Question

What is the relationship between R-Squared and the correlation coefficient of a model?

Answer 1

This question requires knowledge of linear regression topic. It is a topic that comes under statistics and one needs to know all the basic things related to this in order to answer this question. In a linear regression model, we have what are known as correlation coefficient R and ${{R}^{2}}.$ We define these terms and then represent the relation between these terms.

Complete step by step solution:
Let us consider a simple linear model with variables x and y. The coefficient that determines how x is related to y and vice versa is called the correlation coefficient R of that model. These relations are simplified as follows:
If x and y are uncorrelated, the coefficient would be 0.
If x and y are in perfect unison, the coefficient will be equal to +1.
If x increases and y decreases at the same rate in the opposite directions, the coefficient will be equal to -1.
In this case, the value of the correlation coefficient R is sufficient. Now let us suppose that we have more than one independent variable. In this case, it becomes difficult to define what the coefficient of correlation is. The relation between the exact variable and the correlation is unclear. This is when we use the ${{R}^{2}}$ term. This ${{R}^{2}}$ term is nothing but the square of the correlation coefficient R.
Here again, the value 0 for the ${{R}^{2}}$ term indicates no correlation. A value of 1 (always positive since it is a squared term) represents a positive or a negative correlation. The main objective to use the ${{R}^{2}}$ is for the multivariate models. We can use this for more complex models too.

Note: To answer this question, students are required to know the topic of regression in statistics to solve this question easily. Care must be taken while writing this answer in order to make the point clear in the answer. Poor understanding of regression may lead to a wrong answer. It is always best to have a strong hold on these topics to answer these questions.