Regression analysis is the starting point in data science. This is because regression models represent the most well-understood models in numerical simulation. Once we experience the workings of regression models, we will be able to understand all other machine learning algorithms. Regression models are easily interpretable as they are based on solid mathematical bases (such as matrix algebra, for example). In the following sections, we will see that linear regression allows us to derive a mathematical formula that's representative of the corresponding model. Perhaps this is why such techniques are extremely easy to understand.

Regression analysis is a statistical process that's implemented to study the relationship between a set of independent variables (explanatory variables) and the dependent variable (response variable). Through this...

A simple linear regression is easy to understand, but represents the basis of regression techniques. Once these concepts are understood, it will be easier for us to address the other types of regression. To begin with, let's take an example of applying linear regression that's been taken from the real world.

Consider some data that has been collected on a group of bikers, which consists of the following aspects:

• Number of years of use
• Number of kilometers traveled in one year
• Number of falls

Through these techniques, we find that, on average, when the number of kilometers traveled increases, the number of falls also increases. By increasing the number of years of motorcycle usage and by increasing the experience, the number of falls tends to decrease.

The linear regression method consists of precisely identifying a line that is capable...

So far, we have resolved simple linear regression problems that study the relation between a dependent variable, y, and an independent variable, x, based on the following regression equation:

In this equation, the explanatory variable is represented by x and the response variable is represented by y. To solve this problem, the least squares method was used. In this method, we can find the best fit by minimizing the sum of squares of the vertical distances from each data point on the line. As mentioned previously, we don't find that a variable depends solely on another very often. Usually, we find that the response variable depends on at least two predictors. In practice, we will have to create models with a response variable that depend on more than one predictor. These models are...

The real estate market is a market where the sales and purchase between sellers and buyers refer to the exchange of real estate of any kind, such as housing, land, commercial premises, and so on. Real estate prices depend on a series of factors that make the asset more palatable for potential buyers.

These factors include the socioeconomic conditions, environmental conditions, and educational facilities of the area in which the property is located. Analyzing how these factors affect the cost of real estate can be a valuable tool for technicians in the sector in order to predict the market trends, depending on the changes that are occurring.

To do this, we will run a neural network regression for the Boston dataset; the median values of owner-occupied homes are predicted for the test data. The dataset describes 13 numerical properties...

In this chapter, you've learned about the different types of regression techniques. Regression analysis is a statistical process that's done to study the relationship between a set of independent variables (explanatory variables) and a dependent variable (response variable). Regression algorithms show you how the value of the response variable changes when the explanatory variable is varied. The concepts underlying regression were explored. Furthermore, we gained an understanding of the differences between simple and multiple regression. Later, we saw how a simple and multiple linear regression problem is represented algebraically. Thus, we have analyzed how a regression problem is solved through the least squares algorithm.

The second part of this chapter was dedicated to the practical resolution of a multiple regression problem using the keras library. Modeling...