Minimos cuadrados

1. MINIMOS CUADRADOS
 Ajuste Lineal
Y= mx + b y = 1.645x+0.037
 Pendiente
m= (0,684) (1.309)-(5)(0.2192) = 1.645
(0.684)2
-(5) (0.11797)
 Error de Pendiente
∆m= √(5)(0.2746)2
= 1.758
 Ordenada en origen
b= (0.684) (0.2192)-(1.309) (0.1179) = 0.037
(0.684)2
-(5) (0.1179)
 Error ordenada en origen
∆b= √(0.27462)(0.11797) = 0.27
 Parámetros de error
= (0.5) = 0.1
5
X= l-lo (m) F= mg (N)
0.046 0.111
0.076 0.16
0.135 0.260
0.195 0.357
0.232 0.418
  
 


 22
xNx
xyNyx
m
 22
2
 

xxN
N
m

(5 * 0.11797)
  
 


 22
2
xNx
xyxyx
b
 22
22




xxN
x
b

(5*0.1797)-0.6842
N
x
x



2. = (0.005)= 0.001
5
= √(0.0012) + 1.6452(0.12) = 0.164
 Coeficiente de correlación
(0.2192) -
0.684(1.309)
5
r = ___________________________________________=0.1000729
√(0.11797 −
1
5
(0.6842) [0.4086 −
1
5
(1.3092)]
= 0.9999596
N
y
y


222
xy m  
    










  
 
2222 11
y
N
yx
N
x
N
yx
xy
r