When you’ve got two variables, it might be the case that you want to work out the strength and worth of their relationship. A business owner, for example, may want to utilise regression analysis to work out the relationship of the two variables by examining his company’s profits and sales over a defined period of time. The regression analysis results will tell him how valid the relationship between the variables (sales and profit) is. Ergo, it will tell him whether one influences the movement of another. It will also tell him how much, and whether one doesn’t influence the movements of the other at all.

Taking it further, a business can use regression analysis to determine what exactly was responsible for their huge profits last year. They can even use regression analysis to estimate their businesses future value because, by determining the relationship between two events, a business owner is able to use this information to maximise their relationship in a bid to make his company more profitable.

For example, if sales of a particular product were responsible for profits, whilst sales of another product had nothing to do with profits, the business owner can use this information to increase production of one profit whilst discarding the other. Data extracted from a quantative data analysis allows him to do this.

## How to Do A Regression Analysis

To carry out a regression analysis, you need to:

- First, identify the exact relationship between the two (or more) variables you are using. The value of each variable – dependent variable and independent variable – are related to one another. For example, your dependent variable may be sales, and your independent variable may be profit. The sales variable is dependent whilst the profit variable is independent. If there is only one variable, we call it an independent variable, whilst the model is known as a simple regression model.
- Second step of knowing how to do a regression analysis is knowing how to do a linear regression. Essentially, you need to determine whether what you are working with is a linear regression. We refer to a regression analysis as linear when the relationship between the variables can be viewed as a straight line. When something moves from beginning to end without going back on itself, it’s linear. On your chart, what you really want to see is a straight line, with your data points gathered around it.
- Thirdly, if your variables don’t have a linear relationship, it’s possible to alter them so that they become linear. It makes things easier to have a linear regression analysis, but if it isn’t possible, you may need to look for alternative independent variables to help you work out the value of the dependent variable.
- Fourthly, a regression model can be forecast by using a technique we refer to as ordinary least squares. The result are formulas for the intercept and slope of a regression equation that comfortably slot into the relationship between your variables as close as can be.
- Fifthly, you need to extract your coefficient of variation (R²) to understand how your regression model slots into the relationship between the variables. The coefficient of variation may assume a value that lies between 0 and 1. The closer it gets to 1, the better chance you have of understanding your data.
- Sixth, you need to carry out a multiple regression equation to forecast the relationship between your dependent variable and multiple independent variables. The accuracy of the results can be aided by a hypothesis test. This could be a hypothesis that states that the slope coefficients of your regression model amount to 0.
- Seventhly, you need to carry out your hypothesis test(s) on individual regression coefficients. You need to do this to understand if your estimated coefficients are statistically significant. If they are, you have a greater chance of determining the value of the dependent variable.
- At the end of it all, you can interpret your results, before using them to forecast future values.