Linear Regression Cost Function J Visualization A popular machine learning method for forecasting a continuous target variable is linearregression. A straightforward statistical model is used to predict how two variables willinteract. In order to better comprehend the effectiveness of the model, we will talk about thecost 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 thedependent 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 themodel in forecasting the target variable is assessed using the cost function J. The total ofthe 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 idealvalues of w and b that produce the best-ﬁtting line. The cost function J is minimized duringthe optimization procedure. In other words, the objective is to identify the w and b valuesthat 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 yaxes correspond to the values of w and b and the z axis to the value of J. The cost function Jis 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 contourplot, with the values of w and b on the x and y axes and J's values on the contour lines. Thisplot 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 bothplots. The best-ﬁtting line that may be used to generate predictions about the target variableis represented by this point.