Multiple linear regression with Python, numpy, matplotlib, plot in 3d

<br/> Background info / Notes: <br/> Equation:<br/> Multiple regression: Y = b0 + b1*X1 + b2*X2 + ... +bnXn<br/> compare to Simple regression: Y = b0 + b1*X<br/> <br/> In English: <br/> Y is the predicted value of the dependent variable<br/> X1 through Xn are n distinct independent variables<br/> b0 is the value of Y when all of the independent variables (X1 through Xn) are equal to zero<br/> b1 through bn are the slope of the relationship between the dependent variable and the independed variable that is holding constant of all other independent variables.<br/> <br/> Think of it as a system of equations:<br/> Y1 = (b + mX1) + e1<br/> Y2 = (b + mX2) + e2<br/> ...<br/> Yn = (b + mXn) + en<br/> We can then set up a matrix equation with the following matrices:<br/> <br/> &nbsp; &nbsp; &nbsp; &nbsp;|Y1|<br/> Y = |......|<br/> &nbsp; &nbsp; &nbsp; &nbsp;|Yn|<br/> <br/> &nbsp; &nbsp; &nbsp; &nbsp;|1 X1|<br/> X = |... ...|<br/> &nbsp; &nbsp; &nbsp; &nbsp;|1 Xn|<br/> <br/> &nbsp; &nbsp; &nbsp; &nbsp;|b|<br/> A = |m|<br/> <br/> &nbsp; &nbsp; &nbsp; &nbsp;|e1|<br/> E = |......|<br/> &nbsp; &nbsp; &nbsp; &nbsp;|en|<br/> <br/> Which gives us the matrix equation: Y = XA + E<br/> We just need to solve for A<br/> <br/> Use Linear Algebra to solve<br/> Equation: <br/> A = (X^T * X)^-1 * (X^T * Y) <br/> <br/> Two helpful links that explain how we get this equation:<br/> https://www.youtube.com/watch?v=Qa_FI92_qo8<br/> https://www.youtube.com/watch?v=qdOG7YMolmA<br/> <br/> Convert the equation to code:<br/> Using the np.linalg.solve function we will not need to invert the first term<br/> a = np.linalg.solve(np.dot(X.T, X), np.dot(X.T, Y))<br/> <br/> <p> <img src="MultiLinearBPgraph1.png" alt="image"> <br/> <img src="MultiLinearBPGraph2.gif" alt="image"> <br/> <img src="MultiLinearBPgraph3.png" alt="image"> </p>