R-Squared

R-squared is a statistical measure of how well the regression line fits the data points. It is a number between 0 and 1, where 0 means that the regression line does not fit the data at all and 1 means that the regression line perfectly fits the data.

R-squared is calculated by squaring the correlation coefficient, which is a measure of the linear relationship between two variables. The correlation coefficient can range from -1 to 1, where -1 means that the variables are perfectly negatively correlated and 1 means that the variables are perfectly positively correlated.

R-squared is a useful measure of the predictive power of a regression model. A high R-squared value indicates that the regression model is able to accurately predict the values of the dependent variable. A low R-squared value indicates that the regression model is not able to accurately predict the values of the dependent variable.

R-squared is also used to compare the performance of different regression models. A model with a higher R-squared value is generally considered to be a better model than a model with a lower R-squared value.

Here is an example of how R-squared is calculated. Suppose we have a data set of 10 observations of the relationship between the height and weight of people. We can use a linear regression model to predict the weight of a person based on their height. The regression line is shown in the following graph.

The R-squared value for this regression model is 0.8, which indicates that the regression line fits the data points well. This means that the regression model is able to accurately predict the weight of a person based on their height.

R-squared is a useful statistical measure that can be used to evaluate the performance of a regression model. It is a measure of how well the regression line fits the data points and can be used to compare the performance of different regression models.