# What precautions we need to keep in mind when using ‘coefficient of determination’?

The coefficient of determination, also known as R-squared, is a statistical metric used to evaluate how well a regression model fits the data. It measures the proportion of the variance in the dependent variable that can be explained by the independent variables in the model. In other words, it indicates the percentage of the variation in the dependent variable that is explained by the independent variables.

The coefficient of determination ranges from 0 to 1, where 0 indicates that the model does not explain any of the variance in the dependent variable, and 1 indicates that the model explains all of the variance in the dependent variable. An R-squared value of 1 means that the regression model perfectly fits the data, and all the observed variation in the dependent variable can be explained by the independent variables.

R-squared is a widely used metric to evaluate the goodness of fit of a regression model. It is a helpful tool for comparing different models and selecting the best one that fits the data well. However, it is not a perfect metric, and it has some limitations.

For instance, R-squared only measures the proportion of the variance in the dependent variable that is explained by the independent variables in the model. It does not account for other factors that may affect the dependent variable, such as measurement errors or unobserved variables. Therefore, a high R-squared value does not necessarily mean that the model is perfect or that it has a strong predictive power.

Moreover, R-squared is sensitive to the number of independent variables in the model. Adding more independent variables to the model will increase the R-squared value, even if the additional variables do not have any significant impact on the dependent variable. Therefore, it is important to use other metrics, such as adjusted R-squared, that take into account the number of independent variables in the model.

In summary, R-squared is a useful metric for evaluating the goodness of fit of a regression model, but it has some limitations that need to be taken into account. When using R-squared, it is important to keep in mind its sensitivity to the number of independent variables and its inability to account