How can you use regression analysis to predict future trends?

As a chemical engineer, I use regression analysis to predict future trends in industrial processes. By modeling the correlation between variables such as temperature, pressure, and reagent concentration, we can forecast process yields. We collect historical data, choose the appropriate regression model, preprocess the data, and validate the model to ensure accuracy. These predictions allow us to adjust operational conditions to maximize efficiency and reduce costs, driving innovation and excellence in the industry.

Regression is a statistical method used to understand the relationship between a dependent variable and one or more independent variables. It helps predict the dependent variable based on the values of the independent variables. For Example: Imagine you want to predict a house's price based on its size. Here, the house price is the dependent variable, and the size is the independent variable. By collecting data on past house sales, you can create a regression model. For instance, if your data shows that each square foot adds ₹150 to the house price, your model might look like this: Price = 10.373 + 150*{Size} Using this model, you can predict the price of a house based on its size.

Before starting with the linear regression algorithm, data cleaning and exploration should have been carried out through univariate and bivariate analysis to understand the relationship between the variables.

RA is a powerful statistical tool for predicting future trends by examining the relationship between variables. For instance, suppose an online retailer wants to predict future monthly sales. By using past sales data as the dependent variable and factors like advertising spend, website traffic, and seasonal trends as independent variables, the retailer can build a regression model. Once the model is developed, it analyzes the coefficients to understand how each factor impacts sales. The retailer can then input future values of the independent variables to predict upcoming sales. For eg: if the model shows a strong positive correlation between advertising spend and sales, the retailer can predict higher sales with increased advertising.

In essence, regression helps you understand which factors matter most and how they combine to influence the trend you're studying. It's like finding the recipe that best explains your past data to forecast the future. Remember, predictions assume that future patterns will follow historical trends.

Many things should be in mind before fitting a model. First, you should engineer your features properly. Do exploratory analysis on them and understand it very well. You may have missing data, which can introduce bias, be careful when treating this issue. Weak features can introduce overfitting, get rid of them. Correlated variables will introduce a high variance inflation factor. Before starting the engineering of features, you have to split your data into training testing and if you have enough data, you can also have a validation dataset otherwise you can use cross-validation. The relationship between features and outcomes is not always linear so linear or logistic regression may not be good for all cases, you should try other models.

It is crucial to pause and understand some essential characteristics of the variables before proceeding with the regression: Missing Values: Assess their distribution and decide on imputation or removal. Outliers: Use statistical analysis to detect and decide on removal or adjustment. Normality: Check variable distribution and apply transformations if necessary. Scaling: Normalize data to ensure equitable variable contribution. Categorical Variables: Convert to numerical carefully. Multicollinearity: Address any among variables. Data Splitting: Split data for effective model validation.

COntruir un modelo predictivo basado en una regresión lineal , debemos definir cual de las dimensiones que tenemos en nuestra data es la que vamos a determinar como la variable independiente y a su vez , todo los atributos que tenga esta variable , una vez determinado las variables la ecuacion se basará entre la relación de X y Y

In the case of a time series regression model, before proceeding into building the regression model, you have to check the behavior of the determinants as well as the dependent variable. Make sure that they are stationary. Although, non-stationarity series can be modeled as well provided the dependent and independent variable is cointegrated. In this case, an error correction model is best suited.

It is important to first set up expectations and premises before deciding to build any kind of model. It is important to understand the complexity and necessity of developing polinomial equations with several iterations when sometimes only average and variance is needed. Next step is understanding the type of analysis and in which type of model is needed to fulfill the requirements. Then it’s time to clean and transform the dataset and eventually, resample it if needed. And after all these steps, it’s time to test and select the best fit for your model!

Testing validity is crucial and starts with model training. You can use different ways with different levels of generalizability and overfitting/underfitting hazards. It is best to split your data into training, validation and testing. But if you don't have a lot of data, you can use cross-validation or bootstrapping but these methods can produce overfitting in your model. Then you can use the test dataset for testing the near real-world performance. Real-world performance should always be mentored in pilot testing or you can use external validation dataset from a different resource.

Na crucial etapa de avaliação temos que efetuar algumas atividades como: Avaliar a precisão do modelo usando métricas como R² (coeficiente de determinação) ou erro quadrático médio (MSE), Raiz do Erro Quadrático Médio (RMSE), Erro Absoluto Médio (MAE), Erro Percentual Médio Absoluto (MAPE). Fazer uma revisão das suposições: Certifique-se de que as suposições da regressão linear (linearidade, homocedasticidade, preditores não correlacionados, etc) são atendidos para garantir a validade do modelo.

En mi experiencia, se pueden descartar variables que no aportan información al modelo financiero, y que nos pueden ayudar a elevar el nivel de rendimiento del modelo.

These things like correlation and regression, I hv found very useful nowadays. Once the correlation has been done between dependent and independent variables, it is very much essential to do regression analysis. For example, after establishing relationship with both variables, how much plant yields ( dependent)for every unit of change in plant height ( independent)helps in accurate prediction of yield in advance.

Cuando se requiere validar un modelo predictivo de regresión lineal , primero tenemos que tener una mineria de datos adecuada y que se ajuste al negocio , luego de esto determinamos el factor tiempo en la cual se esta moviendo los datos y cuanto historial tengo de ella , por otro lado tenemos que tener en cuenta el valor de error , ya que estos modelos estan basados en hipotesís y en cada ecuación se debe de cosiderar esta desviación , utilizando herramientas como R podriamos determinar el porcentaje de error que pueda tener un modelo predictivo tambien con los graficos de dispersión que son muy utiles para estos calcúlos , se podria tomar como un buen ejemplo la prediccion de las ventas de un articúlo en particular

It is important to realize: the prediction part of a regression follows from the logic outside of the computing, the maths themselves do not differentiate between interdependence, prediction and causality and do not tell you if you actually have causality or prediction in a model that claims to have learnt. Interdependence simply means that for some reason as one variable moves the other also moves. Technically, prediction requires that the predictors precede the outcome (although in statistics that requirement is -for good reason- sometimes taken lightly). For beginners it may help to realize that traditional linear regression with only one predictor is mathematically equivalent to simple correlation. I.e it does not bestow causality.

Once we have a reliable model, we can use it for predictions. We plug in future values of the independent variable (X) into the model's equation to estimate the corresponding values of the dependent variable (Y). This allows us to forecast future trends, like website traffic based on planned advertising campaigns.

En mi experiencia, los modelos de regresión son muy útiles bastante útiles para explicar el comportamiento de variables y su relación con otras variables, así como para predicciones de tendencias o detección de comportamientos cíclicos.

Once your model is all set, you can start to simulate and analyze scenarios and behaviors in order to get better answers and more accurate decisions. It is important to consider all possibilities and situations before making a final assessment using your model. It is important to keep track of errors and eventually update the dataset.

Una vez se cuenta con un modelo validado podremos obtener nuestras predicciones para la variable dependiente, no obstante nuestro trabajo no terminará ahí, ¿cómo lo comunicamos a los interesados en estas predicciones? ¿quienes tienen acceso a la información en caso de que se considere estratégica? ¿cada cuánto comprobamos si el modelo sigue siendo útil o necesita ajustes?

It is important to consider where your analysis is applicable, and where it isn’t. There’s a reason the concept of correlation not indicating causality is reiterated nearly daily in any statistics course. There are potential lurking variables, for example, that you may not have considered that may underly the correlation observed. Additionally, the correlation observed within the parameters you’ve set in your analysis may not hold up when you try to extrapolate beyond the limits of your model. It’s critical to conceptualize your results, and not just generate values.

It is also important to consider that, in a linear model, each parameter, e.g y = ax+b, has an error associated. The more repeated measures of y are made at each value of x, the more accurate the estimate of these errors. It's like in correspondence of each value of x, there is a little gaussian distribution of y's (... if they are normally distributed). As a result, the model looks like y(+/- err.y) = a(+/- err.a)x + b(+/- err.b). If, say, the bracket +/-err.a includes zero, I would seriously put in doubt any predictions based on the model. There are other possibly better ways to estimate the validity of the model (e.g. "goodness of fit"), but I'd leave the explanation of that to someone better qualified.

Si logramos correlacionar las tendencias en las variables con impacto de negocio con otras que pueden ser accionables, por ejemplo el NPS obtenido de la encuesta sobre nuestros clientes o la valoración que los clientes y prospectos hacen de determinadas características de nuestros productos o de nuestro portafolio podemos obtener información accionable, algo que es clave para la mejora.

Regression analysis is a powerful tool, but it's important to remember it deals with statistical relationships, not absolute guarantees. There might be other factors influencing the dependent variable, and unexpected events can always disrupt trends. The key is to interpret the predictions within the context of the situation.

Correlation does not mean explanation. Models represent a reality based on a sample and may not lead to the right place. That’s why keep researching more combinations and variables might help building a robust model and analysis system in your studies!

En mi experiencia, hay que seguirse reinventando, manteniéndose actualizado de las tendencias y nuevas herramientas para el análisis de datos, como la ciencia de datos, big data, machine learning y la IA. Mismas que enriquecerán nuestros análisis y que en los que la sensibilidad y expertiz como ser humano, cobran gran valor para el modelaje de información.

While, due to their high interpretability and fairly simple mathematics linear regression have an immovable spot in statistics and machine learning, they also have important limitations. Thankfully in modern days there are plenty of options of how to go beyond some of those limitations. To mention just two avenues, there are not only non-linear regressions, but also using regularized regressions to help with data reduction and also to deal with outliers, which traditional regressions can be very vulnerable too. However, be careful, such methods have their own backdraws that you need to stay conscious of. Use therefore with a clear mind and with the necessary caution.

Regression is the foundation of all predictions and probabilities.Linear, Multi-Linear and Logistic Regression are the most common regression models. These, are the fundamentals of Calculus, used to predict the future outcomes of variables.