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f8651a64-c3ed-4660-b007-5d86a62898c3 25 Alvaro Diaz Falconi 4 5 false false 0 0 decimal

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Price of an Old Car - the regress analyse

FS a# X# Y# ν μ εx εy δx MI fit.LM X X# eval : Y Y# eval : 12 mat X cols 1 ≡ co 1 : co 1 X cols range : if m X rows : n a# length : r 1 m range : c 1 n range : 14 mat a a# c el : Id n identity eval : 12 mat Na ∞ : upd 1 : FX 0 : Fa 0 : Fb 0 : J 0 : 16 mat x y Φ eval(FS num2str (x num2str, y num2str)) concat str2num : iter 1 MI range upd 1 ≡ FX r el X r co el a Φ : J r c el X r co el a δx Id c col (* + Φ FX r el - δx / eval : Fa r el FX r el Y r el - eval : H J transpose J * eval : 12 mat 31 line continue if s H μ Id * + (1 -^J transpose Fa * (* eval : b a s - : Fb r el X r co el a Φ Y r el - eval : Nb Fb norme : 13 mat μ sqrt Nb * Na < s normi εx a normi * < break a b : Fa Fb : Na Nb : μ μ ν / : upd 1 : 15 mat if μ ν μ * : upd 0 : 12 mat if 41 line for a eval 81 line :

FS# p X Y fit.LM FS# p X Y ν.LM μ.LM εx εy δx MaxIters fit.LM 11 line :

εx 106 -^:

εy 1012 -^:

MaxIters 1000 :

ν.LM 10 :

μ.LM 0.01 ν.LM * :

δx 100 εx * :

b X sHist H 0 : n 1 b length 1 - (range : 12 mat b n 1 + el b n el + 2 / H n el ϑ b n 1 + el : (X ≥ vectorize sum (ϑ b n el : (X > vectorize sum (- eval : augment 21 line :

b X pHist B 02 matrix eval : H b X sHist : 12 mat k 1 b length 1 - (range B B b k el 0 b k el H k 2 el b k 1 + el H k 2 el b k 1 + el 042 mat stack eval : for B 31 line :

polygon b.1 вершок / Рост вершок / pHist 11 mat black solid 2 red stack 11 mat 11 mat 11 sys

M 11.5 880001195 13.5 120000495 7.5 410003495 13.5 103000750 11.5 101000895 13.5 124000850 10.5 820001295 3.5 390004995 10.5 770001595 10.5 650001495 10.5 780001295 6.5 560003495 12.5 97000800 6.5 520002695 12.5 83000895 10.5 700001495 9.5 840001995 9.5 670002495 8.5 510002295 4.5 390003995 4.5 380003990 10.5 800001495 4.5 460003675 6.5 430003400 9.5 790001995 12.5 92000795 13.5 92000795 6.5 570002695 11.5 108000975 11.5 780001295303 mat :

Age M 1 col :

Miles M 2 col :

Price M 3 col :

H 314 range Age pHist :

polygon H 1 1 mat darkgreen solid 2 lightgreen stack 1 1 mat 1 1 mat 1 1 sys

x y.1 Miles Age / vectorize max x * :

x y.2 Miles Age / vectorize min x * :

x y.1 x y.2 Age Miles o 6 red augment 3 1 sys

The Price is the Function of the Age - the linear Regression

x β f.A β 2 el x * β 1 el + :

β.A f.A 1121 mat Age Price fit.LM : 5757.5941 392.7181 - 21 mat

x β.A f.A Age Price o 6 red augment 2 1 sys

The Price is the Function of the MileAge - the exponentioal Regression

x β f.M β 1 el 10 β 2 el x *^* β 3 el + :

β.M f.M 1 0.00001 - 131 mat Miles Price fit.LM : 10562.3604 1105 -^* - 243.0502 - 31 mat

x β.M f.M Miles Price o 6 red augment 2 1 sys

The Price is the Function of the Age and MileAge - the 3D-Regression

x β f.AM β 1 el β 2 el x 1 el * + β 3 el 10 β 4 el x 2 el *^* + :

β.AM f.AM 310001000 - 1000 0.00001 - 41 mat * Age Miles augment Price fit.LM : 4615.8488 301.0521 - 14257.0727 3105 -^* - 41 mat

Age Miles Price Age Miles 12 mat β.AM f.AM :

Example

Ao Mo 21 mat 6.5 5000021 mat :

years
miles

then

Ao Mo Price 3110

x y f3D x y x y Price stack : γ 1 0.0001 0.01 3 1 mat diag 0.5 - 0.6124 - 0.866 0.3536 - 0 0.7071 3 2 mat * : Age max 0 0 0 0 0 0 Miles max 0 0 0 0 0 0 Price max 5 3 mat γ * M γ * o 6 red augment x y f3D Age min Age max Miles min Miles max 20 20 CreateMesh γ * Ao Mo Ao Mo Price 1 3 mat γ * x 6 blue augment 0 0 0 Ao 0 0 Ao Mo 0 Ao Mo Ao Mo Price 4 3 mat γ * 5 1 sys 3 1 line Z 500 5000 1000 range : k 1 Z length range : Π 1 1 1 sys : Π k el x y Price Z k el - 1 6 mat mat2sys.1 : Ao Mo x 6 blue augment 1 3 mat mat2sys.1 Ao 0 Ao Mo 0 Mo 3 2 mat 4 1 sys 4 1 line

Alvaro

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