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Advanced Statistical Analysis & Modeling Suite

Professional regression analysis, correlation matrices, multivariate statistics, and machine learning tools. Free online statistical modeling with assumption checking, diagnostics, and detailed interpretations.

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Multiple Linear Regression with Assumptions

Comprehensive multiple regression analysis with automatic assumption checking, diagnostic plots, and model validation. Includes stepwise selection, multicollinearity detection, and residual analysis.

  • Multiple regression calculator
  • Assumption testing (linearity, normality)
  • Multicollinearity diagnostics (VIF)
  • Residual analysis and plots
  • Model comparison and selection

Logistic Regression Calculator

Binary and multinomial logistic regression for categorical outcomes. Calculate odds ratios, confidence intervals, and model fit statistics with ROC curve analysis and classification metrics.

  • Binary logistic regression
  • Multinomial logistic regression
  • Odds ratios with confidence intervals
  • ROC curve and AUC calculation
  • Classification accuracy metrics

Correlation Matrix Calculator

Comprehensive correlation analysis with Pearson, Spearman, and partial correlations. Generate correlation matrices, significance tests, and correlation network visualizations.

  • Pearson correlation matrix
  • Spearman rank correlation
  • Partial correlation analysis
  • Correlation significance testing
  • Correlation network visualization

Principal Component Analysis (PCA)

Dimensionality reduction and data exploration with PCA. Includes scree plots, component loadings, biplot visualization, and variance explained analysis for multivariate datasets.

  • Principal component extraction
  • Scree plot and eigenvalues
  • Component loadings matrix
  • Biplot visualization
  • Variance explained analysis

Time Series Analysis Calculator

Comprehensive time series analysis with trend detection, seasonality decomposition, and forecasting. Includes ARIMA modeling, exponential smoothing, and forecast accuracy metrics.

  • Trend and seasonality analysis
  • ARIMA model fitting
  • Exponential smoothing
  • Forecast generation
  • Accuracy metrics (MAPE, RMSE)

Factor Analysis & SEM

Exploratory and confirmatory factor analysis with structural equation modeling capabilities. Includes factor rotation, model fit indices, and path analysis for complex relationships.

  • Exploratory factor analysis (EFA)
  • Confirmatory factor analysis (CFA)
  • Factor rotation methods
  • Model fit indices
  • Structural equation modeling

Regression Analysis Guide: Choosing the Right Method

Linear Regression

Use when: Continuous dependent variable, linear relationships
Assumptions: Linearity, independence, normality, homoscedasticity

Logistic Regression

Use when: Binary or categorical dependent variable
Output: Odds ratios, probabilities, classification accuracy

Polynomial Regression

Use when: Non-linear relationships, curved patterns
Caution: Avoid overfitting with high-degree polynomials

Stepwise Regression

Use when: Variable selection needed, exploratory analysis
Methods: Forward, backward, bidirectional selection

Ridge/Lasso Regression

Use when: Multicollinearity present, regularization needed
Benefits: Prevents overfitting, handles correlated predictors

Hierarchical Regression

Use when: Testing incremental variance explained
Application: Theory testing, model comparison

Regression Assumptions & Diagnostics

Ensure your regression analysis meets statistical assumptions for valid results:

Linearity

Check: Scatterplots, residual plots
Solution: Transform variables, polynomial terms

Independence

Check: Durbin-Watson test, residual autocorrelation
Solution: Time series methods, clustered standard errors

Normality of Residuals

Check: Q-Q plots, Shapiro-Wilk test
Solution: Transform dependent variable, robust methods

Homoscedasticity

Check: Residual vs fitted plots, Breusch-Pagan test
Solution: Weighted least squares, robust standard errors

Multicollinearity

Check: VIF values, correlation matrix
Solution: Remove variables, ridge regression, PCA

Outliers & Influence

Check: Cook's distance, leverage, standardized residuals
Solution: Investigate, transform, robust regression

Advanced Statistical Methods Comparison

Method Purpose Data Requirements Key Output
Multiple Regression Predict continuous outcomes Continuous DV, multiple IVs R², coefficients, p-values
Logistic Regression Predict binary outcomes Binary DV, any IV types Odds ratios, classification accuracy
ANOVA Compare group means Continuous DV, categorical IVs F-statistics, effect sizes
PCA Dimensionality reduction Multiple continuous variables Principal components, loadings
Factor Analysis Identify latent factors Multiple correlated variables Factor loadings, communalities
Time Series Analyze temporal patterns Time-ordered observations Forecasts, trend components

Frequently Asked Questions

What is multiple regression analysis?
Multiple regression analysis examines the relationship between one dependent variable and multiple independent variables. It helps predict outcomes, identify significant predictors, and quantify the strength of relationships while controlling for other variables. The model provides R² (variance explained), regression coefficients, and statistical significance tests.
When to use logistic regression vs linear regression?
Use logistic regression when the dependent variable is binary (yes/no, success/failure) or categorical. Use linear regression when the dependent variable is continuous. Logistic regression models probabilities using the logit link function and provides odds ratios for interpretation.
How to interpret correlation coefficients?
Correlation coefficients range from -1 to +1. Values near ±1 indicate strong linear relationships, values near 0 indicate weak relationships. Positive values show direct relationships (as one increases, the other increases), negative values show inverse relationships. Consider both magnitude and statistical significance.
What is Principal Component Analysis (PCA) used for?
PCA reduces dimensionality by creating new variables (principal components) that capture maximum variance in the data. It's used for data visualization, noise reduction, feature extraction, and identifying patterns in high-dimensional data. The first few components often explain most of the variance.

Complete Statistical Analysis Workflow

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