R-Squared is also known as the Coefficient of Determination and is an output from regression analysis. It represents the percentage of response variable variation that is explained by its relationship with one or more predictor variables. In general, the higher the R-squared value, the better the model fits your data. It is always between 0 and 100%.
R-Squared Adjusted is a modified version of R-Squared value. In addition to explaining the percentage of response variable variation that is explained by its relationship with one or more predictor variables, it also takes into account the number of predictor variables. It increases if an additional predictor improves the model more than what is expected by chance. R-Squared Adjusted can be used to compare multiple regression models with different number of predictor variables for the same response variable.
Regression Analysis is a statistical tool that defines the relationship between two or more variables. It uses data on relevant variables to develop a prediction equation, or model. It generates an equation to describe the statistical relationship between one or more predictors and the response variable and to predict new observations.
An application-oriented question on the topic along with responses can be seen below. The best answer was provided by Vastupal Vashisth on 25th March 2019.
Applause for the respondents - Vastupal Vashisth
Also review the answer provided by Mr Venugopal R, Benchmark Six Sigma's in-house expert.