I've got an uni assignment to do and I can't figure out one of the questions.
We have to consider 2 models, the first being Y = Beta1 + Beta2(X) + u
Then the second being Y = Alpha1 + Alpha2(X/100) + u
We've been given a dataset:
82.1 41.3 29.2 18.5 -25.2 -29.3 27 16 57.1 61.9 29.3 45.5 -31.2 -35.8 30 14 50.3 35.3 61.9 31
I've worked out Beta1 = 10.698 and Beta2 = 1.026 ,using the formulas described below for the first model, which is correct, but I'm not too sure on the 2nd model:
For the 2nd model, we have to derive the estimators of the parameters (alpha1 + alpha2).
I know Alpha2 would equal Beta2Hat, which = Summation(xiyi)/Summation(xi^2)
Alpha1 would also equal Beta1Hat?, which = YHat - Beta2Hat*XHat
The thing that has confused me is the (X/100).
How would the (X/100) change the estimators of the parameters?