Regularized-Regression-in-R

Regularized Regression Ridge and Lasso in R Files contain of:

1. Split Training and Test Dara
2. Correlation Study. The results are:

• The Feature tax and rad are positively correlated with each other (0.91)
• The feature age and dis are negatively correlated with each other (-0.75)
• Price (medv) depends upon feature RM (positively correlated 0.75) and lstat (negatively correlated -0.76) -Since Threshold abs(corr) >=0.8, the feature tax and rad are selected to be compared with medv. Since rad -> medv < tax -> medv, rad (Index of accessibility to radial highways) will be drop

3. Model Training (Ridge Regression and Lasso Regression). The Result are:

• The best lambda of ridge regression based on validation data is 0.01. The RSME value or The standard deviation of prediction errors is 4.3464 (lowest).
• The best lambda of lasso regression based on validation data is 0.01. The RSME value or The standard deviation of prediction errors is 4.340783 (lowest).

5. Model Evaluation. The intrepetation of RSME, MAE, and MAPE

RSME

• Ridge: RSME values is 6.820639 which means The standard deviation of prediction errors is 6.820639 i.e. from the regression line, the residuals mostly deviate between +- 6.820639.
• Lasso: RSME values is 6.823445 which means The standard deviation of prediction errors is 6.823445 i.e. from the regression line, the residuals mostly deviate between +- 6.823445.

MAE

• Ridge: On average, our prediction deviates the true medv by 3.898674.
• Lasso: On average, our prediction deviates the true medv by 3.888415.

MAPE

• Ridge: The 3.898674 deviation is equivalent to 17.11394% deviation relative to the true medv
• Lasso: The 3.888415 deviation is equivalent to 17.07025% deviation relative to the true medv