CHAPTER 17 FURTHER DATAANALYSIS 2 17.1 INTRODUCTION Explanatory variable Attribute Measured R Measured E Measured Measured Attnbute Measured P0 Attribute N Attribute Attribute Attribute E Measured
17.1 INTRODUCTION Explanatory variable CHAPTER 17 FURTHER DATA ANALYSIS 2
冷 Example Given sample data from a random sample of students about their lQ and their height %o Does the height of an individual student influence the lQ of the student? Given sample data from a random sample of people about their height and the height of their father %o Does the height of a father influence the height of his son? Given sample data about the number of new born babies in the city per day and the number of the wild gooses flying over the city per day o Does the number of new born babies in the city and the number of the wild gooses flied over the city
❖ Example －Given sample data from a random sample of students about their IQ and their height ❖ Does the height of an individual student influence the IQ of the student? －Given sample data from a random sample of people about their height and the height of their father ❖ Does the height of a father influence the height of his son? －Given sample data about the number of new born babies in the city per day and the number of the wild gooses flying over the city per day ❖ Does the number of new born babies in the city and the number of the wild gooses flied over the city
s Methodology of Data Anylysis Initial Data Analysis Very strong evidence to support a link, & No evidence of any link, o The sample evidence is inconclusive and further more sophisticated data analysis is required Further Data Analysis % The sample evidence is consistent with oG No link between the response variable and the explanatory variable ooA link between the response variable and the explanatory variable, the nature of the relationship needs to be described
❖ Methodology of Data Anylysis －Initial Data Analysis ❖Very strong evidence to support a link, ❖No evidence of any link, ❖The sample evidence is inconclusive and further more sophisticated data analysis is required. －Further Data Analysis ❖The sample evidence is consistent with No link between the response variable and the explanatory variable. A link between the response variable and the explanatory variable, the nature of the relationship needs to be described
Initial Data Analysis Further Data Analysis Yes Descrbe Relationship
17.2 WHAT S MEANT BY A RELATIONSHIP Relationship between a measured response variable and a measured explanatory variable? Y- the response variable X- the explanatory variable Conceptual graph of Y against X
17.2 WHAT IS MEANT BY A RELATIONSHIP ❖ Relationship between a measured response variable and a measured explanatory variable? －Y-- the response variable －X-- the explanatory variable － Conceptual graph of Y against X
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