Given the Multiple Regression Equation,Ŷ = a + B₁X₁

question 75

Essay

Given the multiple regression equation,Ŷ = a + b₁X₁ + b₂X_2,and the bivariate equation Ŷ = a + bX,why is the partial regression coefficient,b₁,different from the regression coefficient,b,obtained by regressing Y on only X₁?

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Definitions:

Longitudinal Design

A special kind of systematic observation, used by correlational researchers, that involves obtaining measures of the variables of interest in multiple waves over time.

Preschoolers

Young children typically between the ages of 3 and 5 years who are in the developmental stage before attending kindergarten.

Experimental Studies

Research methodologies that involve the manipulation of variables to observe the effect on another variable, typically within a controlled environment.

Causality

The relationship between cause and effect where one event (the cause) leads to the outcome (the effect), fundamental to scientific and philosophical inquiry.