Supervised Learning - Prediction Week 3 Challenge
1ans.
It is Submitted in Python Notebook
2ans.
L1 Mean absolute error: finds the mean of the absolute difference between the predicted and actual value. It is good for data set with little or no outliers. However, it needs more complicated tools such as linear programming to calculate the gradients of the parameters.
L2 Mean squared error: Finds the mean of the square of the difference between the predicted and actual value. It is good for data set with outliers, however returns an error in different units. Due to its mathematical properties, it is easier to calculate the gradients of the parameters. The squaring means that larger mistakes result in more error than smaller mistakes, meaning that the model is punished for making larger mistakes.
Finding the root of the mean squared error, i.e. using root mean square error bring the error term to match with the data set in terms of units.
3ans.
Root mean square error
Mean square error
Mean absolute error .
4ans.
Let F be a function that determines the error between the data set and the predicted values. The predicted values depend on two parameters m, and c. Gradient descent is a method to determine the values of the parameters for which F returns the least value.
Learning rate is an important factor that determines how fast the function parameter approaches a nominal value. Gradient descent is a method to determine the values of the function parameters for which the function returns the minimum error.
F = 1/(2n) * E^ni=i ((mxi + c)-Yi)^2
m = m - alfa(6F/6m)
c = c - alfa(6F/6c)
Giving a high learning rate will cause the function to overshoot beyond its lowest value and will never reach its lowest value or will oscillate before arriving at one.
Giving a low learning rate will cause the function to approach the lowest value very slowly leading to a high number of iterations.
5ans.
Linear regression can be evaluated by determining how good the fit is, i.e. what is the error between the predicted value and the data set.
6ans.
When the dependent variable depends on only one independent variable then it is known as the linear coefficient of determination, but when it depends on multiple Independent variables then it is multiple coefficient of determination.
The Adjusted coefficient of determination is the method in which the parameters which do not contribute towards the predicted value are ignored. These parameters are called insignificant independent variables.