Population ure
Population
s Deterministic Relationship Fig 3 shows a Deterministic Relationship between Y and X In the data-analysis context, it would not be deterministic for example, there was any connection between IQ and height, or height of son and height of father
❖ Deterministic Relationship －Fig. 3 shows a Deterministic Relationship between Y and X －In the data-analysis context, it would not be deterministic －for example, there was any connection between IQ and height, or height of son and height of father?
Statistical Relationship GRAPH 1 GRAPH 2 5 *4434 AfA+ X X
❖ Statistical Relationship
Graph 1 Perfect linear relationship Determining intercept and gradient/slope Response Y depends only on the variable X 冷 Graph2 Statistical relationship/ink ☆ As the value of the explanatory variableⅩ increases, the value of the response variable y also tends to increase &the response Y may depend on a number of different variables, say X,U,V,W, Z 令Y=f(x,∪,V,W,Z,…)
❖ Graph 1 －Perfect linear relationship －Determining intercept and gradient/slope －Response Y depends only on the variable X ❖ Graph 2 －Statistical relationship/link ❖As the value of the explanatory variable X increases, the value of the response variable Y also tends to increase ❖the response Y may depend on a number of different variables, say X, U, V, W, Z ❖Y=f(X,U,V,W,Z,….)
&Y=f(X)+ effect of all other variables =Y=f(X)+e .o e is the effect of all other variables &o the influence on Y is from two parts os Variation in Y Explained by changes X(Explained Variation cOVariation in Y not explained by changes in X (Unexplained Variation &o The Total Variation in y='Explained variation+ Unexplained Variation In Graph 1, Unexplained Variation is nil In Graph 2, Explained variation is large relative to the Unexplained variation
❖Y= f(X) + effect of all other variables =Y = f(X) + e ❖ e is the effect of all other variables ❖The influence on Y is from two parts Variation in Y Explained by changes X (Explained Variation ) Variation in Y not explained by changes in X (Unexplained Variation ) ❖The Total Variation in Y' = 'Explained Variation' + 'Unexplained Variation' －In Graph 1, Unexplained Variation is nil －In Graph 2, Explained Variation is large relative to the Unexplained Variation