Final answer:
In evaluating a linear regression model, the appropriate metric is the cost function, which measures the error between predicted and actual values. Other metrics mentioned, such as Goodhart's Law, Accuracy, and ROC, are not suitable for this purpose. The slope, y-intercept, correlation coefficient, and coefficient of determination are important concepts in understanding the regression equation.
Step-by-step explanation:
To evaluate a linear regression machine learning model, the metric used is the cost function. The cost function measures the error between the predicted values and the actual values in the data set. It is often represented as the mean squared error (MSE) or mean absolute error (MAE) during the training of the linear regression model. Examples of the cost function include the sum of squared distances between the prediction and the actual data points. The other options such as Goodhart's Law, Accuracy, and Receiver operating characteristic (ROC) are not commonly used for linear regression models. ROC is used for classification problems, accuracy is a measure of correct predictions in classification, and Goodhart's Law is an adage stating that when a measure becomes a target, it ceases to be a good measure. None of these directly relate to evaluating the performance of a linear regression model.
The slope of the regression equation (slope) signifies how much the dependent variable changes for a unit change in the independent variable. The y-intercept of the regression equation is the value of the dependent variable when all independent variables are zero. The correlation coefficient, represented by r, is a measure of the strength and direction of the relationship between two variables. The coefficient of determination, denoted as R², represents the proportion of the variance for the dependent variable that is explained by the independent variable(s) in the regression model.