Question

Download Regression_Dset.csv and use Feature1 in the dataset as the independent/predictor variable x, and let Feature4 be the dependent/target variable y.

(a) Run simple linear regression to predict y from x. Report the linear model you found. Predict the value of y for new x values 0.3, 0.5, and 0.8.
(b) Use cross-validation to predict generalization error. Describe your methodology.
(c) On the same data, run polynomial regression for p = 2; 3; 4; and 5. Report polynomial models for each. With each of these models, predict the value of y for x values of 0.3, for 0.5, and for 0.8.
(d) Cross-validate to choose the best model. Describe how you did this.

Answer 1

To perform simple linear regression with Feature1 as the independent variable and Feature4 as the dependent variable, calculate the linear model. Use cross-validation to predict generalization error. Run polynomial regression for different values of p and choose the best model by cross-validating each model.

Step-by-step explanation:

The independent variable is Feature1, which will be used as the predictor variable x. The dependent variable is Feature4, which will be used as the target variable y. To perform simple linear regression, we will calculate the slope and intercept of the least-squares regression line. The linear model can be represented as y = mx + b, where m is the slope and b is the intercept.

To predict the value of y for new x values 0.3, 0.5, and 0.8, substitute these values into the linear model equation and calculate the corresponding y values. To use cross-validation to predict generalization error, divide the dataset into training and testing sets. Train the linear regression model on the training set, and then use it to predict the target variable for the testing set. Compare the predicted values with the actual values to measure the model's performance.

For polynomial regression with p = 2, 3, 4, and 5, we will calculate the coefficients of the polynomial models. Each model can be represented as y = apxp + ap-1xp-1 + ... + a1x + a0, where ap, ap-1, ..., a1, a0 are the coefficients of the polynomial terms. To predict the value of y for x values of 0.3, 0.5, and 0.8 in each polynomial model, substitute these values into the corresponding polynomial equation and calculate the corresponding y values.