Linear regression with n variables - Introduction

 Consider a function to be a more than 1 variable 

y = mx this is a one variable ,m 

y = w1*x1 , w1 the variable

y = w1*x1 +w2 *x2 , 2 variables w1 and w2 

y = w1*x1 + w2 * x2  -  -  - - - - - -wn * Xn  n   -variables

these w1 --- w n are also called as weights.

since from the data we have x1 , x2 ,,,,,x n and corresponding y 's 

the idea is to optimise the equation ,that means to find the optimised 

values for w1 .....w n , so why is that 

we cannot change  the values , data as inputs ,the only thing we can do is to vary the data x using a multiplier w. so the input changes.

assume the equation to be 

y = x1 + x2 

x1 be the data from real life scenario the housing data ,like no of bedrooms

x2 be the data as no of floors

y - the price of the house with no of bedroom and no of floors 

y = 3 + 2 = 5 

but the reals price might be  $7 , so difference of the values

7 - 5 =2 so the loss is not zero .

the basic technique here would be 

y = 3 + 2 * 2 what i have done here is multipied my input x2 with w2 = 2 

7 -7 =0 this is a simple optimisation technique 

but in case lets say we have n number of features , we will use certain calculations and formula to 

1. form a equation out of inputs  - y = w1 * x1 +w2 *x2

2 . finding the optimized values for w1 and w2 so that loss or difference is zero or close to zero.