Обследование пяти семей дало следующие результаты

H≔1446215035140301331613090, Y≔35534
A≔(HT×H)-1×(HT×Y)
HTH=1111144504033306235301690×1446215035140301331613090=c11c12c13c21c22c23c31c32c33=519723319780258906233890614325
c11=1×1+1×1+1×1+1×1+1×1=5
c12=1×44+1×50+1×40+1×33+1×30=197
c13=1×62+1×35+1×30+1×16+1×90=233
c21=44×1+50×1+40×1+33×1+30×1=197
c22=44×44+50×50+40×40+33×33+30×30=8025
c23=44×62+50×35+40×30+33×16+30×90=8906
c31=62×1+35×1+30×1+16×1+90×1=233
c32=62×44+35×50+30×40+16×33+90×30=8906
c33=62×62+35×35+30×30+16×16+90×90=14325
(HtH)-1=1HTH×c11c21c31c12c22c32c13c23c33
A11=(-1)1+1×80258906890614325=1×8025×14325-8906×8906=35641289
A12=(-1)1+2×197890623314325=-1×197×14325-8906×233=-746927
A13=(-1)1+3×19780252338906=-1×197×8906-8025×233=115343
A21=(-1)2+1×197233890614325=-746927
A22=(-1)2+2×523323314325=17336
A23=(-1)2+3×51972338906=1371
A31=(-1)3+1×19723380258960=-115343
A32=(-1)3+2×52331978960=1371
A33=(-1)3+3×51971978025=46829
HTH=c11A11+c12A12+c13A13=
=5×35641289+197×-746927+233×115343=57936745
(HTH)-1=1HTH×A11A21A31A12A22A32A13A23A33=157936745×35641289-746927-115343-746927173361371-1145343137146829=8,513-0,178-0,028-0,1780,0040,00033-0,0280,000330,00031
HTY=1111144504033306235301690×35534=20801919
A=8,513-0,178-0,028-0,1780,0040,00033-0,0280,000330,00031×20801919=2,0390,0500,00017
A=2,0390,0500,00017
y=2,039+0,050x1+0,00017x2
YB=1446215035140301331613090×2,0390,0500,00017=4,234,524,033,683,54
YB≔H×A
YB=4,234,524,033,683,54
S2=1n-k×YB1-Y12+YB2-Y22+…+YBn-Yn2
s2≔15-3×i=15(YBi-Yi)2
s2=1,679
s=1,296
Найдем погрешности коэффициентов регрессионного уравнения
s2=(HTH)-1=1,679×8,513-0,178-0,028-0,1780,0040,00033-0,0280,000330,00031=
=14,293-0,300-0046-0,3000,0070,0005-0,0460,0010,0005
s2=(HT×H)-1=14,293-0,300-0046-0,3000,0070,0005-0,0460,0010,0005
sa02=14,293
sa12=0,007
sa22=0,0005
Погрешность коэффициентов
sa0=3,781
sa1=0,0083
sa2=0,0023