What Does Regression Analysis Tell You?

By Indeed Editorial Team

Updated December 30, 2021 | Published February 8, 2021

Updated December 30, 2021

Published February 8, 2021

If you want to predict future sales or better understand the correlation between two variables, consider using regression analysis. Regression analysis can help you develop in the business field and possibly boost a company's or organization's profits. In this article, we discuss what regression analysis is, what it's used for and how it works.

What is regression analysis?

Regression analysis is a statistical technique used for studying the relationship between two or more variables of interest. It has multiple variations depending on its intended use and how many variables are present, and it can help a business or company in several ways.

What is regression analysis used for?

Regression analysis is most often used for two reasons:

Making variable predictions

When a business or organization wants to predict a certain dependent variable, they might use a regression analysis. A business accomplishes this by inputting data for the independent variables and reviewing the effects it has on the dependent variable.

For example, if a company wanted to predict their projected sales income for the quarter (the dependent variable), they could use a regression analysis filling in the details for the number of salespeople they have on staff, the number of days in their sales quarter and the cost of their services (independent variables) to determine what their sales income might look like.

Estimating a variable effect

Another reason you might use regression analysis is to estimate how one independent variable may affect the outcome of the dependent variable. For example, if a colleague suggests that a company's outdated website (the independent variable) is having a direct impact on the company's sales, you can conduct a regression analysis on the theory to see if it might be accurate.

Predicting variables and estimating their effects with a regression analysis can help you confidently find and address challenges that a company is facing, as well as improve its products and services.

How does regression analysis work?

Regression analysis gives a value to one dependent variable and one or more independent variables and addresses how they interact with one another. For example, if you have a hypothesis that a book sells more copies if it has an esthetically pleasing cover, you could determine if there is a correlation between those two variables using these regression analysis steps:

Related: How to Write a Hypothesis

1. Create two sets of data

The first step in analyzing the relationship between the number of books sold (dependent variable) and how nice their covers looked (independent variable), is to create two sets of data. For the first set of data, take a random selection of books and record the number of copies they sold upon release.

Next, for each of the books in your first set of data, conduct a single-question survey to the buyers asking them: "Do you like the cover?". The answers to this question should create the second set of data that you can use to study the regression analysis.

2. Graph them

For this study, because there are only two sets of data and one independent variable you're examining, you can graph the results more easily. The y-axis of the graph can be labeled as the dependent variable, the number of books sold, and the x-axis can be labeled as your independent variable, how many buyers liked the covers. Next, combine the sets of data and graph their results using the corresponding axes.

3. Find any correlations

Once you have your variables graphed, you might begin to see some correlations in the data. For example, you might notice an increasing slope, possibly alluding to a positive correlation between books sold and how people liked the covers, or you might notice a downwards slope, possibly telling you that a fancy cover had a negative effect on how many books were sold.

However, it's also possible that the data might be so random that there is no correlation at all. If this is the case, you could consider collecting more data and see if your results differ, or you could consider changing your hypothesis altogether.

4. Find your regression line

Once you have your data graphed, if you're having trouble seeing a correlation, or you want to investigate your correlation further, consider drawing a line through the middle of your data. Though you can draw this physically using a straight edge and your best-estimated guess, there are also mathematical programs that can help you generate a more accurate graph and line through the center.

This line is known as the regression line, and it can help represent the relationship between your variables. The regression line can help you understand the positive or negative direction of the data and, if you're using a mathematical program, can also provide you with an exact formula that can help you calculate and predict different variables in the future.

Regression analysis variations

Here are a few examples of different regression analysis variations:

Simple Linear

Y = a + bX + ∈

Simple linear regression analysis uses one dependent variable and one independent variable. The example used in the previous section, "Do nice-looking book covers increase books sales?" would be an example of a simple linear regression analysis.

The variables of this equation are:

Y stands for the calculation of the dependent variable
a stands for the intercept of the regression line
b refers to the slope of the regression line
x represents the independent variable
∈ refers to the residual error

In a regression line and any regression analysis, there is always an error term that is included in the calculation because independent variables cannot predict the outcome of dependent variables with 100% accuracy.

Multiple linear

Y = a + bX¹ + cX² + dX³ + ∈

Multiple linear is a form of regression analysis that has one dependent variable, but multiple independent variables. For example, expanding on the previous hypotheses of book sales, along with book covers, if you think book titles and the size of books also contribute to how many copies sell, those can also be independent variables creating a multiple linear regression analysis.

The variables in this equation are:

Y stands for the calculation of the dependent variable
a stands for the intercept of the regression line
b, c and d refer to the slopes of the distinct regression lines
Each of the x's represent the values of every independent variable
∈ refers to the residual error

With multiple linear regression analysis, the independent variables must have different correlations with the dependent variable and varying slopes on their regression lines. Otherwise, if each regression line is similar to the next, the graph might become too difficult to understand.

Nonlinear

A nonlinear form of regression analysis uses dependent and independent variables whose relationship isn't easily defined by a normal linear regression line. Nonlinear regression analysis uses more complicated sets of data, and its regression line is often bent to better reflect the correlation between the variables.