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## Linear Regression [Simplest Implementation]

version 1.0.0.0 (159 KB) by Bhartendu

### Bhartendu (view profile)

Linear regression using: Direct Method, Inbuilt function, SGD Method

Updated 02 Nov 2017

Linear regression attempts to model the relationship between two variables by fitting a linear equation to observed data. One variable is considered to be an explanatory variable, and the other is considered to be a dependent variable. For example, a modeler might want to relate the weights of individuals to their heights using a linear regression model.
Before attempting to fit a linear model to observed data, a modeler should first determine whether or not there is a relationship between the variables of interest. This does not necessarily imply that one variable causes the other (for example, higher SAT scores do not cause higher college grades), but that there is some significant association between the two variables. A scatterplot can be a helpful tool in determining the strength of the relationship between two variables. If there appears to be no association between the proposed explanatory and dependent variables (i.e., the scatterplot does not indicate any increasing or decreasing trends), then fitting a linear regression model to the data probably will not provide a useful model. A valuable numerical measure of association between two variables is the correlation coefficient, which is a value between -1 and 1 indicating the strength of the association of the observed data for the two variables.
A linear regression line has an equation of the form Y = a + bX, where X is the explanatory variable and Y is the dependent variable. The slope of the line is b, and a is the intercept (the value of y when x = 0).
Reference:
(1) https://www.iist.ac.in/sites/default/files/people/in12167/linear_regression.pdf
(2) Andrew Ng’s lecture note (CS 229)
(3) http://www.stat.yale.edu/Courses/1997-98/101/linreg.htm
Check more Machine Learning stuff:

2. SVM using various kernels
https://in.mathworks.com/matlabcentral/fileexchange/63033-svm-using-various-kernels

3. SVM for nonlinear classification
https://in.mathworks.com/matlabcentral/fileexchange/63024-svm-for-nonlinear-classification

5. Support Vector regression
https://in.mathworks.com/matlabcentral/fileexchange/63060-support-vector-regression

6. Maze Solver using SARSA
https://in.mathworks.com/matlabcentral/fileexchange/63089-sarsa-reinforcement-learning

7. Gauss-Seidel Method, Jacobi Method
https://in.mathworks.com/matlabcentral/fileexchange/63167-gauss-seidel-method--jacobi-method

### Cite As

Bhartendu (2020). Linear Regression [Simplest Implementation] (https://www.mathworks.com/matlabcentral/fileexchange/64930-linear-regression-simplest-implementation), MATLAB Central File Exchange. Retrieved .

curry

### curry (view profile)

What is A and P in the code of holdout()?
If someone answers, thank you very much.

Onkarnath Thakur

Bhartendu

### Bhartendu (view profile)

Kannan Thirugnanam

### Kannan Thirugnanam (view profile)

I downloaded the LR code. If i run the code, it's showing error. Someone help to solve/fix this error.

Undefined function or variable 'holdout'.

Error in LinearReg_code (line 19)
[train_set,test_set ] = holdout(data,70 );

Nathan Zhang

Rahul Vashisht

### Rahul Vashisht (view profile)

##### MATLAB Release Compatibility
Created with R2015a
Compatible with any release
##### Platform Compatibility
Windows macOS Linux