Hello there

I have the quadratic regression model y=α+β*x+γ*(x)^2+ε,α,β,γ are unknown
parametres and ε is a random term representing experimental error.
I have that x=0,1,2,3,4,5,6
y=1,4,11,14,21,30,45
I want to fdetermine a,β,γ when the SSE is minimised
the sum of absolute values of the errors is minimised?
and the maximum absolute value of the error is minimised

What I have done is:
I gοt using Excel 4 columns to represent
x,y,y(predicted),y-y(predicted),[y-y(predicted)]^2 for each y,x

and at last one cell to represent SSE:Σ[y-y(predicted)]^2.
and three cells represent the α,β,γ

for a) I want to minimised the SSE by changing cells α,β,γ.
without ε,because we want to estimate and E(ε)=0.(is this correct or I have
to include 7 different ε1,ε2,.... in our y predicted and then I will use them
inthe changing cells with α,β,γ)

for b) I have the column of y-y(predicted)(or I need y(predicted)-y) for
each y.After that I get a column with the abs of previous column.
and one cell with Σ[y(predicted)-y](or other wise) of the abs values.This is
the cell that I want to minimised by changing cells again a,β,γ.

and at last for c) I got the maximum abs value of the error.This is the cell
that I want to minimised by changing cell again α,β,γ.

I am looking forward to hearing you
thanks a lot