Consideranso que el consumo se puede expresar como funcion lineal de la renta \(Y_t=a+bX_t\) determine:
a) Los parametros a y b de la recta de regresion.
b) Los parámetros del valor que tomara el consumo para renta de 650,000 millones de euros.
SOLUCIÓN
\(\Sigma X_it_i=\left(381.7\right)\left(258.6\right)+\left(402.2\right)\left(273.6\right)+\left(426.5\right)\left(289.7\right)\)
\(+\left(454.3\right)\left(308.9\right)+\left(486.5\right)\left(331.0\right)+\left(520.2\right)\)
\(\left(355.0\right)+\left(553.3\right)\left(377.1\right)+\left(590.0\right)\left(400.4\right)=1'263,227.79\)
\(\Sigma x_i=258.6+273.6+289.7+308.9+331.0+355.0+377.1+400.4\)
\(=2594.3\)
\(\Sigma t_i=381.7+402.2+426.5+454.3+486.5+520.2+553.3+590.0\)
\(=3814.7\)
\(\Sigma t_i^2=\left(381.7\right)^2+\left(402.2\right)^2+\left(426.5\right)^2+\left(454.3\right)2+\left(486.5\right)^2\)
\(+\left(520.2\right)^2+\left(553.3\right)^2+\left(590.0\right)^2=1,857,281.7\)
\(\)
\(\left[\Sigma t_i\right]^2=3,8134.7^2=14,551,936.09\)
\(b=\frac{8\left(1,263,227.79\right)-\left(2,594.3\right)\left(3814.7\right)}{8\left(1,857,281.7\right)-\left(14,551,936.09\right)}=\)
\(b=\frac{209306.11}{306317.51}=0.683428479\)
\(x=\frac{2594.3}{8}=324.2875\)
\(t=\frac{3814.7}{8}=476.8375\)
\(a=x-bt=476.8375-\left(0.683428479\right)\left(324.2875\right)=255.210\)
\(a=x-bt=324.2875-\left(0.683428479\right)\left(476.8375\right)=-1.596827355\)
\(x=a+bt=-1.596827355+\left(0.683428479\right)\left(650000\right)=444226.9145\)
\(\)