SAS provides the capability to build regression models to analyze ordinal data correlations and use this model to predict out-of-sample values. Here is the process:
Model settings: One can add simple variables to the indepedent variables set. If one suspects a combinaiton of variables can be influencing the dependent variable, one can add this combination of variables as “Cross” As shown in the below snapshot:
Regression Model selection is also performed here, and the following models are the options: Full Factorial – N-Factorial – Polynomial Order:
The following is an example of the results:
|Dependent Mean||472.22486||Adj R-Sq||0.3194|
|Number of Observations Read||150|
|Number of Observations Used||35|
|Number of Observations with Missing Values||115|
ANOVA for testing whether the predictors’ coefficients collectively are different from 0. In other words if there is a linear relationship of the response variable with the predictor ones, thus whether this (or any) model is good:
|Analysis of Variance|
|F Value||Pr > F|
This indicates that if the average coefficient was 0, there is a tiny chance to get our values of the coefficients. Thus there must be a linear relationship between the variables, and that the regression model is good.
Further analysis on the goodness of the model:
R-Square and Adjusted R-Square also test the collective correlation between the response and all the predictor variables collectively in one number. A value near 1 means high correlation and thus the regression is good, and near 0 means not good.
RMSE tests the goodness of regression fit by measuring the residuals.
Here the test checks whether each predictor variable separately has a significant coefficient. Clearly VIX and Jobless and P_E seem not good predictors (there is high possibility that their coefficients are near 0):
|t Value||Pr > |t||