R-Squared is **a statistical measure of fit that indicates how much variation of a dependent variable is explained by the independent variable(s) in a regression model**.

The R-squared scale ranges from 0 to 100, with 100 indicating that a fund's performance is highly correlated with the index it tracks. A fund that has an R-squared between 85 to 100 is considered one with a good R-squared. A fund with an R-squared of 70 or less is considered a poor R-squared.

Any study that attempts to predict human behavior will tend to have R-squared values less than 50%. However, if you analyze a physical process and have very good measurements, you might expect R-squared values over 90%. There is no one-size fits all best answer for how high R-squared should be.

In general, the higher the R-squared, the better the model fits your data.

For example, in scientific studies, the R-squared may need to be above 0.95 for a regression model to be considered reliable. In other domains, an R-squared of just 0.3 may be sufficient if there is extreme variability in the dataset.

R-square value tells you how much variation is explained by your model. So 0.1 R-square means that your model explains 10% of variation within the data. The greater R-square the better the model.

Any R^{2} value less than 1.0 indicates that at least some variability in the data cannot be accounted for by the model (e.g., an R^{2} of 0.5 indicates that 50% of the variability in the outcome data cannot be explained by the model).

A low R-squared value indicates that your independent variable is not explaining much in the variation of your dependent variable - regardless of the variable significance, this is letting you know that the identified independent variable, even though significant, is not accounting for much of the mean of your ...

All Answers (98) low R-squared values are not always bad and high R-squared values are not always good! In my opinion, the question of "low" or "high" R-square is really subjective. You need to cross-validate the regression to measure the possible inflation of scores due to overfitting.

Generally, an R-Squared above 0.6 makes a model worth your attention, though there are other things to consider: Any field that attempts to predict human behaviour, such as psychology, typically has R-squared values lower than 0.5. Humans are inherently difficult to predict!

Practically R-square value 0.90-0.93 or 0.99 both are considered very high and fall under the accepted range. However, in multiple regression, number of sample and predictor might unnecessarily increase the R-square value, thus an adjusted R-square is much valuable.

- if R-squared value 0.3 < r < 0.5 this value is generally considered a weak or low effect size, - if R-squared value 0.5 < r < 0.7 this value is generally considered a Moderate effect size, - if R-squared value r > 0.7 this value is generally considered strong effect size, Ref: Source: Moore, D. S., Notz, W.

An R^{2} of 1 indicates that the regression predictions perfectly fit the data. Values of R^{2} outside the range 0 to 1 occur when the model fits the data worse than the worst possible least-squares predictor (equivalent to a horizontal hyperplane at a height equal to the mean of the observed data).

R^2 of 0.2 is actually quite high for real-world data. It means that a full 20% of the variation of one variable is completely explained by the other. It's a big deal to be able to account for a fifth of what you're examining.

A fund with a low R-squared, at 70% or less, indicates the security does not generally follow the movements of the index. A higher R-squared value will indicate a more useful beta figure.

Despite the same R-squared statistic produced, the predictive validity would be rather different depending on what the true dependency is. If it is truly linear, then the predictive accuracy would be quite good. Otherwise, it will be much poorer. In this sense, R-Squared is not a good measure of predictive error.

The best fit line is the one that minimises sum of squared differences between actual and estimated results. Taking average of minimum sum of squared difference is known as Mean Squared Error (MSE). Smaller the value, better the regression model.

A correlation coefficient of . 10 (R2 = 0.01) is generally considered to be a weak or small association; a correlation coefficient of . 30 (R2 = 0.09) is considered a moderate association; and a correlation coefficient of . 50 (R2 = 0.25) or larger is thought to represent a strong or large association.

R-squared or R2 explains the degree to which your input variables explain the variation of your output / predicted variable. So, if R-square is 0.8, it means 80% of the variation in the output variable is explained by the input variables.

The relationship between two variables is generally considered strong when their r value is larger than 0.7. The correlation r measures the strength of the linear relationship between two quantitative variables.

Bottom line: R2 can be greater than 1.0 only when an invalid (or nonstandard) equation is used to compute R2 and when the chosen model (with constraints, if any) fits the data really poorly, worse than the fit of a horizontal line.

R-squared is defined as the percentage of the response variable variation that is explained by the predictors in the model collectively. So, an R-squared of 0.75 means that the predictors explain about 75% of the variation in our response variable.

R-squared has Limitations

R-squared does not indicate if a regression model provides an adequate fit to your data. A good model can have a low R^{2} value. On the other hand, a biased model can have a high R^{2} value!

The sign of a regression coefficient tells you whether there is a positive or negative correlation between each independent variable and the dependent variable. A positive coefficient indicates that as the value of the independent variable increases, the mean of the dependent variable also tends to increase.

The value of R squared can change based on the inclusion or removal of variables in the regression model. R squared values are typically used as a measure of the effectiveness of a model. Hence, a high R squared value (anything above 55%), can be an indicator of a capable model.