Best Fit Solution

1. BEST-
BEST-FIT
solution
By Yang Cao

2. Correlation
Regression
Weights
Linearization
Least-
Least-Square solution

3. Learn:
What & How
for each term
twice

4. Then you can calculate :
Coefficient Best-
Best-fit line
Weighted Mean
Linearization

5. Correlation :
Association
between
variables.

6. Direction
positive negative
X Y X Y X Y X Y

7. Strength
1.00 High Strong:
Few exceptions
0.80
Moderate
0.40
Low Weak:
0 Many exceptions

8. Correlation Coefficient: r

10. Regression :
find a formula that can
be used to relate two
variables.
y=mx+b

11. correlation V.S. regression
Correlation: relationship
between variables.
Regression: finding a formula
that represents the relationship
so as to do prediction

12. 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.

14. Weighted mean
• some data points contribute more than others
formula

15. linearize : make linear or get into a linear form.
y
f ( x) = f (a)
We call the equation of the tangent
the linearization of the function.
x
0 x=a

16. Find where y = x3 − x crosses
y =. 1
1 = x3 − x 0 = x3 − x − 1 f ( x ) = x3 − x − 1 f ′ ( x ) = 3x 2 − 1
f ( xn )
xn +1 = xn −
n xn f ( xn ) f ′ ( xn ) f ′ ( xn )
−1
0 1 −1 2 1− = 1.5
2
.875
1 1.5 .875 5.75 1.5 − = 1.3478261
5.75
2 1.3478261 .1006822 4.4499055 1.3252004
3
(1.3252004 ) − 1.3252004 = 1.0020584 ≈1
→

17. Q?

18. 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.