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Regression and regression equation in data analysis.

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Regression analysis is a versatile statistical technique that can be used in a wide range of cases beyond normal distribution (continuous response) and binomial distribution (binary response). There are many different types of regression techniques used in statistics and machine learning, each with its own characteristics and assumptions.

Table 4154. Classes of regression.

Class	Goal	Description
Linear regression	To evaluate h at x, and fit θ to minimize , then return	To find the values of m and b, in y = mx + b, that minimize the sum of squared differences between the observed data points and the predicted values on the line.
Locally Weighted Regression	Fit θ to minimize	is a non-parametric method that doesn't assume a specific functional form for the relationship between variables. Instead, it fits a regression model locally for each data point, giving more weight to nearby data points and less weight to data points farther away. This results in a flexible, adaptive model that can capture both linear and non-linear relationships in the data.
Polynomial Regression		This is an extension of linear regression that allows for the modeling of non-linear relationships by fitting a polynomial (e.g., quadratic, cubic) to the data.
Ridge Regression		This adds a penalty term to linear regression to prevent overfitting. It's especially useful when there's multicollinearity (high correlation between independent variables).
Lasso Regression		This is another regularization technique like Ridge, but it uses a different penalty term that can lead to feature selection by driving some regression coefficients to exactly zero.
Support Vector Regression (SVR)		This is an extension of Support Vector Machines (SVM) to regression problems. It tries to find a hyperplane that best fits the data while minimizing the margin of error.

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[1] Domonkos Varga, No-Reference Video Quality Assessment Based on Benford’s Law and Perceptual Features, Electronics 2021, 10, 2768.