OLS/GLS: The linear projection methods

Defines

#define apop_estimate_r_squared(in)

Functions

apop_data * apop_estimate_coefficient_of_determination (apop_model *in)

Detailed Description

Define Documentation

#define apop_estimate_r_squared ( in )

A synonym for apop_estimate_coefficient_of_determination, q.v.

Function Documentation

apop_data* apop_estimate_coefficient_of_determination ( apop_model * in )

Good ol' $R^2$ . Let $Y$ be the dependent variable, $\epsilon$ the residual, $n$ the number of data points, and $k$ the number of independent vars (including the constant). Returns an apop_data set with the following entries (in the vector element):

$SST \equiv \sum (Y_i - \bar Y) ^2$
$SSE \equiv \sum \epsilon ^2$
$R^2 \equiv 1 - {SSE\over SST}$
$R^2_{adj} \equiv R^2 - {(k-1)\over (n-k-1)}(1-R^2)$

Internally allocates (and frees) a vector the size of your data set.

Parameters:

in

The estimate. I need residuals to have been calculated, and the first column of in->data needs to be the dependent variable.

Returns:

: a $1 \times 5$ apop_data table with the following fields:

"R_squared"
"R_squared_adj"
"SSE"
"SST"
"SSR"