Question

How to solve for a and b using the method of least squares for: y = ax/b+x?

Answer 1

Let us consider a model of the form

However it is not easy to deal with such type of model therefore we reframe the model by using some approximation.

Here we have consider only the first term as we have to perform least square.

According to least square concept the residual sum of squares is to be minimized which is given by

Now we differentiate above equation with respect to a and b and therefore normal equations is to be obtained.

Now we differentiate SSE with respect to b given by

Thus from the given equation (1) and (2), we can see that the we have relationship between a and b therefore for given x we can obtain z and consequently we have we have two equation with two unknown a and b therefore using least square estimate a and b can be obtain.