Linear Regression - finding thetha using Normal equation This is to find thetha which will give minimum cost function. Why is the x0 column required? why cant we assign size as x0? why do we need the feature count to be n+1?
Consider the 1-D equivalent of the table you have provided. In this case, you have one input x and one output y (see figure). If you try to fit the data points with y=mx equation, you can not fit the data successfully. You need an equation like y=mx+c to have a good fit. y=mx will be a good fit only if the line goes through the origin.
Now you can look at

y=mx+c

as

y = m * x + c * 1
y = m * X1 + c * X0
y = W1 * X1 + W0 * X0

I hope the figures below will clarify why we need the intercept term X0 and its weight W0=c.