In some fields, such as the social sciences, even a relatively low R-squared value, such as 0.5, could be considered relatively strong. In other fields, the standards for a good R-squared reading can be much higher, such as 0.9 or above.
For example, a model with an R-squared value of 0.9 means that approximately 90% of the variance in the dependent variable is explained by the independent variables. This suggests a strong relationship between the variables and indicates that the model provides a good fit to the data.
In fact, if R-squared is very close to 1, and the data consists of time series, this is usually a bad sign rather than a good one: there will often be significant time patterns in the errors, as in the example above.
Remember, coefficient of determination or R square can only be as high as 1 (it can go down to 0, but not any lower). If we can predict our y variable (i.e. Rent in this case) then we would have R square (i.e. coefficient of determination) of 1. Usually the R square of . 70 is considered good.
Researchers evaluate their models based on r-square values or in other words effect sizes. According to Cohen (1992) r-square value . 12 or below indicate low, between . 13 to . 25 values indicate medium, . 26 or above and above values indicate high effect size.
For example, an r-squared of 60% reveals that 60% of the variability observed in the target variable is explained by the regression model. Generally, a higher r-squared indicates more variability is explained by the model. However, it is not always the case that a high r-squared is good for the regression model.
An R2 of 1.0 indicates that the data perfectly fit the linear model. Any R2 value less than 1.0 indicates that at least some variability in the data cannot be accounted for by the model (e.g., an R2 of 0.5 indicates that 50% of the variability in the outcome data cannot be explained by the model).
So r squared vs adjusted r2 squared gives the degree of variability in the target variable that is explained by the model or the independent variables. If this value is 0.7, then it means that the independent variables explain 70% of the variation in the target variable. R-squared value always lies between 0 and 1.
R2 < 0: This case is only possible with linear regression when either the intercept or the slope are constrained so that the "best-fit" line (given the constraint) fits worse than a horizontal line, for instance if the regression line (hyperplane) does not follow the data (CrossValidated, 2011b).
R-squared is used as a measure of fit, or accuracy of the model, but what it actually tells you is about variance. If the dependent variable(s) vary up and down in sync with the independent variable (what you're trying to predict), you'll have a high R-squared, as demonstrated in these charts (link to spreadsheet):
The reliability of a measurement determines its maximal correlation or R2 and slope (or effect size) in regression models, its sensitivity and specificity when used for classifications or predictions, and the power of a statistical test employing the measurement.
Another interpretation of R2 is that it tells the fraction of the variance that is explained by the best-fit line. An R2 of 0.94 means that 94% of the variance in the data is explained by the line and 6% of the variance is due to unexplained effects.
0.6 to 0.9 (High R-squared): This range indicates that the model explains a substantial amount of variance. It is often seen as a good fit in fields like engineering and physical sciences, where relationships tend to be more deterministic.
An R^2 value above 0.6 is considered good as it indicates a strong relationship between variables, but its credibility should be rigorously tested to avoid overfitting issues.
No! Regression models with low R-squared values can be perfectly good models for several reasons. Some fields of study have an inherently greater amount of unexplainable variation. In these areas, your R2 values are bound to be lower.
A R-squared between 0.50 to 0.99 is acceptable in social science research especially when most of the explanatory variables are statistically significant.
An R squared value between 0.25 (25%) and 0.5 (50%) is considered a moderate relationship, and an R squared value of 0.5 (50%) or higher is considered a strong relationship. Therefore, an R squared value of 12.1% would be considered a weak to moderate relationship.
An R2 of . 04 may explain the past data in a statistical significant manner and may have some value in doing so, but its predictive ability is practically zero when wanting to extrapolate beyond the available data.
R-squared gives a measure of how predictive the regression is and how much variation is explained by the regression. The lowest R-squared is 0 and means that the points are not explained by the regression whereas the highest R-squared is 1 and means that all the points are explained by the regression line.
The coefficient of determination (R²) measures how well a statistical model predicts an outcome. The outcome is represented by the model's dependent variable. The lowest possible value of R² is 0 and the highest possible value is 1.
Adjusted R2 is always less than or equal to R2. A value of 1 indicates a model that perfectly predicts values in the target field. A value that is less than or equal to 0 indicates a model that has no predictive value. In the real world, adjusted R2 lies between these values.
We often denote this as R2 or r2, more commonly known as R Squared, indicating the extent of influence a specific independent variable exerts on the dependent variable. Typically ranging between 0 and 1, values below 0.3 suggest weak influence, while those between 0.3 and 0.5 indicate moderate influence.
