What is logistic regression?

Logistic regression is a statistical method used when the outcome variable is binary (e.g., pass/fail, yes/no). It uses the sigmoid function to model the probability of an event occurring, constrained between 0 and 1. StatMate's logistic regression calculator provides odds ratios, classification tables, and model fit statistics automatically.

When should I use logistic regression instead of linear regression?

Use linear regression when your outcome is continuous, and logistic regression when your outcome is binary (0/1). For example, predicting exam scores calls for linear regression, while predicting pass/fail status requires logistic regression. Applying linear regression to a binary outcome violates key assumptions and produces misleading results.

How do I interpret odds ratios?

An odds ratio (OR) represents the multiplicative change in odds of the outcome for a one-unit increase in the predictor. OR > 1 indicates increased odds, OR < 1 indicates decreased odds, and OR = 1 means no effect. For example, OR = 1.5 means the odds increase by 50% for each one-unit increase in the predictor.

How do I report logistic regression results in APA format?

APA 7th edition requires reporting the omnibus chi-square test, Nagelkerke R², classification accuracy, and each predictor's B, Wald χ², p-value, OR, and 95% CI. StatMate automatically generates all of these results in APA format, ready to copy into your research paper or dissertation.

ロジスティック回帰計算ツール

ロジスティック回帰（IRLS法）を使用して二値アウトカム（0/1）を1つ以上の予測変数から予測します。オッズ比、分類表、モデル適合統計量を含みます。

What is Binary Logistic Regression?

Binary logistic regression is a statistical method used to model the relationship between one or more predictor variables and a binary (dichotomous) outcome variable. Unlike linear regression, which predicts a continuous outcome, logistic regression predicts the probability that an observation belongs to one of two categories (coded as 0 and 1). The model uses the logistic (sigmoid) function to constrain predicted probabilities between 0 and 1.

Key Concepts in Logistic Regression

Odds Ratio — Exp(B)

The odds ratio represents the multiplicative change in the odds of the outcome for a one-unit increase in the predictor. An odds ratio greater than 1 indicates increased odds, while a value less than 1 indicates decreased odds. A value of exactly 1 means the predictor has no effect.

Wald Test

The Wald test evaluates whether each individual predictor is statistically significant. It is calculated as the squared ratio of the coefficient to its standard error (Wald = (B/SE)²) and follows a chi-square distribution with 1 degree of freedom.

Pseudo R² Measures

Unlike linear regression, logistic regression does not have a true R². Cox & Snell R² and Nagelkerke R² are approximations that indicate how much of the variation in the outcome is explained by the model. Nagelkerke R² adjusts the Cox & Snell measure to range from 0 to 1.

Understanding the Classification Table

The classification table (confusion matrix) compares predicted categories with observed categories using a 0.5 probability cutoff. Sensitivity (true positive rate) measures how well the model identifies actual positives, while specificity (true negative rate) measures how well it identifies actual negatives. Overall accuracy indicates the percentage of all cases correctly classified.

Hosmer-Lemeshow Goodness-of-Fit Test

The Hosmer-Lemeshow test evaluates how well the model fits the data by dividing observations into groups based on predicted probabilities and comparing observed and expected frequencies. A non-significant result (p > .05) indicates adequate model fit, meaning the model's predictions are consistent with the observed data.

How to Report Logistic Regression Results in APA Format

Example APA Report

A binary logistic regression was conducted to predict purchase behavior from age and income. The overall model was statistically significant, χ²(2) = 15.43, p < .001, Nagelkerke R² = .42. The model correctly classified 85.0% of cases. Age was a significant predictor, B = 0.12, Wald χ²(1) = 6.78, p = .009, OR = 1.13, 95% CI [1.03, 1.24].

Calculation Accuracy

StatMate's logistic regression uses the Iteratively Reweighted Least Squares (IRLS) algorithm, the same method used by R's glm() and SPSS. Convergence is checked at each iteration with a tolerance of 10&sup-;8. The implementation includes separation detection and uses jstat for chi-square probability distributions.

他の計算ツールを試す

t検定

2群の平均値を比較

分散分析

3群以上の平均値を比較

カイ二乗検定

カテゴリ変数の関連を検定

相関分析

関係の強さを測定

記述統計

データを要約

サンプルサイズ

検出力分析・標本計画

1標本t検定

既知の値との比較

マン・ホイットニーU

ノンパラメトリック群間比較

ウィルコクソン検定

ノンパラメトリック対応検定

回帰分析

X-Yの関係をモデル化

重回帰分析

複数の予測変数

クロンバックのα

尺度の信頼性

因子分析

潜在因子構造の探索

クラスカル・ウォリス

ノンパラメトリック3群以上比較

反復測定

被験者内分散分析

二元配置分散分析

要因計画の分析

フリードマン検定

ノンパラメトリック反復測定

フィッシャーの正確検定

2×2表の正確検定

マクネマー検定

対応のある名義データの検定