what is a good r squared value
A “good” R-squared value depends on context rather than a single magic cutoff.
Quick Scoop: Core idea
- R-squared measures how much of the variation in your outcome your model explains (0 to 1, or 0% to 100%).
- Higher is not always better; very high values can signal overfitting or issues with the data, especially in time series.
- What counts as “good” varies a lot by field, data type, and purpose.
Typical “good” ranges by field
Here’s a rough feel for how different areas interpret R-squared:
| Field / context | Often acceptable | Often considered “good” |
|---|---|---|
| Social & behavioral sciences | 0.10–0.30 can be meaningful because human behavior is noisy. | [1][9][3]0.30–0.50 often seen as very good. | [9][1][3]
| Clinical / medical studies | ≈0.15 may be a reasonable threshold for a “meaningful” model in some proposals. | [7]Higher is nice, but small values can still matter for complex human data. | [7]
| Finance (e.g., factor models) | Below 0.40 often viewed as weak correlation. | [3]Above 0.70 usually treated as a strong relationship. | [3]
| Physical sciences & engineering | 0.50–0.70 may be workable depending on the problem. | [3][7]0.70–0.99 commonly expected for a “good” fit in many experiments. | [7]
| Time-series (after differencing / stationarizing) | 0.10–0.25 can still be useful when signals are weak. | [5]“Good” is defined more by predictive performance and error diagnostics than raw R². | [5]
Why “it depends” is the real answer
- In messy human domains, even an R-squared of 0.10 can reveal an important relationship, especially if predictors are statistically significant.
- In controlled lab physics or engineering, people often expect R-squared much closer to 1 because measurement noise is lower and relationships are more stable.
- Some authors explicitly argue that thresholds like 0.15 or 0.25 can be meaningful in areas such as clinical medicine or weak-signal time series.
A quick mental rule:
- Noisy, human data → don’t be surprised by “good” models with R² between 0.1 and 0.4.
- Clean, physical/engineering data → aim for R² above 0.7 if you’re calling it “good.”
Pitfalls: when a high R-squared is misleading
Even a very high R-squared can be bad news if:
- You added lots of predictors just to boost R-squared.
- R-squared never goes down when you add more variables, even if they’re useless.
* That’s why adjusted R-squared is often preferred; it increases only when new variables really help.
- You’re working with time series and did not “stationarize” the data.
- For trending series, R-squared close to 1 can reflect shared trends, not real predictive structure.
- You ignore residual diagnostics.
- Good models also have residuals that are roughly pattern-free and appropriately distributed, not just a high R-squared.
How to judge your own R-squared
To decide if your R-squared is “good,” ask:
- What field am I in and how noisy is my outcome?
- Human behavior/clinical/finance → lower R² can still be useful.
* Physics/engineering → expect higher R² for a model you call strong.
- What is my goal?
- Explanation: Even modest R² can be valuable if it clarifies which variables matter.
- Prediction: Look at out-of-sample error (test set, cross-validation) rather than just R² on training data.
- Am I checking adjusted R-squared and other metrics?
- Adjusted R² helps control for overfitting.
* Combine it with RMSE, MAE, or other fit and validation checks.
A simple way to think about it:
- “Good” R-squared is whatever gives you reliable, validated insight for your field and question, not a fixed magic number.
Mini example
Imagine you build a linear regression predicting exam scores from study hours and prior GPA in a university sample:
- You get R² = 0.32 and adjusted R² = 0.30.
- In an educational or behavioral context, that means about 30% of the variance in exam scores is explained, which is often considered quite solid.
- If residuals look healthy and validation error is reasonable, you could honestly call this a “good” R-squared for that use case.
TL;DR:
There is no universal “good” R-squared value. In noisy human fields, 0.1–0.4
can be meaningful; in physical sciences and engineering, people often expect
values above 0.7. Always interpret R² alongside your field norms, model
purpose, adjusted R², and validation performance.
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