What is R square and how R square is different from Adjusted R square

Question

Accepted Answer

R square is a statistical measure that represents the proportion of the variance in the dependent variable explained by the independent variables.

R square is a value between 0 and 1, where 0 indicates that the independent variables do not explain any of the variance in the dependent variable, and 1 indicates that they explain all of it.
It is used to evaluate the goodness of fit of a regression model.
Adjusted R square takes into account the number of predictors in the model and adjusts the R square value accordingly.
Adjusted R square penalizes the addition of unnecessary predictors that do not significantly contribute to the model's performance.
Adjusted R square is always lower than or equal to R square.
The formula for R square is: R square = (SSR / SST), where SSR is the sum of squared residuals and SST is the total sum of squares.
The formula for Adjusted R square is: Adjusted R square = 1 - [(1 - R square) * (n - 1) / (n - k - 1)], where n is the number of observations and k is the number of predictors.

Accepted Answer

R square explain the explained variation by the total variation in the model. Higher R square indicate better fit and less multicollinearity. R square had its own disadvantages as if we add an insignificant variable to the model it doesn't decrease. R square either increase or stays as it is hence we should see adjusted R square. If u add any insignificant variable adjusted R square decreases.

What is R square and how R square is different from Adjusted R square

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