- Implement the normal equation (closed form) regression for the Bosto n housing dataset. The dataset description can be found her e. The target feature is variable no. 14, ’MEDV’, and the input variables are the remaining 13 variables.
- Divide the dataset into training and testing using an 80:20 split ratio.
- Perform Linear regression for all features and compute the RMSE for training as well as the testing set. (Note: There is no need to perform k-fold cross-validation for this part.)
- Select the feature named ‘LSTAT’ for polynomial regression.
- Perform k-fold cross-validation for k=5 on the training dataset. (Note: You can not use any inbuilt library to implement k-fold cross-validation.)
- Perform step (d) for different degrees of polynomials using Polynomial Regression (Ex. For degree=1 perform 5-fold cross-validation, For degree=2, perform 5-fold cross-validation and so on.)
- Use RMSE as an evaluation metric (Note: You can’t use any inbuilt library for it). Compute mean RMSE of training and validation set separately from 5-fold cross-validation for each degree of the polynomial and plot it.
- Choose the degree of a polynomial with the least mean validation RMSE and use that degree of polynomial to perform final regression on the whole training dataset (i.e., 80% dataset). State the RMSE of the test dataset (i.e., 20% dataset).
- Use the following dat a that contains only 1 input feature and 1 target variable i.e X and Y. Consider the dataset as a whole i.e. Don’t split it into train or test data.
- Perform the steps (d), (e), (f) of Part-1.
- Show the plots of line/curve fitted for the dataset using the different degrees of polynomials (degree). I.e, degree = [1,2,4,5,10,15,30]. Compute and state their RMSE also.
Note: Mention all the observations, results, analysis, visualizations and experiments in the report for each part (if any).
