Statistics: given total sum of squares, find R²

[939]

Homework Statement

Given:
Σ(xi - x̄)² = 500
Σ(yi - ybar)² = 800 (total sum of squares, SST))
Σ(ŷ - ybar)² = 400 (total sum of estimators, SSE)
Σ(xi - x̄)²(yi) = 200
Σ(xi - x̄)²(εi) = 0
n = 1000
s² = 4

Find (or explain why you cannot find):
β1
β0
variance of β
R²

Homework Equations

[/B]
Σ(xi - x̄)² = 500
Σ(yi - ybar)² = 800 (total sum of squares, SST))
Σ(ŷ - ybar)² = 400 (total sum of estimators, SSE)
Σ(xi - x̄)²(yi) = 200
Σ(xi - x̄)²(εi) = 0
n = 1000
s² = 4

The Attempt at a Solution

R² = SSE/SST = 400/800 = 200

But to be honest, I have no idea how to find β1, β0, or the variance of β... Can anyone help?

 

[RUber]

Normally, in a regression equation like this, $\beta_0 = \mu$ which is the overall sample mean. I don't see any immediately discernible information for finding those parameters, but it maybe in there with some algebra.
Your $R^2$ equation looks right, but that is not equal to 200. $R^2$ is always between 0 and 1.

 

[SteamKing]

The Attempt at a Solution

R² = SSE/SST = 400/800 = 200

But to be honest, I have no idea how to find β1, β0, or the variance of β... Can anyone help?

Since when is 400 / 800 = 200? Is this the New Math everyone keeps talking about?

 

[939]

lol yea stupid error, 0.5, sorry :(

 

[WWGD]

Most statistical packages will spit out all the estimators if you input relatively little data.

This Wiki page has explicit formulas for $\beta$ and $\beta_0$:

http://en.wikipedia.org/wiki/Simple_linear_regression