When to use this calculator
Find the ordinary-least-squares slope for Y on X. X must have nonzero variance. The model is unweighted and includes an intercept.
Explore the regression & paired data calculators for other questions in this topic. For a related calculation, use the Pearson Correlation Calculator: Measure linear association between two equal-length numeric datasets.
PUTTING IT INTO PRACTICE
Linear Regression Slope: a worked example
The values below are an illustrative example, not a recommendation. Replace them with measurements or assumptions that match your question.
| Input | Example value |
|---|---|
| X observations | 1,2,3 |
| Y observations | 3,5,7 |
| Result | 2 |
- Check the input labels and enter the example values above.
- Apply the relationship: Slope = sum((x−mean x)(y−mean y))/sum((x−mean x)²)..
- The result is 2 , rounded for display.
How to interpret your result
X must have nonzero variance. The model is unweighted and includes an intercept.
Pair observations in the same order and use equally long lists. A least-squares line describes a linear association; it does not establish causation or guarantee future values. Outliers and extrapolation can strongly affect interpretation.
Frequently asked questions
Can a high correlation prove that one variable causes the other?
No. Association can arise through confounding, selection, coincidence or a causal relationship. Correlation alone does not identify which explanation applies.
When is the linear regression slope calculator useful?
Find the ordinary-least-squares slope for Y on X. X must have nonzero variance. The model is unweighted and includes an intercept.
How do I use the linear regression slope calculator?
Enter x observations, y observations. The result updates automatically. Use the units shown beside each input; the example values illustrate the method.
Which formula does this calculator use?
Slope = sum((x−mean x)(y−mean y))/sum((x−mean x)²)..
What should I check before using the result?
X must have nonzero variance. The model is unweighted and includes an intercept.
How are results rounded?
Scalar numbers display up to six decimal places, with scientific notation for very large or small values. Text, fraction, date and schedule outputs use the format described on the tool. Intermediate calculations use JavaScript floating-point arithmetic. Keep sensible precision for your measurements.
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