## Introduction to Statistical Learning

Statistics can be comprehended as a study of collecting and analyzing a bunch of data. Statistical Learning servers as a means to extract facts and summarize the available data. Statistics has been in practice since the 18th century, mainly for taxes and military use. Later towards the end of the 20th century, with the advent of computers, the applications of statistical concepts broadened with its contributions towards technologies such as Machine Learning and Neural Nets. In this topic, we are going to learn about Introduction to Statistical Learning.

Statistical Learning makes data prediction and classification possible by dealing with a huge volume of data, performing hundreds of iterations to analyze and select only the best and relevant data to be used to obtain the optimized result.

### What is Statistical Learning?

Data is the fuel that drives Statistical Learning, and statistics is all about making sense of the data in hand. The results obtained from statistical learning help us in determining trends and predict a possible outcome for the future.

Statistical Learning serves as a tool to accomplish the goals of both supervised and unsupervised Machine Learning techniques. With supervised statistical learning, we get to predict or estimate an outcome based on previously present output, whereas with unsupervised statistical learning, we find various patterns present within the data by clustering them into similar groups.

This article gives a glimpse of Supervised Statistical Learning methodologies, namely Regression and Classification

#### 1. Regression

Ever wondered how stock market predictions work? or how a realtor estimates a house price? or wanted to know if a new car in the market is worth the buy? If yes, then you can find answers to these in a statistical methodology named Regression. Regression equations and analysis are used for making unbiased and accurate predictions on quantitative (numeric) data. In addition, regression Analysis helps us to identify the relationship between two or more variables.

The relationship between one dependent variable (Y) and one independent variable(X) is determined in Simple Linear Regression (SLR). The estimate of how any change in X will affect Y is given by the equation illustrated below.

##### Bias – Variance Trade-off:

Linear Regression is all about finding the best fit straight line. Errors in regression models are mainly due to bias and variance. Minimizing these two prediction errors is essential to obtain a generalized model that works well on both training and testing data sets.

##### Bias:

Linear Regression Model assumes the target variable has a linear relationship with its features. In reality, though this might not be the case, and the inability of the Linear Regression model to capture the true relationship is termed as bias. Error due to bias is calculated as the difference between the predicted value and the actual value.

##### Variance:

The variance gives us a picture of how far the data points under consideration are spread. The Variance error refers to the fluctuations in the predictions when data sets are changed and is calculated as the variability of a model prediction from a given data point.

Consider the scenarios where a model is having high bias and low variance; then it is likely to be less complex and probably will tend to underfit the data. Now, if the model has low bias and high variance, it is likely to overfit the data, making it more complex and inconsistent when tried for unseen inputs. Hence to avoid such scenarios, there is a need to come to a common ground w.r.t the bias and variance to have an acceptable model.

An ideal model is selected to have a low bias that can capture the true relationship between its variables and low variance that produces consistent predictions across different datasets. This can be achieved by obtaining a sweet spot between a simple and complex Regression Model. Methods such as regularization, bagging and boosting help in achieving the sweat spot.

#### 2. Classification

Classification is applied to qualitative (non-numeric) data wherein the target variable can be classified or grouped into two (Binary Classification) or more classes (Multi-Class Classification). Examples for Classification Statistical Learning include Tagging of an e-mail as “spam” or “ham,” predicting customer churn, classifying animals based on their breeds, and so on.

In classification, the output is often obtained using probabilistic approaches so that the results from the statistical inference give out a probability of an instance belonging to a class rather than just assigning the best class.

##### Logistic Regression:

Logistic Regression is one of the widely used classification algorithms for binary classification. This model uses a logistic function to determine the target value between the range of 0 to 1 and can be represented as the Sigmoid function shown below.

### Why do we need Statistical Learning?

In today’s age, if there is one thing that is becoming more abundant than the natural resources, then hands down, that ought to be Data. The million bytes of data that we generate every passing day needs a source for analyzing and summering them. If not used wisely, these data can easily be misinterpreted or can be manipulated to showcase only a certain point-of-view. Therefore, to avoid dangerous mishaps with data, Statistical Learning becomes a tool to ensure data integrity and its proper and efferent usage.

Statistical Learning helps us understand why a system behaves the way it does. It reduces ambiguity and produces results that matter in the real world. Statistical Learning provides us with accurate results that can find its application in the fields of medical, business, banking, and government.

### Advantages

Easily identifies patterns and trends. With the identified trends, it becomes easier to target specific customers for specific products. | |

Saves time. Hundreds and thousands of epochs for achieving the optimized result are possible within a span of a few minutes. | |

Can work with large numbers and a wide variety of parameters. | |

Improves Decision Making and Prediction techniques by logically analyzing the data rather than calling shots based on “gut feeling.” | |

No Human Intervention is required once the system is functional, other than occasional updates required to keep the system functional. |

### Conclusion – Introduction to Statistical Learning

With our advancing technologies, we are now dealing with more statistics in our daily life than ever before. Every billion bytes of data we accumulate tells us various stories that require correct interpretation, which is not possible without statistics being intersected with other branches like Data Mining, Machine Learning, and Artificial Intelligence.

### Recommended Articles

This is a guide to Introduction to Statistical Learning. Here we discuss the Supervised Statistical Learning methodologies, namely Regression and Classification. You may also have a look at the following articles to learn more –

- Statistical Analysis Tools
- Statistical Analysis Regression
- Statistical Analysis Methods
- Statistical Analysis Types

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