What does an R-Squared value indicate about a linear regression?

Question

Josiah Allen · Accepted Answer

It indicates to what extent, the independent variable explains the dependent variable.

Suppose your dependent variable #y# is a social variable. It is affected by so many forces. # x #is one of the forces. Now we shall have it like this. #y# is affected by# x# and variables other than # x.# In regression we collect data relating to #x# and #y.# We want to know how far the variation in #y# is caused by# x# alone. We calculate #R^2#. If its value is 0.74. Our conclusion is that 74% variation in #y# is attributable to #x#. It goes without saying the rest 26% change in #y# is caused by variables other than #x#.

Greyson Taylor · Answer

undefined The R-squared value, also known as the coefficient of determination, indicates the proportion of the variance in the dependent variable (y) that is predictable from the independent variable(s) (x) in a linear regression model. In other words, it measures how well the regression line fits the actual data points.

The R-squared value ranges from 0 to 1, where:
- 0 indicates that the regression line does not explain any of the variability in the dependent variable.
- 1 indicates that the regression line perfectly explains all of the variability in the dependent variable.

Therefore, a higher R-squared value suggests a better fit of the regression line to the data points, meaning that a larger proportion of the variability in the dependent variable can be explained by the independent variable(s). Conversely, a lower R-squared value indicates that the regression line does not fit the data well and that the independent variable(s) may not be good predictors of the dependent variable.

However, it's important to note that the R-squared value alone does not determine the appropriateness or validity of a regression model. It is crucial to consider other factors such as the significance of the regression coefficients, the residual analysis, and the context of the data before drawing conclusions about the effectiveness of the regression model.