By Yang By Yang By Yang By Yang CaoCaoCaoCao

BESTBESTBESTBEST----FITFITFITFIT

solutionsolutionsolutionsolution

CorrelationCorrelationCorrelationCorrelation

RegressionRegressionRegressionRegression

WeightsWeightsWeightsWeights

LinearizationLinearizationLinearizationLinearization

LeastLeastLeastLeast----Square solutionSquare solutionSquare solutionSquare solution

Learn:Learn:Learn:Learn:

What & HowWhat & HowWhat & HowWhat & How

for each termfor each termfor each termfor each term

twicetwicetwicetwice

Then you can calculate :Then you can calculate :Then you can calculate :Then you can calculate :

BestBestBestBest----fit linefit linefit linefit line

Weighted MeanWeighted MeanWeighted MeanWeighted Mean

LinearizationLinearizationLinearizationLinearization

CoefficientCoefficientCoefficientCoefficient

Correlation :Correlation :Correlation :Correlation :

Association Association Association Association

between between between between

variables.variables.variables.variables.

Direction Direction Direction Direction

positivepositivepositivepositive negativenegativenegativenegative

XXXX YYYY XXXX YYYY XXXX YYYY XXXX YYYY

Strength Strength Strength Strength

High Strong:High Strong:High Strong:High Strong:

Few exceptions Few exceptions Few exceptions Few exceptions

ModerateModerateModerateModerate

Low Weak:Low Weak:Low Weak:Low Weak:

Many exceptions Many exceptions Many exceptions Many exceptions

1.001.001.001.00

0.800.800.800.80

0.400.400.400.40

0000

Correlation Coefficient: Correlation Coefficient: Correlation Coefficient: Correlation Coefficient: rrrr

Regression :Regression :Regression :Regression :

find a formula that can find a formula that can find a formula that can find a formula that can

be used to relate two be used to relate two be used to relate two be used to relate two

variables.variables.variables.variables.

y=mx+b

correlation V.S. regression correlation V.S. regression correlation V.S. regression correlation V.S. regression

Correlation: relationship

between variables.

Regression: finding a formula

that represents the relationship

so as to do prediction

residual

Residual = Actual – Predicted

The regression equation or formula meets the

"least Square" criterion: the sum of square of

the residual is at its minimum.

Weighted mean

• some data points contribute more than othersformula

linearizelinearizelinearizelinearize : : : : make linear or get into a linear form.make linear or get into a linear form.make linear or get into a linear form.make linear or get into a linear form.

y

x0 x a=

( ) ( )f x f a=

We call the equation of the tangent

the linearization of the function.

nx ( )nf xn ( )nf x′

( )

( )1

n

n n

n

f xx x

f x+ = −

′

Find where crosses .3y x x= − 1y =

31 x x= − 3

0 1x x= − − ( ) 31f x x x= − − ( ) 2

3 1f x x′ = −

0 1 1− 21

1 1.52

−− =

1 1.5 .875 5.75.875

1.5 1.34782615.75

− =

2 1.3478261 .1006822 4.4499055 1.3252004

( )3

1.3252004 1.3252004 1.0020584− = 1≈→

Q?

http://www.nvcc.edu/home/elanthier/methods/correlation.htm

http://www.pindling.org/Math/Statistics/Textbook/Chapter3_Re

gression_Correlation/Chapter3_Regres_Corr_Overview.htm

http://graphpad.com/curvefit/linear_regression.htm

http://www.answers.com/topic/weighted-mean

4.5: Linear Approximations, Differentials. and Newton's

Method. Greg Kelly, Hanford High School, Richland, Washington.