# Application of Regression Analysis in Business

The application of regression analysis in business helps show a correlation (or lack thereof) between two variables. Using basic algebra, you can determine whether one set of data depends on another set of data in a cause-and-effect relationship. You might already suspect that your sales figures depend on the time of day, for example, but a regression analysis provides hard evidence to prove or disprove your hypothesis.

The uses of regression analysis in business can influence every aspect of your company, from efficient use of resources to planning marketing efforts for maximum impact. The key is to collect accurate data for unbiased results and correctly choose the independent and dependent variables for each regression analysis. From there, you don't need to worry too much about remembering your high school algebra classes. You can use spreadsheet software like Microsoft Excel or Google Sheets to run a regression analysis and then interpret the results yourself.

## Collecting Accurate Data

First, you'll want to make sure that the data you collect is accurate. Accurate data is crucial for **reducing the margin of error**. You don't want to get a false positive and completely revamp a process or campaign for little to no return. In general, automated computer systems will give you better results than handwritten data collection.

For example, say you wanted to look at whether you tend to sell high-price items at certain times of the day. If you use a computer program to log all sales, you should be able to export this data with times logged to the second. If you rely on handwritten notes, chances are that you'll get busy and forget to write things down right away, or you'll end up estimating the price and time.

Keep in mind that the more data points you can collect, the more accurate the regression analysis will be. An ideal minimum target is 100 data sets. Anything less than 25 sets is unreliable, and the more sets you have, the more accurate your analysis will be. In scenarios where the data is limited to begin with, just work with what you can get and take the results with a grain of salt.

## Determining the Independent and Dependent Variables

You'll also need to make sure you identify which of your data sets is independent of the other and which one may be dependent on the other. The time of day is always an independent variable because no matter what we do, we cannot influence it. On the other hand, the amount of people shopping for your products and services *depends* on the time of day, so the number of shoppers is the dependent variable in this situation.

Determining the dependent variable for a regression analysis is always just a guess in the beginning. The dependent variable may not depend on the independent variable whatsoever. That's the point of the regression analysis: **Does this variable depend on this other variable?**

For example, a person's height has nothing to do with the time of day in which the person shops. However, you can still label them as independent (time of day) and dependent (height) variables in order to perform a regression analysis to tell you that no relationship exists. "No correlation" variables are not always this obvious to pinpoint, which is exactly why you have to do a regression analysis in the first place.

## Performing a Regression Analysis

Before you worry about formulas and calculators, learn how to perform a regression analysis in a **spreadsheet program** like Microsoft Excel or Google Sheets. Simply enter your data sets in two columns to start. In Excel, go to the Data tab and click "Data Analysis." Once a window pops up, you'll select "Regression" and then input the range for your X (independent) and Y (dependent) variables.

A linear regression calculator does not come standard in Google Sheets, but you can download a free add-on tool that makes it easy to do so. Go to the Add-Ons tab and select "Get Add-Ons." From there, search for "regression analysis" to find plenty of tools that will allow you to perform this mathematical function. When you're ready to use it, just go back to the Add-Ons menu, hover over the one you chose for regressions and then click "Start."

## Interpreting the Regression Data: R Squared

Once you successfully complete the regression analysis on these spreadsheet programs, some numbers and letters will display on your spreadsheet. Unfortunately, the regression analysis programs don't come with an interpretation cheat sheet. It's up to you to determine what each statistic means and to decide whether the dependent variable correlates to the independent variable.

R-squared, also called the coefficient of determination, is one such statistic, and it shows how closely the data points match the line of best fit on a scale of 0 to 1. In other words, if you were to plot the data points on a graph and draw a straight line through them, would the line pass through each of the data points? If so, R-squared would have a value of 1, but that would be in a perfect scenario.

In general, **a higher R-squared is desirable**. However, lower R-squared values don't automatically mean there's no correlation between data sets, especially when the dependent variable is a human behavior. After all, human behavior is inherently unpredictable.

## Understanding the P Value

The P value is another statistic displayed on a spectrum of 0 to 1 that you'll see after a regression analysis. Unlike R-squared, the P value tells you **how likely it is that there is no correlation whatsoever**. A high P value tells you that it's likely there is zero correlation, whereas a low P value indicates that the two variables are correlated.

If the outcome of the dependent variable truly does depend on the independent variable, the P value will be low. If you're way off base and comparing apples to oranges, the P value will be high.

## Common Uses of Regression Analysis in Business

When you know the importance of regression analysis in general, you can understand some of the common uses of regression analysis in the business world in particular. You can perform a linear regression analysis after virtually any type of A/B test to determine if one of your variables (A or B) led to a statistically significant improvement in results. Even if the results of your A/B testing seem to lean a certain way, further examination with a regression analysis can give you unbiased insight.

Using a regression analysis to understand **how customers react to different price points** can also help you target your marketing campaigns and maximize your revenue. The price of an item represents the independent variable, and you can play with all kinds of dependent variables to determine which demographic is most likely to make a higher purchase. Maybe it's men between the ages of 40 and 44 who are willing to pay premium prices for your products, whereas women between the ages of 55 and 59 prefer to wait for sales. Why would you waste your ad budget by showing sale ads to men between the ages of 40 and 44 and vice versa?

The key is to stay curious and creative. How does one factor affect another? If you can collect accurate data, it's easy enough to perform a regression analysis and discover the answer.