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