adjrsq#

Purpose#

Finds the adjusted R-Squared statistic following the estimation of a linear regression model. It requires both the original data and the residuals from the estimate as inputs.

Format#

{ r_sq, adj_rsq } = adjRsq(yt, res, num_vars)#

Parameters:

yt (TxM matrix) – data.
res (TxM matrix) – estimation residuals.
num_vars (Scalar) – number of estimated coefficients (including constant) in the original regression.

Returns:

r_sq (Mx1 matrix) – standard R-Squared statistics.
adj_rsq (Mx1 matrix) – adjusted R-Squared statistics.

Example#

This example utilizes a simple multivariate linear model. To begin we generate a sample of independent data (Y):

rndseed 89102;
xt = rndn(100, 5);
yt = 0.4 + 4.75*xt[., 1] + 0.9*xt[., 2] + 3.2*xt[., 3] - 2.1*xt[., 4] - 2.9*xt[., 5] + rndn(100, 1);

Next, estimate an ols model using the generated data:

// Estimate OLS model
struct olsmtControl oc0_2;
struct olsmtOut oOut_2;
oc0_2 = olsmtControlCreate();

// Compute residuals
oc0_2.res = 1;

// Estimate model
oOut_2 = olsmt(oc0_2, 0, yt, xt);

res = oOut_2.resid;
num_var = cols(xt) + oc0_2.con;

Finally, call adjRsq:

// Residual input
res = oOut_2.resid;

// Number of variables
num_var = cols(xt) + oc0_2.con;

// Compute adjust Rsq
{ r, adj_r } = adjRsq(yt, res, num_var);

This produces the following output:

Valid cases:        100      Dependent variable:       Y
Missing cases:        0      Deletion method:       None
Total SS:      3461.187      Degrees of freedom:      94
R-squared:        0.972      Rbar-squared:         0.971
Residual SS:     95.912      Std error of est:     1.010
F(5,94):        659.640      Probability of F:     0.000
Durbin-Watson:    2.093
Standard         Prob   Standardized Cor with
Var  Estimate Error   t-value  >|t|  Estimate  Dep Var
--------------------------------------------------------
CONST  0.2996  0.1032   2.9036   0.005   ---        ---
X1     4.7128  0.1076  43.7811   0.000   0.7671   0.6528
X2     0.9561  0.1058   9.0379   0.000   0.1600   0.3434
X3     3.3507  0.1178  28.4434   0.000   0.5081   0.3188
X4    -2.0465  0.1078 -18.9913   0.000  -0.3302  -0.2412
X5    -2.8348  0.1055 -26.8741   0.000  -0.4814  -0.3634

The standard R squared is 0.972289

The adjusted R squared is 0.970502

Library#

tsmt

Source#

var_lm.src