# Regression Analysis in Artificial Intelligence – 6 Points

## Introduce to Regression Analysis in Artificial Intelligence

As part of today’s reading, let’s delve into the topic “Regression Analysis in Artificial Intelligence”.

### Defining terms

Understanding from the very basics, what is Regression? Regression can be simply explained as the estimation or relationship of a continuous dependent variable from a list of input variables.                                 From the perspective of statistics, Regression analysis is a predictive modelling technique that analyzes the relation between the outcome or dependent variable and one or more independent variables in a dataset, and determines the best fit line which passes through all the data points in such a way that distance of the line from each data point is minimal.

### Purpose of Regression Analysis

So, what is the actual purpose of regression analysis for analysts? Typically, a regression analysis serves two purposes: Foremostly, it helps to predict the value of the dependent variable for individuals and secondly, it estimates the effect of some explanatory variable on the result variable. On a deeper note, the different techniques in regression are used mainly to determine time series, predictor strength, or the forecast trend only when the independent variables depicts either a linear or non-linear relationship between each other, and the target variable contains the continuous values.

### Case Study

Let’s check out a few case studies to understand it better:

Case 1: Agricultural scientists often make use of regression analysis techniques such as linear regression to measure the effect of fertilizer and water and check its effect on crop yield.

Case 2: Medical researchers implement regression analysis to understand and administer the relationship between the appropriate drug dosage and blood pressure of various patients, and finally check its response on the human body.

### Regression Analysis Techniques

I hope with the help of the above examples, you all have understood the basic meaning of regression, its analytical perspective and its goal in the domain of Artificial Intelligence. The most advantageous part of regression analysis is that it allows us to make better decisions for our business currently and for the upcoming times. In this upcoming section, we will check out the different types of regression analysis techniques and learn to implement linear regression and logistic regression using R programming from a beginners point of understanding.

Below mentioned are the different regression techniques explained in a detailed manner:

1. Linear Regression- It is considered to be one of the most basic types of regression which consists of a predictor variable and a dependent variable related linearly to each other.

The given equation denotes the linear regression model: y=mx+c+e, where m denotes slope of line, c is the intercept, and e represents the error in the model.

The implementation of linear regression generates insights on understanding the business trend and makes estimates or forecasts, consumer behaviour, and the factors influencing profitability. As an example, let us consider a company’s sales which have increased steadily for the past few years. On conducting a linear analysis for the following sales data on a monthly basis, the company could forecast sales in the future months.

In R programming, the lm() function creates the relationship model between the predictor and the response variable. Its basic syntax for lm() function is lm(formula,data).

1. Logistic Regression- Logistic regression is considered as the type of regression analysis technique, which measures the relationship between the independent and target variable and gets used when the dependent variable is discrete, i.e., 0 or 1, true or false, etc.

The equation that denotes the logistic regression is: logit(p) = ln(p/(1-p)) = b0+b1X1+b2X2+b3X3…. +bkXk, where p denotes the probability of occurrence of the feature.

A real life example where logistic regression is implemented : In order to understand the relationship between the predictor variables and the probability of having or not having a heart attack, researchers can perform logistic regression to know how exercise and weight impact it.

Logistic regression can be broadly categorized into three categories namely

• Binary logistic regression which is impacted with conditions where the observed outcome for the dependent variableis having only two possible labels, either “0” and “1”.
• Multinomial logistic regressionis where the outcome is having three or more possible types such as “negative” vs. “positive” vs. “neutral”.
• Ordinal logistic regressionparticularly deals with ordered dependent variables.

Logistic regression using R can be performed using the glm() function. Its syntax is glm(formula,data,family)

3. Ridge Regression – This is the type of regression technique which is implemented when there is a high correlation between the independent variables. Given is the equation representing Ridge Regression: β = (X^{T}X + λ*I)^{-1}X^{T}y, where λ solves the problem of multicollinearity. This regression technique was demonstrated in the water storage computation for Lake Okeechobee, Florida.

1. Lasso Regression – Lasso Regression performs regularization along with feature selection and allows selecting a set of features within the dataset to build the model. The equation that represents the Lasso Regression method is as follows: N^{-1}Σ^{N}_{i=1}f(x_{i}, y_{I}, α, β). The lasso procedure encourages simple, sparse models (i.e. models with fewer parameters).
2. Polynomial Regression –Polynomial Regression is another one of the techniques of regression analysis where least mean squared method is mainly used. It is a linear model as an estimator. The equation which represents the Polynomial Regression is: l = β0+ β0x1+ε. It can be used in various experiments which involves the study of the isotopes of the sediments, and the rise of different diseases within any population.

6. Bayesian Linear Regression- Bayesian Regression makes the use of Bayes theorem to find out the value of regression coefficients.

## Conclusion

From the above understanding, we can conclude by saying that regression analysis is a reliable method of identifying which variables have impact on a topic of interest, and allows us to confidently determine which factors matter most, or which can be ignored, and how these factors influence each other.

I hope all my readers have got a complete and deep understanding of regression analysis in AI. Let’s have a few takeaways to summarize what we’ve covered: What is regression and regression analysis, purpose/goals of regression analysis, few case studies to understand it more, and then finally the six regression analysis techniques explained in a brief manner.

### Author Bio

Senior Data Scientist and Alumnus of IIM- C (Indian Institute of Management – Kolkata) with over 25 years of professional experience Specialized in Data Science, Artificial Intelligence, and Machine Learning.