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Multiple Linear Regression Algorithm In Machine Learning

This article describes the Multiple Linear Regression Algorithm.

Purpose

In the Linear Regression Algorithm, the dependent variable depends on a single independent variable. In the Multiple Linear Regression Algorithm, the dependent variable depends on two or more independent variables.

Matrix Transpose

In the matrix transpose, we create a new matrix by changing the rows and columns of the original matrix. Consider the following matrix.

Picture showing the original matrix to be transposed

The matrix after transposition is.

Picture showing the matrix after transpose

How Do You Multiply A 3 X 3 Matrix?

Consider the following example.

Picture showing multiplying two 3x3 matrix

The formula for each element is.

Output Element	Input elements	Actual Calculation	Actual Result
c11	(a11b11) + (a12b21) + (a13*b31)	(11) + (11) + (1*1)	3
c12	(a11b12) + (a12b21) + (a13*b32)	(1170) + (1160) + (1*180)	510
c13	(a11b13) + (a12b23) + (a13*b33)	(125) + (130) + (1*28)	83
c21	(a21b11) + (a22b21) + (a23*b31)	(1701) + (1601) +(180*1)	510
c22	(a21b12) + (a22b22) + (a23*b32)	(170170) + (160160) +(180*180)	86900
c23	(a21b13) + (a22b23) + (a23*b33)	(17025) + (16030) +(180*28)	14090
c31	(a31b11) + (a32b21) + (a33*b31)	(251) + (301) + (28*1)	83
c32	(a31b12) + (a32b22) + (a33*b32)	(25170) + (30160) + (28*180)	14090
c33	(a31b13) + (a32b23) + (a33*b33)	(2525) + (3030) + (28*28)	2309