Statistical Analysis
Statistical models, particularly those considered core subjects like regression and time series analysis, are a practical aspect of statistics. This section introduces the principles and applications of these models, with examples using basic built-in datasets in R for easy copy-pasting and learning.
Regression Analysis
Multiple Regression Analysis
- What is Regression Analysis?
- Simple Regression Analysis
- Multiple Regression Analysis
- Definition of Regression Coefficients and Derivation of Estimators
- Variable Selection Procedures in Statistical Analysis
- Variable Selection Criteria in Statistical Analysis
Residual Analysis
- Model Diagnostics in Regression Analysis
- Checking Linearity of Residuals in Model Diagnostics
- Checking Homoscedasticity of Residuals in Model Diagnostics
- Checking Independence of Residuals in Model Diagnostics
- Checking Normality of Residuals in Model Diagnostics
- Estimates of Residual Variance and Standard Errors of Regression Coefficients in Multiple Regression
- Regression Analysis with Qualitative Variables
Multicollinearity
- Multicollinearity
- Principal Component Analysis in Statistics
- Solving
not defined because of singularities
in R Regression Analysis
Derived Models
- Logistic Regression Analysis
- Nonlinear Regression Analysis: Variable Transformation in Regression
- Sparse Regression
- Ridge Regression
- LASSO Regression
- Compressed Sensing
- Sparse Identification of Nonlinear Dynamics (SINDy)
Time Series Analysis
Internal Factors
- Moving Average Process $MA$
- Autoregressive Process $AR$
- ARMA Model $ARMA$
- ARIMA Model $ARIMA$
- Seasonal ARIMA Models
External Factors
Heteroskedasticity
Spatial Statistics Analysis
Matheron School
- Spatial Processes
- Stationarity of Spatial Processes
- Variogram $2 \gamma \left( \mathbf{h} \right)$
- Isotropy in Variograms $d = \left| \mathbf{h} \right|$
- Empirical Variogram $\gamma^{\ast}, \hat{\gamma}$
- Ordinary Kriging
- Universal Kriging
Areal Data Analysis
- Proximity Matrix
- Moran’s I
Geary’s C
Conditional Autoregressive Model (CAR Model)
- Spatial Autoregressive Model (SAR)
- Spatial Error Model (SEM)
- Spatial Durbin Model (SDM)
References
- Banerjee. (2015). Hierarchical Modeling and Analysis for Spatial Data(2nd Edition)
- Brunton. (2022). Data-Driven Science and Engineering : Machine Learning, Dynamical Systems, and Control(2nd Edition)
- Cryer. (2008). Time Series Analysis: With Applications in R(2nd Edition)
- Hadi. (2006). Regression Analysis by Example(4th Edition)
- James. (2013). An Introduction to Statistical Learning with Applications in R
All posts
- Independence Does Not Imply No Correlation
- What is Regression Analysis?
- Design Matrix
- Fitted Values, Predicted Values, Residuals, Errors
- Simple Regression Analysis
- How to View Simple Regression Analysis Results in R
- Multiple Regression Analysis
- How to Interpret Multiple Regression Analysis Results in R
- Regression Model Diagnostics
- Residual Linearity Verified through Model Diagnostics
- Homoscedasticity of Residuals Verified through Model Diagnostics
- Residual Independence Verified through Model Diagnosis
- Checking the Normality of Residuals through Model Diagnostics
- Regression Analysis Including Qualitative Variables
- Influence of Interaction in Regression Analysis
- Nonlinear Regression Analysis: Variable Transformation in Regression Analysis
- Multicollinearity
- Variance Inflation Factor VIF
- Principal Component Analysis in Statistics
- How to Perform Principal Component Regression in R
- Variable Selection Procedures in Statistical Analysis
- Variable Selection Criteria in Statistical Analysis
- Logistic Regression
- How to Read Logistic Regression Results in R
- Time Series Analysis
- Time Series Analysis: White Noise
- Stability in Time Series Analysis
- Moving Average Process
- Autoregressive Process
- Autoregressive Moving Average Model
- Differencing in Time Series Analysis
- Transformation in Time Series Analysis
- Arima Model
- Seasonal ARIMA Model
- Drift in the ARIMA Model
- How to Analyze Time Series with ARIMA Models in R
- How to View Time Series Analysis Results Obtained with ARIMA Model in R
- Predicting with ARIMA Models in R
- Reversibility of ARMA Models
- Autocorrelation Function
- Autocorrelation Function
- Extended Autocorrelation Function
- Selecting an ARMA Model Using EACF in R
- Residual Analysis of ARIMA Models
- Time Series Regression Analysis
- Cross-Correlation Function
- Encyclopedia
- Time Series Regression and Spurious Correlation
- Intervention Analysis
- Step Function and Pulse Function
- Time Series Analysis of Additive Outliers
- Time Series Analysis and Innovative Outliers
- Dynamic Regression Models
- Heteroskedasticity and Volatility Clustering in Time Series Analysis
- Arch Effect
- Time Series Analysis in Valuation Models
- Analyzing Time Series with Valuation Models in R
- How to Open a shp File with QGIS
- The Definition of Regression Coefficients and Derivation of Estimator Formulas
- Estimation of the Variance of Residuals and Standard Errors of Regression Coefficients in Multiple Regression Analysis
- What is Spatial Data Analysis?
- Spatial Processes
- Stationarity of Spatial Processes
- Definition of Variogram
- Isotropy of Variogram
- Models of Semivariograms
- Empirical Variogram
- Kringing in Spatial Data Analysis
- Universal Kriging
- Resolving not defined because of singularities in R Regression Analysis
- Introduction to PROJ in Earth Statistics
- What is Sparse Regression?
- What is Ridge Regression?
- What is LASSO Regression?
- What is Compressive Sensing?
- Uniform Uncertainty Principle: Restricted Isometry Condition
- What is STLSQ?
- What is the SINDy Algorithm?