This calculator performs Inverse Regression and produces an equation for the line of best fit for the provided predictor and response values. It also calculates the correlation coefficient.
The equation takes the form: \( y = A + \frac{B}{x} \)
To use the calculator, provide a list of values for the predictor and the response, ensuring they are the same length, and then click the "Do Inverse Regression" button.
Inverse Regression Equation:
y = A + B/x
Correlation Coefficient (r):
Inverse Regression and Correlation Coefficient
The Inverse Regression finds the best-fit equation in the form:
This regression is useful for modeling relationships where the response variable \(Y\) changes inversely with the predictor variable \(X\). The correlation coefficient \(r\) tells us how well the model fits the data.
Correlation Coefficient Interpretation
You can interpret the correlation coefficient \(r\) as follows:
- 0.7 < |r| ≤ 1 — Strong correlation
- 0.4 < |r| < 0.7 — Moderate correlation
- 0.2 < |r| < 0.4 — Weak correlation
- 0 ≤ |r| < 0.2 — No correlation
Caveats and Conditions
- Assumption of Inverse Relationship: Inverse regression assumes that the relationship between \(X\) and \(Y\) follows an inverse pattern. If this assumption is incorrect, the model may not fit well.
- Outliers: Large outliers can significantly distort the regression equation and the correlation coefficient.
- Non-Linear Relationships: Inverse regression is suitable only for relationships that follow the inverse pattern. Other relationships may not fit well.
Further Reading
Suf is a senior advisor in data science with deep expertise in Natural Language Processing, Complex Networks, and Anomaly Detection. Formerly a postdoctoral research fellow, he applied advanced physics techniques to tackle real-world, data-heavy industry challenges. Before that, he was a particle physicist at the ATLAS Experiment of the Large Hadron Collider. Now, he’s focused on bringing more fun and curiosity to the world of science and research online.