RSquared  Explained
What is R Squared?
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Table of Contents
What is RSquared?How is RSquare Used?How RSquared Works (Steps in Calculating Rsquared)The Difference Between RSquared and Adjusted RSquaredThe Difference between RSquared and BetaRSquared UsesRSquared LimitationsAcademic Research on RSquaredWhat is RSquared?
Rsquared, also referred to as the coefficient of determination, is a measure of statistics that gives relationships estimate between dependent variables movements based on the movement of the independent variable. In finance, it is a measure of statistics between the performance of an investment and an identified benchmark index.
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How is RSquare Used?
Coefficient of determination is the one that will try to tell you the number of data points that fall within the lines formed results through the regression equation. Linear regression is expressed in percentage, and when the coefficient is higher, so is the points percentage which the line passes through when plotting of data points, and the line is done. Note that 1 or 0 values are an indication that either the regression line represents all the data or none at all. Also, Rsquared is negative, when a model being used is not a good fit for the data. In addition, if an intercept is not set, then the coefficient of determination will definitely be negative too.
How RSquared Works (Steps in Calculating Rsquared)
Generally, the calculation of Coefficient of determination (Rsquared) goes through several steps. They are as follows:
Step one: Take the observations (data points) of the dependent and independent variables, then use a regression model to find the line of best fit.
Step two: Calculate the values that have been predicted by subtracting the actual values, and then squaring the results. After the calculation, you will notice that it will yield several errors squared. When the errors are summed up, they will equal the explained variance.
Step three: Here the variance is calculated by simply subtracting the average real value from the values that have been predicted. You will take results of this square them and then sum them.
Step four: You will divide the first errors sum (Explained variance) by the sum of the second errors (total Variance). You will then minus the derivation from 1 in order to get the Rsquared (coefficient of determination.
The formula of Rsquared, therefore, looks like this:
R = Total variance/Explained variation
Note that the coefficient of determinations range value is 0 to 1, which are commonly expressed as a percentage from 0% to 100%. A coefficient of 100% is an indication that all the security's movement (dependent variable) is explained by the movements in the independent variable(s) that are of interest to you.
Generally, in investment, a high coefficient of determination between 85 percent and 100 percent is an indication that the stocks performance is relatively moving in line with the index. On the other hand, a stock with Rsquared that is low (either at 70 percent or below) is a sign that the movement performance is not in line with the index. Note that a higher Rsquared value indicates a beta figure that is useful. For instance, a stock with Rsquared value that is near 100%, but with a beta below a figure of 1, it is probably producing higher riskadjusted returns.
The Difference Between RSquared and Adjusted RSquared
For Rsquared to work as expected, a simple linear regression model with one variable that is explanatory must be applied. Rsquared is usually adjusted by the use of various independent variables that has multiple regressions. Note that it is the adjusted Rsquared which compares the regression models descriptive power, which is inclusive of diverse predictors numbers. Also, it is important to note that a rise in Rsquared is as a result of each one of the predictors added to a model. In other words, the addition of predictors to a model does not decrease it but rather increases it. Therefore, more terms on a model have a good fit, whereas the adjusted Rsquared compensates the added variables. Generally, Rsquared incorrectly high value which decreases prediction ability happens under overfitting condition. However, this does not happen with the adjusted Rsquared. While the comparison of a standard can compare the goodness of two or more models, adjusted Rsquared is not an ideal metric when it comes to comparing multiple linear regressions or nonlinear models.
The Difference between RSquared and Beta
Rsquared and Beta are correlation measures which are related and at the same time different. However, beta is a measure of relative riskiness. In other words, it is a mutual fund that has a high Rsquared which correlates with a benchmark. Note that when they are used together, the beta is also usually high and is likely to give higher returns than the benchmark. This more likely to happen in the bull market where the rsquare measures the closeness of each change in the assets price and how it correlates to the benchmark. In this case, the beta would measure the magnitude of such changes in relation to a benchmark. This way, it is able to give investors a clear picture of the assets managers performance.
RSquared Uses
Rsquare has many uses. Some of its uses are as highlighted below:
 Investors can use Rsquare measurement to make a comparison between the performances of portfolios with the broader market, predicting the possible occurrence of future trends.
 Secondly, Rsquared can be a measure that investors use to determine the history movement of funds in mutual fund performance industry and its correlation with a benchmark index.
 Also, Rsquare can be used by investors to hedge funds. In other words, they use it to determine their models risk level and its association with given factors.
 Finally, investors can use Rsquared to assist them in determining how their stocks are moving and its market correlation. To determine this, investors will need Rsquared. Note that when a coefficient of determination is close to one, it is an indication that most stock the movement of the stock can be explained by the movement of the market.
RSquared Limitations
 Rsquare will not show you the models reliability you have chosen. Meaning you are not in a position to tell if it is good or bad.
 It also does not tell whether or not your predictions and data are biased. In other words, it does not tell the models reliability.
 With Rsquare, there is a possibility that you will end up with a low rsquared when you use a good model and at the same time, high Rsquare for a model that is poorly fitted and vice versa. This means that it will not tell you how adequate the regression model is.
Academic Research on RSquared
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