considerando que el consumo se puede expresar como función lineal de la renta \(Y_t=a+bX_t\) determine:
A) Los parametros a y b de la recta de regresion.
B)La predicción del valor que tomara el consumo para una renta de 650,000 millones de euros.
SOLUCIÓN
\(\Sigma X_iT_i=\left(381'7\right)\left(258'6\right)+\left(402'2\right)\left(273'6\right)+\left(426'5\right)\left(289'7\right)\)
\(+\left(454'3\right)\left(308'9\right)+\left(486'5\right)\left(331'0\right)+\left(520'2\right)\left(355'0\right)\)
\(+\left(553'3\right)\left(377'1\right)+\left(590'0\right)\left(400'4\right)\) =1'263,227.79
\(\Sigma X_i=381.7+402.2+426.5+454.3+486.5+520.2+553.3+590.0\)
=3814.7
\(\Sigma T_i=258.6+273.6+289.7+308.9+331.0+355.0+377.1+400.4\)
=2594.3
\(\Sigma X^i=\left(381.7\right)^2+\left(402.2\right)^2+\left(426.5\right)^2+\left(454.3\right)^2+\left(486.5\right)^2\)
\(+\left(520.2\right)^2+\left(553.3\right)^2+\left(590.0\right)^{^2}=1,857,281.7\)
\(\left[\Sigma X_i\right]^2=3814.7^2=14,551,936.09\)
\(b=\frac{8\left(1'263,227.79\right)-\left(3814.7\right)\left(2594.3\right)}{8\left(1,857,281.7\right)-\left(14,551,936.09\right)}\)
\(b=\frac{209,346.11}{306,317.51}=\ 0.683428479\)
\(X=381.7+402.2+426.5+454.3+486.5+520.2\)
\(+553.3+590.0\) =3814.7/8=476.8375
\(T=258.6+273.6+289.7+308.9+331.0+355.0+377.1+400.4\)
=2594.3/8=324.2875
A)
A=x-bt
=476.8375-(0.683428479)(324.2875)
=255.210
\(A=X^--BT^-\)324.2875-(0.683428479)(476.8375)=-1.596827355
B)
^
X =a+bt= -1.596827355+(0.683428479)(650,000) = 444,226.9145