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pandaBee
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Homework Statement
In my statistics notes/lectures my professor will oftentimes use an identity that looks like the following:
x_i is a non random variable, the summand is from i=1 to n;
This segment comes from notes on linear regression (y_0 = b_0 + b_1*x_i)
I actually forgot to mention that x-bar is supposed to be squared on the LHS, sorry about that.
∑(x_i)^2 - n*x-bar^2 = Σ(x_i - x-bar)^2
However I just do not see how this works out at all!
When I work it It turns out that x-bar = 1 but this doesn't make sense to me at all in the context.
Does anyone have some insight they could provide me?
********EDIT*****
After working through it a few times I actually solved the identity myself, however I am still curious if there's perhaps a more elegant way to power through the proof compared to the way I personally did below. Sorry for the confusion.
Homework Equations
The Attempt at a Solution
Σ(x_i - x-bar)^2
= Σ(x_i^2 - 2*x-bar*x_i + x-bar^2)
= Σ(x_i^2) - 2*x-barΣ(x_i) + n*x-bar^2 = ∑(x_i)^2 - n*x-bar^2 (by the above equation in part 1)
⇒-2*x-barΣ(x_i) + n*x-bar^2 = - n*x-bar^2
If you divide both sides by x-bar^2;
-2Σ(x_i)/(x-bar) + n = -n
= -2*n*x-bar/(x-bar) + n = -n
= -2n + n = -n
or - n = - n
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