A Look into Regression Analysis

Data is a vital asset to modern economics. Whether you are a consumer or a producer, you need data to make informed decisions. At work, you will need to make a data-driven decision to present more accurate information about the task you may be working on. And it is through stored data that we get to know about the economies of the past and relate that to current or future situations. Econometrics is a branch of economics that deals with economic relations. In other words, statistical data is used to understand the previous process and how they affect the current situation.

But many people confuse econometrics with statistics because these terms deal with data altogether. They are very different, though, and should not be used to mean the same thing. 

The relationship that exists is based on how econometrics uses statistics to establish models and or find clearer information about a particular subject. Data has become a critical asset to modern economies, and only those who know how to use it will benefit. The availability of data is necessary for a maximum input of workers within an organization, whereby every decision they make can be backed by facts and probably used to encourage more findings.

But do you know how to parse through all the data at your disposal? This is the most important question you should be answering. We always have data around us, but many people do not know how to put it into maximum profitability. And the good news is, you may not even have to do the numbers yourself. If you have experts working on the number, you probably won't have to struggle yourself working your way out. Nevertheless, you still need to understand how to understand and interpret the analysis created by others in the correct manner.

There are many ways to do this. And one of the most popular methods is through regression. For many years, companies have been using data driven-approaches to create the best environments for their employees as well as their products on the market. Tom Redman, in his book, "Data-Driven: Profiting from Your Most Important Asset," gives guidance to companies on how to maximize their data and data quality programs.

Regression Analysis in Details

Not that you understand the importance of data, it should be easy to explain what regression analysis is all about and how to do it. Consider the example that Redman offers. Think about a situation where you are the sales manager, and you are trying to figure out what next month will turn out like – to predict the numbers for the coming months. As you may already know, there are many factors that influence the production of a company, including but not limited to competition's promotions, the weather, rumors of new and improved models, and the general business environment. Sometimes the people in your organization may have already established several theories on what might affect sales more in your organization. One may say the rains always affect how they sell, whereas others may quote several weeks of competition's proms.

One needs a sort of which of these variables has the most substantial impact. And there are many ways to do this. Some just look at consumer behaviors, others at the general market orientation, whereas others may just base their findings on assumptions. The mathematical sorting out of the most impacting variable is called regression analysis. In this case, it seeks to answer the following questions:

- Which factors are of the uttermost importance?

- Which variables should be ignored?

- How do these factors relate to and affect each other?

- How sure are we about these variables?

The last question is perhaps the most important because it establishes the ground for a more substantial decision-making process. It creates an environment where everything can be related to numbers, and a large percentage of the prediction comes true.

Note that, the factors that affect decisions in this regard as known as variables. And there are two major types of variables:

- Dependent variables. These are factors that you are trying to understand or predict. In other words, it is what you are trying to learn or improve. In the example above, monthly sales are the dependent variable – upon which the other variables are built.

- Independent variable. Take, for instance, you have established that a pandemic that broke out a few months ago is likely to extend into the next few months, and affect your sales negatively. This becomes an independent variable. They are the factors that you suspect to will affect the dependent variable.

Regression analysis is very crucial to the general economy. One firm's decision may not have a large impact on the whole market or economy, but when several companies are involved, it becomes catastrophic to the economy. Hence, it is important for economies to understand factors that may impact their growth negatively and positively in order to make shielding decisions.

How regression works

We have already seen the importance of regression analysis in business. But it is more crucial to understand how it works, or else you may not fully understand its impacts. There are several things that are involved in this process, as shown below:

Gathering data

There is no business or economy that grows without data analysis. Even the daily person needs data to establish their consumption needs and go for what is most important. Such data could be in form or budget limitations expenses from the previous months. Likewise, once you, as the sale manager in the example above, has come up with a list of most crucial variables in the questions above, you will need to gather data on them. And just to remind you, there are many sources of data, and you don't have to go directly into the field again to find it. One good source is what your colleague has already done. It can help you save time, especially if you are working on a short period.

For instance, you can take all the sales numbers within the organization over the past two years and calculate the average monthly rainfall for the same time. In order to establish the best data, you can plot this information on a chart, which is the first step of figuring out the information you need. Graphs help us understand the direction certain processes are taking in order to predict the most probable outcomes.

Once you have these data, you need to establish a relationship between them. Let's say you have the number of sales on the y-axis (remember this is the dependent variable, what you are interested in studying, and that it is always plotted in the y-axis), and on the x-axis, you have the total average rainfall. You can have each month's data represented by a certain color, like blue dots. This should indicate on the graph how much it rained that particular month and how much sales were made.

When you look at the data closely, you may have noticed that sales were the highest in the days it rained the most. This is very interesting to capture, but also by how much. For instance, how much sales will you achieve if it rains by three inches, or by four? Now, if you draw a line that runs roughly through the middle of the data points, it will help you answer these questions with some certainty. You want to know how much you will probably sell when it rains by a known amount. This may be all the data you need to make your decisions on where to focus your next month's sales.

Build the regression model

A model is like a map that carries the representation of what the ground situation should be. Models are very crucial in making economic analysis and decisions because they can be carried directly into a real-life situation. Without modeling, it can be very hard to do work with numbers in a real-life situation. Econometric models use statistical data, just like the sales and rainfall information over a specified period shown above.

Think of the line you have drawn through the middle of the graph – it is called the regression, and it is drawn to bring out the line that describes the data most appropriately. This line is drawn on the graph using special applications like SPSS or STATA, though Excel also works well. As Redman explains, the red line is the perfect representation of the link between the variables. Apart from drawing the line, programs used in statistics can also outline the best formula that explains the slope of the line. It may look like this:

Y=100+3x + error term

For now, you don't need to worry about the error term. It only means that it lacks perfect precision in the regression. The most important model for you is Y = 100 + 3x.

What does this formula mean? That when there is no "x" then "y" is equal to 100. When we consider historical data where there was no rain at all, the average sales were 100, and you may expect the same results if the variables don't change. Additionally, for every extra inch of rain, the sales team made ten more sales. This is represented generally as "for every increment where x goes higher by one, they increase by 10," as stated by Redman.

We have not forgotten about the error term. Now, looking at the figures and how the rain has affected sales in the past, one may be tempted to assume that for every extra inch, there are ten additional sales. However, where this variable is important depends on the error term. And there is always an error term in the regression line. This is because, in real life, dependent factors are never perfect predictors of independent factors. Instead, the line is only used to estimate figures based on the available information. The error term is important because it explains how certain one should be about the formula. If the error term is too large, for instance, it means the regression line is less certain.

We have used the rain to predict rain in the example above – which is only one variable. But before you start regression analysis, you need to come up with several dependent factors. In other words, you can include in the graph information about competitor's promotion alongside the rain data. Redman suggests that you should just keep doing this until the error term has been completely reduced because you are attempting to know the line that best explains your data. Indeed, there is always danger in trying to include so many variables in the regression analysis; however, expert analysis already knows how to maximize these risks and come up with more useful information. Besides, the most significant advantage of regression is looking at many variables at the same time. It gives you a wider perspective of the situation on the ground.

How Do Firms Apply Regression Analysis?

Redman says, "regression analysis is the go-to method of analytics." Hence, a smart company will want to use it in making all decisions regarding business issues. Managers always want to figure out how to make an effective contribution to sales and achieve great employee retention or recruit new people on the team. They need data to help them understand what to expect next. A good number of companies use regression analysis to explain a specific occurrence they want to understand more. For instance, one may want to know why customer service sales dropped in the previous month. They can also use it to predict the future, like how much sales to be expected over the next ten months. Sometimes they use the data to understand what they need to do next – for instance, whether to go for a promotion or introduce a different product.

When it comes to understanding regression analysis, it is important to note that correlation is causation. Whenever you are working with any analysis that tries to establish how one factor affects the other, it is always to put this in mind. Why is this important? Because we can easily state that there is a coexistence between rain and monthly sales, and regression approves this relationship. But we cannot say for sure that rain caused the sales – at least for most products.

Author: James Hamilton