What is a linear regression and what is it used for?
Franco Brutti
Have you ever wanted to know what will happen in the future? Well, there’s a mathematical formula that can help you in this regard and it’s linear regression.
This model is easier than many people think and it provides you with a series of steps that allow you to generate predictions about different variables.
It’s a subject that not only applies to mathematics, but also to areas as deep as biological and environmental sciences and the business world.
Want to know how to apply it in your day-to-day life? Find out below:
What is linear regression?
Let's define linear regression. It’s a data analysis technique that predicts the value of unknown information through the use of another data value.
In other words, this analysis is used to predict the value of one variable based on the value of another variable. The variable you want to predict is called the dependent variable, while the second one is called the independent variable.
The method takes into account the coefficients of the linear equation and involves different variables that can best predict the value of the variable that is dependent.
In this sense, linear regression conforms to a straight line that reduces the differences between the predicted and actual output values. For this purpose, there are now linear regression calculators that use the "least squares" model to choose the line that best fits a set of paired data.
The good news is that linear regression can be applied in Excel or in specific programs that simplify the whole process of calculating and running equations.
Importance of linear regression
Although many people think otherwise, the reality is that linear regression models provide a formula that is very easy to interpret to generate predictions.
One of the reasons why it’s so important is because it can be applied in different businesses and academic studies. It’s currently used in the natural and physical sciences and very often in the business world to predict user behavior.
Many experts agree that linear regression models are a very accurate way to predict the future in a reliable and scientific way as it’s a 100% statistical procedure.
Usefulness in business
Linear regression is very useful in companies regardless of the industry. Nowadays, companies tend to collect a large amount of data and can apply this model to understand what their users' needs are instead of leaving everything to chance.
This data can be transformed into valuable information that we can use to create accurate strategies to serve customers.
Likewise, with linear regression we can obtain better insights to discover the consumption habits of our audience and thus adjust the strategies we have in our hands.
It’s not only about selling, but also about understanding which days and times your customers are most likely to be open to negotiation. Therefore, you will be able to anticipate a high demand for your products and obtain higher profitability.
Linear regression hypotheses
There are several hypotheses that we must take into account when working with linear regression. Some of them are:
1. For each variable
When we are going to work with each variable it¿s essential to take into account the number of valid cases, the standard deviation and the current mean.
2. For each model
For each model it’s essential to assess the regression coefficients, their correlation matrix, partial correlations, multiple correlations, standard errors in the estimation and the residual and predicted values.
On the other hand, it’s advisable to consider 95% confidence intervals for all coefficients, variance inflation factor and distance measures in general.
3. Charts
With respect to graphs we should consider scatter plots, partial histograms and probability histograms.
4. Data
On the other hand, all variables, both dependent and independent, have to be quantitative. However, categories such as field of study, area of residence, have to be coded from scratch to be binary variables.
5. Other hypotheses
For each value of the independent variables, the distribution of the dependent variable has to be 100% normal. Meanwhile, the variance of the distribution of the latter variable has to be constant for the values of the independent one.
How can I test the hypotheses?
Before starting to work on our linear regression model, it’s essential to make sure that the data we have can be analyzed with this model.
For this, each of the data has to pass through several hypotheses that we will explain below:
The variables have to be measured continuously. Some of them are sales, time, weight and test scores.
It’s important to use a scatter plot to detect in a short time if there is a linear relationship between the two variables involved.
On the other hand, the observations have to be independent of each other, which means that there cannot be any dependence.
Under no circumstances can the data be outliers.
It’s essential to check homoscedasticity, a term related to the variances of the linear regression line.
Advantages of linear regression
There are many advantages of linear regression.
It’s a statistical model that displays information about cost structures and determines the roles of the different variables affecting the product in question. Also, the coefficients can be interpreted in terms of the factors that are determinants of the item's costs.
On the other hand, it’s a very useful tool for detecting the relationships between the changes observed in two different groups of variables. In addition, it gives you data to confirm hypotheses about whether two variables are related to each other or not.
In this sense, it provides a 100% visual alternative to measure the strength of a possible relationship for mobilizing decision making.
Disadvantages of linear regression
Yes, not everything can be perfect. Just as linear regression models have many advantages, we must also take into account the problems it generates in the medium term.
Let's look at some of them below:
First, linear regression models only the relationships between variables that are dependent and independent that are linear. Anything else is left aside.
It’s very sensitive to anomalies in the data, which can lead to erroneous results.
Current uses of linear regression:
One of the advantages of linear regression is that it can be applied in different branches of daily life. Whether or not you are a fan of mathematics and statistics, the reality is that you have directly or indirectly applied it at some point in time.
There are many uses for them today. Let's take a look at some examples:
1. Advertising
We know that investment in advertising is essential to achieve sales in the medium or long term, but what’s even more important is to detect the relationship between advertising expenditures and revenues.
So, with a simple linear regression model with advertising expenditure as the predictor variable and earnings as the response variable we can find out if we are on the right or wrong track.
From here we will determine whether we should increase or decrease ad spend.
2. Medical research
Have you ever noticed that each drug has an ideal dose for each patient depending on their condition? Well, these numbers are not made at random, and with linear regression we can understand the relationship between the amount of medicine that a patient with a specific problem should take.
So, professionals can administer different doses of a drug to different patients to observe the behavior of their blood pressure.
How do we adjust the equation? We use the dose as the predictor variable, while the response variable will be the blood pressure. Then we will know whether we should increase or decrease the amount of product.
3. Agricultural scientists
Believe it or not, agricultural scientists often use linear regression to monitor the effects of fertilizer and water on crop yields.
So, professionals can mix different amounts of water and products on different patches of land to study their performance. In this case, fertilizers and water would be the predictor variables and crop yield would be the response variable.
With the result the professionals will modify the amounts they will add in the future.
4. Professional sports
We couldn't leave out an industry as powerful as professional sports.
Data scientists from various sports teams use linear regression models to measure the effect of training programs on their players.
They can then meet with physiotherapists and physical trainers to determine whether the number of gym and weight training sessions is sufficient to achieve the right performance at the most relevant time of the season.
Each of the sessions corresponds to the predictor variables and the team's result would be the response variable. Subsequently, the specialists will modify the training regimen according to the needs of the team and the player himself.
Final recommendations
We cannot deny that we are very happy because today we realized that linear regression is a simpler model than it seems and that it can be used in different industries without major drawbacks.
Predicting the behavior of some variable in the future is a necessity for all companies. It’s true that there will always be a margin of error, but with this equation we reduce the possibilities and make much more accurate decisions.
Do you know the best part of it all? Nowadays there are programs that do the formula for us, so you just have to add the data and the software will do the hard work.
Are you now convinced to use linear regression in your business? Leave us your impressions in the comments box and show us the results after you apply this wonderful formula.
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