Regression Power Analysis Calculator

Build better regression studies with confident planning. Compare sample size, power, predictors, and expected effects. Save outputs quickly for reporting, review, and future checks.

Calculator Form

Example Data Table

These sample planning cases show how power, sample size, and effect size can change across regression designs.

Case Mode Alpha Power Predictors Effect Sample Size
1 Required sample size 0.05 0.80 4 f² = 0.15 59
2 Required sample size 0.05 0.90 6 f² = 0.10 98
3 Achieved power 0.05 5 R² = 0.20 120
4 Minimum detectable effect 0.05 0.80 8 Detectable 150
5 Achieved power 0.01 3 f² = 0.35 70

Formula Used

This page uses a practical planning approximation for the overall regression test.

Convert R² to Cohen's f²: f² = R² / (1 − R²)

Convert Cohen's f² to R²: R² = f² / (1 + f²)

Required sample size: N ≈ ((Z1−α + Zpower)² / f²) + p + 1

Approximate achieved power: Power ≈ Φ(√(f²(N − p − 1)) − Z1−α)

Minimum detectable effect: f² ≈ (Z1−α + Zpower)² / (N − p − 1)

Here, p is the number of predictors, N is sample size, and Φ is the standard normal cumulative distribution.

How to Use This Calculator

  1. Select the calculation mode.
  2. Enter the significance level.
  3. Enter the number of predictors in the regression model.
  4. Choose effect input type when effect size is needed.
  5. Enter either Cohen's f² or R².
  6. Enter target power for planning tasks.
  7. Enter sample size when checking achieved power or detectable effect.
  8. Press Calculate to view the result above the form.
  9. Use the export buttons to save results in CSV or PDF format.

About This Regression Power Analysis Calculator

What this calculator does

A regression power analysis calculator helps you plan stronger studies. It estimates sample size, statistical power, and detectable effect size for regression models. This page is built for practical planning. You can check whether your design is likely to detect a meaningful relationship. You can also test whether your current sample is strong enough for the number of predictors in the model.

Why power analysis matters

Power analysis reduces guesswork. A study with low power can miss real effects. A study with too many observations can waste time and budget. Regression planning is especially important when you add several predictors. Each extra variable uses degrees of freedom. That changes the sample size needed for stable estimates and useful significance testing.

Key inputs explained

This calculator uses alpha, target power, predictor count, sample size, and effect size. Alpha is the false positive threshold. Target power is the probability of detecting a true effect. Predictor count is the number of independent variables in the regression model. Effect size is entered as Cohen's f² or R². The tool converts one format into the other, so you can work with the measure you already use.

How to read the outputs

The required sample size result helps you plan future data collection. The achieved power result shows whether your current design is likely to detect the effect you entered. The minimum detectable effect result shows the smallest effect your planned sample can reasonably detect at the chosen alpha and power. These outputs are useful for thesis work, surveys, experiments, audits, business analytics, and applied research reports.

This page also includes CSV and PDF export options, an example table, formula notes, and a usage guide. That makes it useful for fast planning, review meetings, and documentation. For final publication work, confirm the result with dedicated statistical software when you need exact noncentral F calculations.

FAQs

1. What does regression power analysis measure?

It estimates whether your regression design can detect a meaningful effect. It links sample size, effect size, alpha, and predictor count in one planning step.

2. Should I enter R² or Cohen's f²?

Use whichever measure you already have. Many published regression studies report R². Many planning guides discuss Cohen's f². This calculator converts between them automatically.

3. Why does the number of predictors matter?

More predictors use more degrees of freedom. That often increases the sample size needed for stable estimation and acceptable power in regression testing.

4. What is a common target power level?

Many studies use 0.80 as a planning target. Some researchers choose 0.90 for stricter designs, especially when missing an important effect would be costly.

5. Can this be used for multiple regression?

Yes. It is intended for general regression planning where you specify the number of predictors and an expected effect size for the overall model test.

6. Why are the results described as approximate?

This page uses a practical normal approximation. It works well for fast planning. Exact software may differ slightly because it uses noncentral F distributions.

7. What is a small, medium, or large effect?

A common guide for Cohen's f² is 0.02 for small, 0.15 for medium, and 0.35 for large. Context still matters.

8. When should I recalculate power?

Recalculate when your sample target changes, your predictor count grows, your alpha changes, or new pilot data suggests a different expected effect size.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.