PREDICTIVE MODELLING REGRESSION ANALYSIS
“Da jeg gikk på ungdomskolen, ble vi testet for å finne ut hva slags yrke vi passet til. Jeg svarte feil på alt, så de anbefalte meg å bli metereolog.” Herodes Falsk (29) klovn til NÅ
PREDICTIVE MODELLING Process control Process Analysis/Calibration Product properties
STEPS IN PREDICTIVE MODELLING 1) Collect representative data 2) Establish a validated predicted model between the response(s) and the input variables.
STARTPOINT Obs. no.XY
LEAST SQUARES METHOD Calculate the parameters b 0 and b 1
LEAST SQUARES METHOD x y xkxk Minimise for model
LEAST SQUARES METHOD (1) (2) (2) in (1): (3) Partial derivation: 2 equations, 2 unknown (b 0,b 1 )!!
LEAST SQUARES METHOD Error in b 0 and b 1 : Solved for b 0,b 1 :
PREDICTIVE MODEL y x
y x Measured x Predicted y PREDICTIVE MODEL
VALIDATION x y Model 1 Model 2 i) Model group 1, residual sum group 2 ii) Model group 2, residual sum group Group 1: 1,3,5,7,9,11,13,15 Group 2: 2,4,6,8,10,12,14
CHOLESTEROL AND AGE 1. Is there a correspondence between cholesterol and age? 2. Find the correspondence using a Predictive Model 3. Check the MODEL
The Cholesterol example: Age Cholesterol Is there a mathematical relationship between the concentration of cholesterol in the blood and age?
SCATTER DIAGRAM FOR THE CHOLESTEROL (x,y)
REGRESSION LINE FOR THE CHOLESTEROL (Average point (x,y))