So I am currently learning some regression techniques for my research and have been reading a text that describes linear regression in terms of basis functions. I got linear basis functions down and no exactly how to get there because I saw this a lot in my undergrad basically, in matrix notation y=wTx you then define your loss function as 1/n Σn(wi*xi-yi)2 then you take the partial derivatives with respect to w set it equal to zero and solve. So now I want to use a non-linear basis functions, lets say I want to use m gaussians basis functions, φi, the procedure is the same but I am not sure exactly on the construction of the model. Lets say I have L features is the model equation of the form yn=ΣmΣLwiφi(xj) in other words I have created a linear combination of M new features, φ(x), which are constructed with all L of the previous features for each data point n: yn=w0+w1(φ1(x1)+φ1(x2)...+...φ1(xL) ......+......wm(φ1(x1)+φ2(x2)...+...φm(xL)) where xi are features / variables for my model and not data values? I hope this makes sense. Thanks in advance.