A 100% R-squared means that all movements of a security (or other dependent variable) are fully explained by the movements of the index (or the independent variable(s) you are interested in). R-squared values range from 0 to 1 and are commonly referred to as 0% to 100%. From there, divide the first sum of the errors (explained variance) by the second sum (total variance), subtract the result from one, and you have the R square. To calculate the total variance, you subtract the average real value from the predicted values, square the result and add it up. In this way you get a list of errors squared, which is then added up and is equal to the explained variance. From there you calculate the expected values, subtract the actual values and square the result. This includes collecting data points (observations) of dependent and independent variables and finding the best fit line, often from a regression model. The actual calculation of R-squared requires several steps.
The same can be applied to a stock relative to the S&P 500 index or any other relevant index. For example, an R-squared for a fixed income security compared to a bond index identifies the percentage movement in the price of the security that can be expected based on a movement in the index price. When investing, R-squared is generally interpreted as the percentage of the movements of a fund or security that can be explained by the movements of a reference index. \beginR2=1−Total VariationExplained Variation
So, if R2 of a model is 0.50, then about half of the observed variation can be explained by the model inputs. While correlation explains the strength of the relationship between an independent variable and a dependent variable, R-squared explains the extent to which the variance of one variable explains the variance of the second variable. R-squared (R2) is a statistical measure representing the proportion of the variance for a dependent variable that is explained by one or more independent variables in a regression model.
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