# ML | Types of Regression Techniques

**When Regression is chosen?**

A regression problem is when the output variable is a real or continuous value, such as “salary” or “weight”. Many different models can be used, the simplest is linear regression. It tries to fit data with the best hyperplane which goes through the points.

**Regression Analysis** is a statistical process for estimating the relationships between the dependent variables or criterion variables and one or more independent variables or predictors. Regression analysis explains the changes in criteria in relation to changes in select predictors. The conditional expectation of the criteria is based on predictors where the average value of the dependent variables is given when the independent variables are changed. Three major uses for regression analysis are determining the strength of predictors, forecasting an effect, and trend forecasting.

**Types of Regression: **

**Linear regression****Polynomial regression**is used for curvilinear data. Polynomial regression is fit with the method of least squares. The goal of regression analysis is to model the expected value of a dependent variable y in regards to the independent variable x. The equation for polynomial regression is: l = .**Stepwise regression**is used for fitting regression models with predictive models. It is carried out automatically. With each step, the variable is added or subtracted from the set of explanatory variables. The approaches for stepwise regression are forward selection, backward elimination, and bidirectional elimination. The formula for stepwise regression is .**Ridge regression**is a technique for analyzing multiple regression data. When multicollinearity occurs, least squares estimates are unbiased. A degree of bias is added to the regression estimates, and as a result, ridge regression reduces the standard errors. The formula for ridge regression is .**Lasso regression**is a regression analysis method that performs both variable selection and regularization. Lasso regression uses soft thresholding. Lasso regression selects only a subset of the provided covariates for use in the final model. Lasso regression is .**ElasticNet regression**is a regularized regression method that linearly combines the penalties of the lasso and ridge methods. ElasticNet regression is used for support vector machines, metric learning, and portfolio optimization. The penalty function is given by:.

Below is the simple implementation:

## Python3

`# importing libraries` `import` `numpy as np` `import` `matplotlib.pyplot as plt` `from` `sklearn.linear_model ` `import` `LinearRegression` `x ` `=` `11` `*` `np.random.random((` `10` `, ` `1` `))` `# y = a * x + b` `y ` `=` `1.0` `*` `x ` `+` `3.0` `# create a linear regression model` `model ` `=` `LinearRegression()` `model.fit(x, y)` `# predict y from the data where the x is predicted from the x` `x_pred ` `=` `np.linspace(` `0` `, ` `11` `, ` `100` `)` `y_pred ` `=` `model.predict(x_pred[:, np.newaxis])` `# plot the results` `plt.figure(figsize ` `=` `(` `3` `, ` `5` `))` `ax ` `=` `plt.axes()` `ax.scatter(x, y)` `ax.plot(x_pred, y_pred)` `ax.set_xlabel(` `'predictors'` `)` `ax.set_ylabel(` `'criterion'` `)` `ax.axis(` `'tight'` `)` `plt.show()` |

**Output:**