What is the Coefficient of Determination?

The coefficient of determination is a famous statistical concept that focuses on how variations in a specific Factor can be clarified by the variation in another factor. Simply put, the coefficient is used to evaluate the relationship between two or more variables. This term is commonly used at R-square, and is also referred to as ‘goodness of fit’.

Coefficient of Determination Formula

The formula of coefficient of determination is:

(R²) = 1 – SS regression / SS total

The coefficient of determination is used in a wide Range of concepts, and the concept where the coefficient is applied plays a significant role in determining the outcome of the event. Sometimes, the insights generated from this statistical concept can vary. It depends on the nature of the model, context, and other such details.

If we draw a graph of the coefficient of determination, then the goodness of fit will be assessed based on the distance between the data points spread throughout the graph and the line. The closer the line is in the data points, the better the fit is. In other words, the good fit means the R2 is closest to the value of 1.0.

Researchers use the coefficient of determination when performing trend analysis.

Coefficient of Determination Example

For better understanding, let's take a look at the example:

If a woman conceives a child on a specific date, how much is the chance of the delivery on the given date? Here, the coefficient aims to find out the linear relationship between the child’s conception and delivery.

The coefficient of determination uses the values between 0 and 1 to represent the relationship between two variables. If you get 0.30, it means 30% of one variable is anticipated by another variable. Similarly, the model is considered as a best fit if the value is 1.0. If the value is 0.50, then it implies that 50% of the data matches the regression model.

Coefficient of Determination Interpretation

Even though this statistical concept offers some powerful insights about the regression model, one should avoid making predictions based on the coefficient of determination solely. While it does focus on the linear relationship, at the same time, the model does not tell you the causation relationship between two variables.

Besides that, it cannot suggest the integrity of the regression model. It is, therefore, important for researchers to use the coefficient of determination in conjunction with different statistical models before drawing any conclusion. The more statistical concepts you use for finding the relationship between different variables, the better and more accurate the outcome will be.

Contrary to popular beliefs, the high coefficient percentage may not always be effective for the regression model. The reliability of this model relies on a few important factors, such as the type of variables you have used, applied data, and more. In some cases, the high coefficient percentage might show problems with the regression model. Then again, it depends on the variables you employ. There is no specific rule that shows how the coefficient is to be applied to the regression model for assessing the relationship between two variables.