Linear Regression - finding thetha using Normal equation
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.