Basic statistical modelling

Basic statistical modelling plays a fundamental role in analysing data in a variety of areas, enabling the extraction of meaningful patterns and relationships that support decisions and predictions. This article aims to explore the fundamental concepts, common techniques and essential tools used in statistical modelling.

Introduction to statistical modelling:

In the information age, data analysis has become an indispensable practice in a variety of fields, from business and finance to science and health. Basic statistical modelling, as an integral part of this process, provides the tools needed to understand and interpret data, enabling professionals to extract valuable insights and make informed decisions.

By exploring the fundamentals of basic statistical modelling, we can identify hidden patterns in data, understand the relationships between variables and make reliable predictions about future events. This analytical ability is crucial in fields such as marketing, where understanding consumer behaviour can guide sales strategies, or in medicine, where analysing clinical data can help identify effective treatments for diseases.

What is it?

It is a set of statistical methods and techniques used to describe and analyse the relationship between variables in a set of data. It allows us to understand how an independent variable influences a dependent variable and to make inferences about this relationship. In essence, basic statistical modelling seeks to find a simple mathematical model that represents the observed data in the best possible way.

What is it used for?

It is used in a variety of fields, including social sciences, economics, health, among others. It helps us answer questions such as "What is the impact of the level of education on income?" or "How do weather conditions affect sales of agricultural products?". By understanding the relationships between variables in a data set, we can make predictions, identify trends and make informed decisions.

Simple linear regression:

One of the most common methods of basic statistical modelling is simple linear regression. In this method, we try to find the best straight line that fits our data, with the aim of predicting the value of a dependent variable based on an independent variable. The simple linear regression equation is represented by Y = β0 + β1X + ε, where Y is the dependent variable, X is the independent variable, β0 and β1 are the regression coefficients and ε is the random error.

Evaluating models:

After building a statistical model, it is important to evaluate it to determine its effectiveness and accuracy. There are various metrics and methods for evaluating models, including the coefficient of determination (R²), which measures the proportion of the variability in the dependent variable that is explained by the model, and the standard error of the regression, which indicates the dispersion of the points around the regression line. It is also important to carry out hypothesis tests to check the statistical significance of the model's coefficients.

Types of Statistical Modelling

In addition to simple linear regression, there are other types of basic statistical modelling that can be used, depending on the nature of the data and the relationship you want to investigate.

• Logistic regression: Logistic regression is used when the dependent variable is a binary categorical variable, i.e. it has only two distinct categories. For example, we can use logistic regression to predict whether or not a student will pass an exam based on their study hours. In this case, the dependent variable would be "passed" or "failed", and the independent variables would be study hours.

• Polynomial regression: Polynomial regression is used when the relationship between variables is not linear, i.e. it cannot be represented by a straight line. For example, imagine that we are studying the relationship between the age of a car and its resale value. Instead of a linear relationship, we can see a curve, where the resale value decreases rapidly in the first few years and then stabilises. In this case, polynomial regression can be used to model this relationship more accurately.

• Analysis of Variance (ANOVA): Analysis of variance is used to compare the means of three or more independent groups. For example, suppose we are studying the effect of different types of fertiliser on plant growth. We can use ANOVA to determine whether there is a statistically significant difference between the growth averages of the groups treated with different types of fertiliser.

• Multiple Regression Analysis: Multiple regression analysis is used when we want to study the relationship between a dependent variable and two or more independent variables. For example, suppose we are studying the impact of physical activity levels and diet on cardiovascular health. We can use multiple regression analysis to determine how these two independent variables influence cardiovascular health, controlling for other relevant factors.

• Time Series Analysis: Time series analysis is used when data is collected over time and there is a time dependency between the observations. For example, we can use time series analysis to forecast demand for a particular product over time based on historical sales data.

Each of these methods has its own applications and underlying assumptions, and choosing the right method will depend on the nature of the data and the research question at hand. By understanding these different types of statistical modelling, we can select the most appropriate approach to analyse our data and gain meaningful insights.

Most commonly used tools:

There are several tools and software that are widely used in day-to-day basic statistical modelling. R is a popular statistical programming language that offers a wide range of packages and functions for data analysis and statistical modelling. Python, with libraries such as NumPy, Pandas and Matplotlib, is also widely used due to its ease of use and versatility. In addition, Excel is a common tool for basic data analysis and statistical modelling, especially for users less familiar with programming.

Professional experience:

During my professional journey, I have had the opportunity to apply basic statistical modelling in various sectors, contributing to data analysis and informed decision-making. I will share some significant experiences in which basic statistical modelling played a crucial role.

Basic statistical modelling has been applied in a variety of contexts, including data analysis in databases. Faced with challenges such as incomplete and inconsistent data, imputation and exploratory analysis techniques were used to understand and improve data sets. This has resulted in valuable insights for customer segmentation, demand forecasting and understanding user behaviour, contributing to significant improvements in the services and products offered.

In retail, basic statistical modelling was essential for analysing sales data and forecasting future product demand. I encountered challenges such as seasonality in the data and unexpected variations in sales. Using regression techniques and time series analysis, we were able to identify seasonal patterns and long-term trends. This allowed us to proactively adjust stock and optimise the supply of products, reducing storage costs and increasing profitability.

Conclusion

Basic statistical modelling plays a key role in analysing data in various sectors. When faced with challenges such as incomplete, inconsistent or seasonal data, basic statistical modelling techniques allow us to extract valuable insights and make informed decisions. In my professional experience, I have seen first-hand how basic statistical modelling has a direct impact on business results, driving growth and innovation. By understanding the principles and techniques behind statistical modelling, we can extract valuable insights, make accurate predictions and make informed decisions. I hope this article has provided a clear and concise introduction.