Supervised Learning - Prediction Week 3 Challenge
1) attached as a file.
2)Please provide the answer with a proper explanation.
3)Mean Squared Error: The MSE is the most commonly used loss function for regression. It measures the average of the squared differences between the predicted and actual values. The formula for the MSE is: MSE = (1/n) * sum((y_pred - y_true)^2)
Mean Absolute Error: The MAE measures the average of the absolute differences between the predicted and actual values. The formula for the MAE is: MAE = (1/n) * sum(|y_pred - y_true|)
Huber Loss: The Huber loss is a hybrid of the MSE and MAE loss functions. It is less sensitive to outliers than the MSE while being differentiable. The formula for the Huber loss is: Huber_loss = (1/n) * sum(L)
Log-Cosh Loss: The Log-Cosh loss is a smooth approximation of the MAE loss function. It is also differentiable and less sensitive to outliers than the MSE. The formula for the Log-Cosh loss is:
Log_Cosh_loss = (1/n) * sum(log(cosh(y_pred - y_true)))
4)The learning rate determines the step size taken in the direction of the negative gradient of the cost function. In other words, it determines how quickly the model learns and how quickly the model converges to the optimal solution. The learning rate is a critical hyperparameter in gradient descent optimization that affects the speed and accuracy of the model's training. Choosing an appropriate learning rate is important for achieving good performance and avoiding common optimization problems such as slow convergence or overshooting.
5)Mean Squared Error: MSE is a common metric used to evaluate the accuracy of a linear regression model. It measures the average squared difference between the predicted and actual output values. A lower MSE indicates a better fit of the model to the data.
R-squared Score: R-squared is a measure of how well the linear regression model fits the data. It represents the proportion of variance in the target variable that is explained by the independent variables. R-squared ranges from 0 to 1, with a higher value indicating a better fit of the model to the data.
Mean Absolute Error: MAE is another metric that measures the average absolute difference between the predicted and actual output values. It is less sensitive to outliers than the MSE.
Root Mean Squared Error: RMSE is a variant of the MSE that takes the square root of the average squared difference between the predicted and actual output values. It is in the same units as the output variable, which makes it easier to interpret.
Cross-Validation: Cross-validation is a technique used to evaluate the performance of a model on a test set that is different from the training set. It can help estimate the generalization performance of the model.
6)Multiple R-squared and adjusted R-squared are both measures of how well a regression model fits the data. Multiple R-squared is the proportion of variance in the dependent variable explained by all the independent variables in the model, while adjusted R-squared is a modified version that adjusts for the number of predictors in the model. Adjusted R-squared is preferred when comparing models with different numbers of predictors.