ML — Linear Regression
Regression.
The term “linearity” in algebra refers to a linear relationship between two or more variables. If we draw this relationship in a two-dimensional space (between two variables), we get a straight line. The term regression is used when you try to find the relationship between variables.
How do we determine the best fit line?
The line for which the the error between the predicted values and the observed values is minimum is called the best fit line or the regression line. These errors are also called as residuals. The residuals can be visualized by the vertical lines from the observed data value to the regression line.
Linear Regression.
Three major uses for regression analysis are:-
(1) determining the strength of predictors, (2) forecasting an effect, and (3) trend forecasting. First, the regression might be used to identify the strength of the effect that the independent variable(s) have on a dependent variable.
Linear regression performs the task to predict a dependent variable value (y) based on a given independent variable (x). So, this regression technique finds out a linear relationship between x (input) and y(output).
Linear regression uses the relationship between the data-points to draw a straight line through all them.
This line can be used to predict future values.
Types of Linear Regression
Simple linear regression
1 dependent variable (interval or ratio), 1 independent variable (interval or ratio or dichotomous)
Multiple linear regression
1 dependent variable (interval or ratio) , 2+ independent variables (interval or ratio or dichotomous)
Logistic regression
1 dependent variable (dichotomous), 2+ independent variable(s) (interval or ratio or dichotomous)
Ordinal regression
1 dependent variable (ordinal), 1+ independent variable(s) (nominal or dichotomous)
Multinomial regression
1 dependent variable (nominal), 1+ independent variable(s) (interval or ratio or dichotomous)
Examples of Linear Regression.
# Visualizing the Training set results
viz_train = plt
viz_train.scatter(X_train, y_train, color='red')
viz_train.plot(X_train, regressor.predict(X_train), color='blue')
viz_train.title('Salary VS Experience (Training set)')
viz_train.xlabel('Year of Experience')
viz_train.ylabel('Salary')
viz_train.show()
The Output will be as:
# Visualizing the Test set results
viz_test = plt
viz_test.scatter(X_test, y_test, color='red')
viz_test.plot(X_train, regressor.predict(X_train), color='blue')
viz_test.title('Salary VS Experience (Test set)')
viz_test.xlabel('Year of Experience')
viz_test.ylabel('Salary')
viz_test.show()
Resources.
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