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1. Se cunosc informatii cu privire la notele obtinute de 10 studenti la disciplina Econometrie, precum si numarul de absente acumulate de acestia.
Sa se determine ecuatia de regresie liniara si valorile ajustate.
X ( Nr absente) 5 4 6 3 2 0 4 3 1 1
Y ( Note) 5 8 7 6 9 10 5 6 9 8
Rezolvare:
y ̂ = a+b* x_i
{█(n*a+b∑_(i=1)^n▒〖*x_i=∑_(i=1)^n▒y〗;@a∑_(i=1)^n▒〖xi+b∑_(i=1)^n▒〖* x^2=∑_(i=1)^n▒〖x,y;〗〗〗)┤
Nr x_i y_i x_i^2 x,y y ̂ i
1 5 5 25 25 5.9
2 4 8 16 32 6.55
3 6 7 36 42 5.25
4 3 6 9 18 7.2
5 2 9 4 18 7.85
6 0 10 0 0 9.15
7 4 5 16 20 6.55
8 3 6 9 18 7.2
9 1 9 1 9 8.5
10 1 8 1 8 8.5
Total 29 73 117 190 72.65
y ̂ = a+b* x_i
{█(n*a+b∑_(i=1)^n▒〖*x_i=∑_(i=1)^n▒y〗;@a∑_(i=1)^n▒〖xi+b∑_(i=1)^n▒〖* x^2=∑_(i=1)^n▒〖x,y;〗〗〗)┤
{█(10*a+29b=73@29a+117=190)┤
∆=|- (10&29@29&117)|=10*117-29*29=1170-841=329
∆ a=|- (73&29@190&117)|=73*117-29*190=8541-5510=3031
∆ b=|- (10&73@29&190)|=10*190-73*29=1900-2117= -217
a=∆a/∆=3013/329=9.15
b= ∆b/∆=(-217)/329= -0.65
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- Tema de control Econometrie.docx