I generated six eqautions, 3 for soaked CBR, 3 for unsoaked CBR. How will I know the best two equations to choose one from h CBR from the equations generated? Thank you.
You can use the goodness of fit criteria, residual plots, estimate of the standard errors or the nature of the equations. For the goodness of fit criteria, you can compare their adjusted r squares or r squares. The higher the R² or Adj R² , the better the fit hence the better the equation.
For the standard error estimates, the lower the SSE, the higher the precision of the model (equation) thus greater the predictive power of the model and will provide more accurate predictions or estimates of the CBR values.
For the nature or structure of the equations, the simple equation is preferred. Simple in terms of the number of variables, terms and mathematical operations in the equation. The less complex the equation, the more reliable it is to be applied to unseen data and it reduces model risks including overfitting, multicollinearity etc.
For the residual plots, the equation that demonstrates randomly distributed residuals thus no definite pattern revealed and residuals closer to the zero line is preferred. This indicates that the model has captured all the underlying pattern in the data and the errors are due to random factors other than systematic.
Can you tell us more about the three equations that you generated for each of your two conditions?
Damilola Ogundare If i understand you properly. You want to know the best model that fit the data from the equation due to the regression result. If that is the case. To know the best model, i will recommend RMSE, SE rather than R-squared or Adj. R-Squared. The lower the RMSE and SE value the better. It implease the theorised model is close to reality (data).However, the R-squared only tell us how much variance in the DV is accounted by the IV. That doesn't dictate how fit the model is to the data.
Select appropriate statistical metrics to evaluate the accuracy and reliability of the equations. Common metrics include:
- R-squared (R²): Indicates the proportion of variance in the dependent variable that is predictable from the independent variables.
- Root Mean Squared Error (RMSE): Measures the average magnitude of the error.
- Mean Absolute Error (MAE): Measures the average absolute error.
The three equations generated each for oth soaked and unsoaked CBR are for different mix ratio of the additives used.
If these are the only variables in your equation (i.e., there are no covariates), then it sounds like you could perform a 2 x 3 Analysis of Variance.
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