If anyone could help me in anyway, by answering or even just guiding as to where I could find some sort of help to help me figure out the question or even just how to start it I will be very grateful.

Q)

Consider the simple linear regression model of y on x, y = β0 + β1x + ε where ε ∼ N(0, σ2)

Define z = x − x¯, i.e., x centered around the mean.

(a) Show that the regression of y on z has intercept equal to y¯.

(b) Show that the slope from the regression of y on z is the same as that fromthe regression of y on x.