Linear Regression Cost Function J Visualization

University:
Stanford University
Course:
CS229 | Machine Learning
Academic year:

2023
Views:

30

Pages:

2
Author:

anon

Linear Regression Cost Function J Visualization A popular machine learning method for forecasting a continuous target variable is linear regression. A straightforward statistical model is used to predict how two variables will interact. In order to better comprehend the effectiveness of the model, we will talk about the cost function J in linear regression, its relevance, and how it might be displayed. Understanding Linear Regression's Cost Function J Finding the line that best fits the connection between the independent variable (x) and the dependent variable is the objective of linear regression (y). The model's parameters, w (weight) and b, select the line that fits the data the best (bias). The effectiveness of the model in forecasting the target variable is assessed using the cost function J. The total of the squared discrepancies between the actual and anticipated values is used to calculate it. A key element of linear regression is the cost function J, which aids in identifying the ideal values of w and b that produce the best-fitting line. The cost function J is minimized during the optimization procedure. In other words, the objective is to identify the w and b values that lead to the cost function J's lowest value. Cost Function Visualization J There are two ways to represent the cost function J visually: The cost function J can be represented graphically as a 3D-surface plot, in which the x and y axes correspond to the values of w and b and the z axis to the value of J. The cost function J is plotted here to show how it changes as w and b are changed. Contour Plot: The cost function J can alternatively be represented graphically as a contour plot, with the values of w and b on the x and y axes and J's values on the contour lines. This plot shows more clearly how the cost function J alters as w and b are changed. The optimal values of w and b are those where the cost function J is at its minimum in both plots. The best-fitting line that may be used to generate predictions about the target variable is represented by this point.