linear regression analysis is helpful in determining the two components of a mixed cost (also known as semivariable cost):

- The amount that is fixed or constant
- The variable rate (the rate by which the total cost changes when there is one additional unit of the independent variable)

## Example of Simple Linear Regression Analysis

Assume that a manufacturer wants to know the amount of its monthly electricity bill that is a fixed amount and how much the electricity bill changes when the number of production machine hours change. The manufacturer will look at the amount of each month's electricity bill (the dependent variable) and then determine the number of production machine hours (the independent variable) that occurred between the meter reading dates indicated on the bill.

The amount of each bill and the related production machine hours for the bill are entered into the regression software. The software determines the best fitting line based on the amounts entered. The line is expressed as *y = a + bx*, where:

**y**is the estimated monthly electricity cost (the dependent variable)**a**is the average fixed amount of a monthly electricity bill- b is the rate per machine hour that causes a change in the monthly electricity bill
- x is the number of production machine hours (the independent variable) for the period of the electricity bill

The software will also provide statistics for the following: correlation, confidence, dispersion around the line, and more.

In all likelihood there will be more than one independent variable that causes the change in the amount of the dependent variable. The multiple independent variables along with the dependent variable for each observation can be entered into *multiple regression software.*

It's always wise to review a graph of the past observations. You may be able to see a pattern of the points as well as any outlier(s). Also keep in mind that correlation does not guarantee there is a cause and effect relationship.