What is multiple regression analysis? We will explain it to beginners, including a marketing perspective!

Multiple regression analysis is one of the analysis methods used in statistics, and is used when you want to predict the future. The “heavy” in multiple regression analysis has the meaning of multiple, and the “regression” has the meaning of a causal relationship. However, although many people have heard of the term multiple regression analysis, many people do not know in what situations it should be used or how to use it in the first place.

In this article, we will provide an overview of multiple regression analysis, how it differs from simple regression analysis, and explain the steps to perform multiple regression analysis. We will also explain several points to be aware of when performing multiple regression analysis, so please refer to them.

What is multiple regression analysis?

First, I will explain the meaning of multiple regression analysis. Multiple regression analysis is an analysis method used in statistics, where multiple indicates multiple relationships and regression indicates causal relationships. Multiple regression analysis is used when you want to explain a certain result, such as a target variable, by analyzing multiple factors related to the explanatory variables and examining how much causal relationship each has with the target. . In addition, since we can understand the cause and effect relationships between each, it is possible to make future predictions based on them.

For example, let’s say there is a taxi company that has 20 offices across the country. In multiple regression analysis, we will analyze the number of employees, number of cars that can operate per day, number of users per day, time of day, distance from the station, etc. for this taxi company. Based on these results, multiple regression analysis is used to determine the area in which the taxi office should be opened, the number of employees, and the number of taxis.

In other words, multiple regression analysis is one of the most important analyzes for increasing the probability of business success, and is useful when predicting sales and formulating marketing strategies.

Difference between simple regression analysis and multiple regression analysis

We have provided an overview of multiple regression analysis. However, many people may not understand the difference between this and simple regression analysis. In conclusion, making predictions for the future based on one factor is called simple regression analysis. For example, let’s say you earn 10 million yen in sales for a monthly advertising expense of 1 million yen. From this, we can see that 1,000% of advertising costs are returned as sales. In this way, the outline of simple regression analysis is to analyze the future with respect to one factor, advertising expenses.

Multiple regression analysis, on the other hand, performs analysis based on multiple factors, such as advertising costs, advertising area, age and annual income of users, and concerns they have. Multiple regression analysis is often used in small business and marketing to increase the probability of success. However, when launching a large-scale campaign or spending more than a certain amount on advertising, simple regression analysis is sometimes used to increase awareness of a product or service.

Multiple regression analysis is compatible with “factor analysis” and “predictive analysis”

So far, we have provided an overview of multiple regression analysis and explained how it differs from simple regression analysis. Multiple regression analysis can support the following two types of analysis.

Let’s look at each in turn.

Factor analysis

First, multiple regression analysis allows analysis of each factor. For example, using the taxi company mentioned above, factors include the number of employees, number of taxis, time of day, and distance from the station. Factor analysis then analyzes how much impact these factors have on a taxi company’s sales and number of customers. If the factor that has the most impact on sales is “distance from the station,” then we can hypothesize that taxi offices should be located within 5 minutes from the station. In other words, factor analysis is about forming a hypothesis as to what factors should be given the most importance in terms of goals such as sales and number of customers.

Predictive analytics

Multiple regression analysis can also perform predictive analysis. In predictive analysis, the items identified in the factor analysis described above are replaced with numerical values.

Note that multiple regression analysis involves multiple explanatory variables (factors), so the formula is expressed as “y=ax1 + bx2+C”. a and b are called coefficients, and C is called a constant term (intercept), and a constant term is not affected by changes in explanatory variables. If, among the factors mentioned above, the factors with the greatest influence are “distance from the station,” “number of employees,” and “number of taxis,” the equation is “sales (y) = 0.5 x distance from the station + 0.3. × Number of employees + 0.1 × Number of taxis + 0.8.” The numbers listed above are samples, but with predictive analysis using multiple regression analysis, you can apply different numbers to the current numbers and use them to predict future sales. Therefore, it can be said to be useful when starting a new business or opening a new office.

As an example of sales analysis, multiple regression analysis is introduced in detail in
the Statistical Analysis Institute
column.

Steps to perform multiple regression analysis

Up to this point, I have explained about multiple regression analysis, but many people may not know exactly how to perform it. From here, we will explain the steps to perform multiple regression analysis.

Let’s look at each in turn.

Determination of objective variables

First, let’s decide on the objective variable. Basically, there is no problem if you decide according to your business model and management strategy. Most of the objective variables in multiple regression analysis are determined by sales, number of customers, etc.

Consider explanatory variables

After determining the objective variables, the next step is to consider explanatory variables. For example, suppose the objective variable is “sales of 10 restaurants nationwide.” There are countless possible explanatory variables, but the most typical ones are listed below.

From these, we will decide on the explanatory variables that have a particular impact on the objective variable of sales. One thing to keep in mind is that if you include too many explanatory variables, it will be difficult to obtain detailed data for each analysis, so it is important to narrow it down to only important variables.

Actual data collection and analysis

Once the objective variables and explanatory variables have been determined, we can move on to the stage of actually collecting data. At this time, it is very important to decide on a specific period, such as one month or one year. This is because by determining the period, you can compare each factor and identify more optimal measures and improvement plans.

Develop marketing strategies based on predictions

Once you’ve collected data over a set period of time, use the predictions to develop your marketing strategy. For example, let’s say that prior to the analysis, you predicted that location would have a greater impact on sales than advertising costs. However, if you find that advertising costs actually have a greater impact, consider strategies such as increasing your monthly advertising budget.

In addition, we will consider which media to invest advertising costs in, based on the age group and market size of the customers who are seeking our products. If you can understand each factor in detail through multiple regression analysis, you can safely assume that the probability of success for your business or service will increase.

Points to note when performing multiple regression analysis

So far, we have explained the steps to perform multiple regression analysis, but it is important to understand the following two points.

I will explain each in turn.

Convert all variables into numbers

First, be sure to quantify all variables. For example, gender and parenthood are indicators that cannot generally be quantified. However, it is important to always quantify it, such as 0 for men and 1 for women. This is because all non-numeric indicators are difficult to analyze and it is not possible to make specific predictions for each factor. Even if you have qualitative variables other than numbers, be sure to convert them to numbers before performing analysis.

Don’t add too many explanatory variables

As I explained a little earlier, it is important not to increase the number of explanatory variables too much. This is because if there are too many explanatory variables, the influence of each explanatory variable on the target variable will become small, making it impossible to obtain useful data.

Generally, it is said that around 7 explanatory variables are good for multiple regression analysis. Therefore, let’s narrow down the analysis to the explanatory variables that are most likely to have an impact. If you are unable to obtain useful data after performing an analysis, you can simply change the explanatory variables used in the next analysis.

summary

In this article, we explained the overview of multiple regression analysis, the difference from simple regression analysis, and the steps to perform multiple regression analysis. Multiple regression analysis allows you to perform factor analysis and predictive analysis, allowing you to predict the impact each factor will have on sales and sales when launching a new business. In other words, it can be said to be one of the indispensable analytical methods for doing business.

In order to solve current issues and increase the probability of business success, why not try multiple regression analysis first?