# Adjusted R Squared Formula – Problem Solution with Solved Example

## R Squared Formula

R squared is also termed as the coefficient of determination that could be given either through R2 and R-squared in mathematics. This is the number indicating the variance for the dependent variable that could be predicted through independent variable too. This is a statistics model that can be used for the future predictions or outcomes. It is also used as hypothesis or testing technique too. The linear relationship between dependent or independent variables could be given though formula. Here is given the R squared formula in mathematics –

#### Following is the R Squared formula:

$\large R^{2}=\frac{N\sum xy-\sum x \sum y}{\sqrt{\left[N\sum x^{2}-\left(\sum x\right)^{2}\right]\left[N\sum y^{2}-\left(\sum y\right)^{2}\right]}}$

Where,
N = No of scores given
Σ XY = Sum of paired product
Σ X = X score sum
Σ Y = Y score sum
Σ X2 = square of X score sum
Σ Y2 = square of Y score sum

Once you find the linear model with regression analysis, next you need to check how well the model fits the data. Today, there are a plenty of software applications too that can be used for the same purpose. Keep in mind that R-squared values are not always bad but they are not always good as well. Linear regression calculates the equation that minimizes the distance between fitted line and all data points too.

Technically, ordinary least squares minimize the sum of squared residuals. In simple words, the model fits the data well when the differences between the observed values and model’s predicted values are unbiased and small. Before we check the fitness of statistical measures or goodness of fit, also check the residual plots too. In general, residual plots could never reveal the unwanted residual patterns and it indicates that biased results are always more effective when compared to other numbers.  R squared value always lie between zero to hundred percent.