Przemysław Gawłowski 08.01.2013
127086
Metody probabilistycze i statystyka
Laboratorium
Sprawozdanie 10
2FDI grupa L04
Zadanie 1
x y
xi yi xi- yi- (xi- ( yi-
x y
x)2 y)2 (xi-)"( yi-)
1 62 83.00 4.70 -0.60 22.09 0.36 -2.82
2 62 94.00 4.70 10.40 22.09 108.16 48.88
3 59 90.00 1.70 6.40 2.89 40.96 10.88
4 56 86.00 -1.30 2.40 1.69 5.76 -3.12
5 57 86.00 -0.30 2.40 0.09 5.76 -0.72
6 56 85.00 -1.30 1.40 1.69 1.96 -1.82
7 55 82.00 -2.30 -1.60 5.29 2.56 3.68
8 55 80.00 -2.30 -3.60 5.29 12.96 8.28
9 55 70.00 -2.30 -13.60 5.29 184.96 31.28
10 56 80.00 -1.30 -3.60 1.69 12.96 4.68
573 836 0 0 68.10 376.40 99.20
"
xi

xi yi yi ui=xi-x zi= yi- y
  
u2 z2 ui"zi
i i
1 62.00 83.00 57.14 90.45 4.86 -7.45 23.60 55.45 -36.18
2 62.00 94.00 60.04 90.45 1.96 3.55 3.84 12.63 6.96
3 59.00 90.00 58.99 86.08 0.01 3.92 0.00 15.39 0.05
4 56.00 86.00 57.93 81.71 -1.93 4.29 3.73 18.44 -8.30
5 57.00 86.00 57.93 83.16 -0.93 2.84 0.87 8.05 -2.65
6 56.00 85.00 57.67 81.71 -1.67 3.29 2.79 10.85 -5.50
7 55.00 82.00 56.88 80.25 -1.88 1.75 3.53 3.06 -3.29
8 55.00 80.00 56.35 80.25 -1.35 -0.25 1.83 0.06 0.34
9 55.00 70.00 53.72 80.25 1.28 -10.25 1.65 105.05 -13.16
10 56.00 80.00 56.35 81.71 -0.35 -1.71 0.12 2.91 0.60
573 836 573 836 0 0 41.96 231.90 -61.12
"
x = 57.3

y = 83.6

n = 10
cov( x , y)
= 9.92 - kowariancja
S
= 2.61
x
2
S = 6.81  wariancja X
x
S
= 6.14
y
2
S = 37.64  wariancja Y
y
rxy
= 0.62
r2 = 0.38  współczynnik determinacji
xy
a1 =
1.457  współczynnik prostej
a0 =
0.132  współczynnik prostej
b1 =
0.264  współczynnik prostej
b0 =
35.267  współczynnik prostej
S (z)
= 5.38
2
= 28.98
S (z)
S (u)
= 2.29
= 5.24
S2(u )
V ( z)
= 6.44%
V (u)
= 4 %
Ć^2 yx = 0.62
Ć^2 xy = 0.62
Wykres prostej regresji