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Interpreting R Squared in Details

r squared interpretation help

Image credit: cognitiveperformancegroup.com

R Squared Meaning

R squared meaning = understood variation / total variation

R squared is a measure of how close to the fitted regression line the data is. Other names for it include the coefficient of multiple determination for multiple regression – or simply the coefficient of determination.

In plain simple English, R squared meaning is basically the relationship between two events. If for example, one event begets another – such as sales inducing high profit margins – the R squared will demonstrate this by being high. If two events have absolutely no relation to one another, the R squared will demonstrate this by being low – zero, in fact. Interpreting R squared is essentially determining how high or low t is.

R squared typically veers between 0% and 100% on a graph and is defined as the % of response variable variation as understood by data and results extracted from a linear regression model.

Why Does It Veer Between 0% and 100%?

R squared is always rooted between one of these two points. The closer it is to 0%, the less chance that you regression linear model explains the variability of the response data centred around its mean.

The closer R squared is to 100%, the greater the chance that your model explains your data analysis. If R squared is 100%, you’ve hit the jackpot because your model explains all the variability of the response data. For example, if you’re trying to understand the relationship between the movements of a security and the movements of an index, and your R squared interpretation is 100%, it means that the movements of one is explained by the movements of another.

The higher your R squared – let’s say it’s 100% – the better your data fits the mode. The lower the R squared – let’s say it’s 0% – the more worthless it becomes because one variable doesn’t explain the other.

Interpreting R Squared

R squared interpretation means that you are measuring the proportion of variability via data. If your R squared is low, it means that your variance is high, thus one variable doesn’t necessarily explain the other variable. If your R squared is high, it consequently means that the variance is low – which is pretty much what you want. Essentially, R squared interpretation means understanding how closely two variables work together, and how closely one affects the other. For example, sales affecting profits.

On the data graph below, when the activities of two variables are closely related, the R squared rises. When two variables are not closely related, the R squared plummets. If the two variables are completely random events that have no relation to one another whatsoever, the R squared will drop all the way down to zero.

Interpreting R squared means you are interpreting statistics. Whilst statistics in and of themselves are useful, they do not help us understand the actual events.

Whilst R squared interpretation can help you identify relationships between two events, and whilst it does act as a good forecaster of future events, it isn’t all you need to do to understand a causal relationship!