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Queremos ajustar una recta que exprese las ventas de una empresa en función de los gastos en publicidad que hace a lo largo de 6 años:
Ventas Gastos publicidad
10 mill. 2 mill.
15 mill. 4 mill.
20 mill. 6 mill.
22 mill. 7 mill.
30 mill. 8 mill.
32 mill. 10 mill.
Para obtener la recta ajustada habrá que realizar los siguientes cálculos:
| X | Y | X * Y | X2 |
| 2 | 10 | 20 | 4 |
| 4 | 15 | 60 | 16 |
| 6 | 20 | 120 | 36 |
| 7 | 22 | 154 | 49 |
| 8 | 30 | 240 | 64 |
| 10 | 32 | 320 | 100 |
Total | 37 | 129 | 914 | 269 |
"Y = n·a + "X·b ! 129 = 6·a + 37·b ! a = (129 - 37·b) / 6 ! a = 3,604
"X·Y = "X·a + "X2·b ! 914 = 37·a + 269·b
! 914 = 37 · [(129 - 37·b) / 6] + 269·b ! b = 2,902
Teniendo los resultados de a y b asignaremos valores a Y según la fórmula Y = 3,604 + 2,902·X, obteniendo así la siguiente tabla y gráfica:
X | Y |
2 | 9,40816327 |
4 | 15,2122449 |
6 | 21,0163265 |
7 | 23,9183673 |
8 | 26,8204082 |
10 | 32,6244898 |
Debe de haber otros factores que determinen las ventas a parte de los gastos en publicidad.
Y = 3,604 + 2,902·9 = 29,7 mill.
Y = 3,604 + 2,902·12 = 38,4 mill.
35 = 3,604 + 2,902·X ! 35 - 3,604 = 2,902·X ! X = (35 - 3,604) / 2,902 = 10,8
Gastos publicidad = X = 10,8 mill.
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Enviado por: | Victor |
Idioma: | castellano |
País: | España |