قارن الطرق

	Panel Simple Linear Regression	النموذج الخطي الهرمي (HLM)
المجال	الإحصاء	الإحصاء
العائلة	Regression model	Regression model
سنة النشأة	1986	1992
صاحب الطريقة	Hsiao (1986); Baltagi (seminal textbook treatments)	Bryk & Raudenbush
النوع	Linear regression (panel data)	Multilevel linear regression
المصدر التأسيسي	Wooldridge, J. M. (2010). Econometric Analysis of Cross Section and Panel Data (2nd ed.). MIT Press. ISBN: 978-0262232586	Raudenbush, S. W., & Bryk, A. S. (2002). Hierarchical Linear Models: Applications and Data Analysis Methods (2nd ed.). Sage Publications. ISBN: 978-0761919049
الأسماء البديلة	panel SLR, longitudinal simple regression, two-way panel simple regression, fixed-effects simple linear regression	HLM, multilevel linear model, nested data model, random coefficient model
ذات صلة	5	4
الملخص	Panel simple linear regression models a continuous outcome as a linear function of a single predictor using data that track the same entities (individuals, firms, countries) across multiple time periods. It separates within-entity variation from between-entity variation, enabling control for unobserved time-invariant characteristics that would confound a plain cross-sectional regression.	The Hierarchical Linear Model (HLM) is a multilevel regression method designed for data in which lower-level units (e.g., students, patients) are nested within higher-level groups (e.g., schools, hospitals). It simultaneously models within-group relationships and between-group variation, producing unbiased estimates and correct standard errors that ordinary regression cannot provide for nested data.