I – Mínimos Cuadrados.
Cuando "n" es par.
Desifentante de un 1 Galón
Años | Y | X | XY | X2 |
98 | 31.4 | 0 | 0 | 0 |
99 | 26.6 | 1 | 26.6 | 1 |
00 | 25.3 | 2 | 50.6 | 4 |
01 | 30.5 | 3 | 91.5 | 9 |
02 | 28.0 | 4 | 112.0 | 16 |
03 | 34.2 | 5 | 171.0 | 25 |
N = 6 | ∑ Y = 176 | ∑ X = 15 | ∑ XY = 451.7 | ∑ X2 = 55 |
Y= A0 + A ix
A0 = (∑Y) (∑X2) – (∑X) (∑Y)
N (∑X2) – (∑X)2
A0 = (176) (55) – (15) (451.7)
6 (55) – (15)2
A0 = 9680 – 6775.5 =
330 – 225
A1 = N (∑ XY) – (∑X) (∑Y)
N (∑ Y2) – (∑ Y)2
A1 = 6 (451.7) – (15) (176) =
6 (55) – (15)2
A1 = 3710.2 – 2640 = 70.2
330 – 225 105
A1 = 0.66
Y = 27.6 + 0.66 (6)
Y = 27.6 + 3.96
Y04 = 31.56
Años | Y | X | XY | X2 |
1998 | 28.2 | 0 | 0 | 0 |
99 | 22.5 | 1 | 22.5 | 1 |
00 | 21.2 | 2 | 42.4 | 4 |
01 | 27.4 | 3 | 82.2 | 9 |
02 | 25.1 | 4 | 100.4 | 16 |
03 | 33.0 | 5 | 165.0 | 25 |
N = 6 | ∑ Y = 157.4 | ∑ X = 15 | ∑ XY = 412.5 | ∑ X2 = 55 |
A0 = (∑Y) (∑x2) – (∑X) (∑XY) =
N (∑X2) – (∑X)2
A0 = (157.4) (55) – (15) (412.5)
6 (55) – (15)2
A0 = 8657 – 6187.5 =
330 – 225
A0 = 2469.5 = 23.5
105
A1 = N (∑ XY) – (∑X) (∑Y) =
N (∑X2) – (∑X)2
A1 = 6 (412.5) – (15) (15734) =
N (∑X2) – (∑X)2
A1 = 2475 – 2361 = 114 = 1.08
330 – 225 105
Y = 23.5 + 1.08 (6)
Y = 23.5 + 6.48
Y 04 = 29.98
Años | Y | X | XY | X2 |
1998 | 33.2 | 0 | 0 | 0 |
99 | 29.5 | 1 | 29.5 | 1 |
00 | 27.4 | 2 | 54.8 | 4 |
01 | 32.6 | 3 | 97.8 | 9 |
02 | 30.4 | 4 | 121.6 | 16 |
03 | 36.1 | 5 | 180.6 | 25 |
N = 6 | ∑ Y = 189.2 | ∑ X = 15 | ∑ XY = 484.3 | ∑ X2 = 55 |
Y = A0 + A ix
A0 = (∑ Y) (∑X2) – (∑X) (∑XY)
N (∑ X2) – (∑ X)2
A0 = 10406 – 7264.5
330 – 225
A0 = 3141.5
105
A0 = 29.9
A1 = N (∑ XY) – (∑ X) (∑ Y)
N (∑ X2) – (∑ X)2
A1 = 6 (484.3) – (15) (189.2)
6 (55) – (15)2
A1 = 2905.8 – 283.8
330 – 225
A1 = 262.2
105
A1 = 2.49
Y = A0 + A1X
Y = 29.9 + 2.49 (6)
Y = 29.9 + 14.94
YX04 = 44.84
Años | Y | X | XY | X2 |
1998 | 20.1 | 0 | 0 | 0 |
99 | 19.4 | 1 | 19.4 | 1 |
00 | 18.1 | 2 | 36.2 | 4 |
01 | 22.3 | 3 | 66.9 | 9 |
02 | 21.0 | 4 | 84.0 | 16 |
03 | 31.0 | 5 | 155 | 25 |
N = 6 | ∑ Y = 131.9 | ∑ X = 15 | ∑ XY = 361.5 | ∑ X2 = 55 |
A0 = (∑ Y) (∑X2) – (∑X) (∑XY)
N (∑ X2) – (∑ X)2
A0 = (131.9) (55) – (15) (361.5)
6 (55) – (15)2
A0 = 7254.5 – 5422.5
330 – 225
A0 = 1832
105
A0 = 17.4
A1 = N (∑ XY) – (∑ X) (∑ Y)
N (∑ X2) – (∑ X)2
A1 = 6 (361.5) – (15) (131.9)
6 (55) – (15)2
A1 = 2169 – 1978.5
330 – 225
A1 = 190.5
105
A1 = 1.81
Y = A0 + A1 4
Y = 17.4 + 1.81 (6)
Y = 17.4 + 10.86
YX04 = 28.26
Ventas Para 04 1 Galón.
Meses | 98 | 99 | 00 | 01 | 02 | 03 | % | 2004 |
Enero | 2.5 | 2.2 | 2.1 | 2.6 | 2.4 | 3.0 | 8.4 | 2.65 |
Febrero | 1.8 | 2.3 | 1.7 | 2.4 | 2.2 | 2.8 | 7.5 | 2.36 |
Marzo | 2.7 | 2.4 | 1.6 | 2.4 | 2.2 | 2.6 | 7.8 | 2.46 |
Abril | 2.6 | 1.8 | 1.9 | 2.3 | 2.0 | 2.7 | 7.5 | 2.36 |
Mayo | 2.6 | 1.9 | 1.8 | 1.9 | 2.6 | 3.1 | 7.8 | 2.46 |
Junio | 1.9 | 1.7 | 1.8 | 2.1 | 2.0 | 2.5 | 6.8 | 2.14 |
Julio | 1.7 | 1.6 | 1.8 | 2.0 | 1.9 | 2.6 | 6.5 | 2.05 |
Agosto | 1.9 | 2.0 | 2.0 | 2.2 | 2.0 | 2.8 | 7.3 | 2.32 |
Septiembre | 2.4 | 2.1 | 2.2 | 2.6 | 2.5 | 2.8 | 8.2 | 2.59 |
Octubre | 3.8 | 3.0 | 2.2 | 3.0 | 2.7 | 3.0 | 10.5 | 3.31 |
Noviembre | 3.7 | 2.8 | 3.0 | 3.6 | 2.7 | 3.1 | 10.7 | 3.38 |
Diciembre | 3.8 | 2.8 | 3.1 | 3.7 | 2.8 | 3.2 | 11.0 | 3.48 |
Totales | 31.4 | 26.6 | 25.3 | 30.5 | 28.0 | 34.3 | 100.0 | 31.56 |
98/03 = 14.8 Enero
Totales 98/03 = 176.0
14.8 = % = 8.4
176.0
31.56 X 0.084 = 2.65
Ventas para el 2004
RD $ 29.98
Enero – Diciembre
Meses | 98 | 99 | 00 | 01 | 02 | 03 | % | 2004 |
Enero | 2.6 | 2.3 | 2.0 | 2.2 | 2.3 | 3.9 | 9.7 | 2.91 |
Febrero | 2.4 | 2.2 | 2.1 | 2.0 | 1.8 | 2.0 | 8.0 | 2.40 |
Marzo | 2.0 | 1.9 | 1.7 | 1.4 | 2.0 | 2.2 | 7.1 | 2.15 |
Abril | 2.1 | 2.0 | 2.1 | 2.0 | 1.6 | 2.9 | 8.0 | 2.40 |
Mayo | 1.9 | 1.3 | 1.4 | 2.6 | 2.3 | 2.7 | 7.7 | 2.32 |
Junio | 2.0 | 1.9 | 1.7 | 2.4 | 2.2 | 2.1 | 7.8 | 2.33 |
Julio | 2.1 | 1.2 | 1.0 | 2.1 | 1.7 | 2.6 | 6.7 | 2.05 |
Agosto | 1.5 | 2.3 | 2.0 | 2.2 | 1.8 | 2.0 | 8.3 | 2.45 |
Septiembre | 2.0 | 1.8 | 1.5 | 2.6 | 2.1 | 3.4 | 8.6 | 2.54 |
Octubre | 2.5 | 1.3 | 1.0 | 2.3 | 2.1 | 3.3 | 8.0 | 2.37 |
Noviembre | 3.1 | 1.5 | 2.3 | 2.1 | 2.0 | 2.4 | 8.5 | 2.56 |
Diciembre | 3.0 | 2.8 | 2.4 | 3.5 | 3.2 | 3.5 | 11.6 | 3.50 |
Totales | 28.2 | 22.5 | 21.2 | 27.4 | 25.1 | 33.0 | 100.0 | 29.98 |
98/03 = 15.3 Enero
Totales 98/03 = 157.4
15.3 = % = 9.72
157.4
29.98 X 0.0972 = 2.91
Ventas para el 2004
RD $ 44.84
Enero – Diciembre
Meses | 98 | 99 | 00 | 01 | 02 | 03 | % | 2004 |
Enero | 3.6 | 3.4 | 2.9 | 3.0 | 2.8 | 3.0 | 9.8 | 4.42 |
Febrero | 3.2 | 2.1 | 2.0 | 3.2 | 3.1 | 2.9 | 8.7 | 3.90 |
Marzo | 2.3 | 2.1 | 1.6 | 2.0 | 2.1 | 2.7 | 6.7 | 3.09 |
Abril | 2.4 | 2.3 | 2.0 | 2.2 | 1.8 | 2.9 | 7.1 | 3.20 |
Mayo | 3.1 | 2.0 | 2.9 | 2.6 | 2.3 | 2.2 | 8.0 | 3.54 |
Junio | 2.0 | 1.8 | 1.7 | 2.8 | 2.6 | 2.9 | 7.2 | 3.24 |
Julio | 2.1 | 1.9 | 1.5 | 2.5 | 2.2 | 2.7 | 6.9 | 3.04 |
Agosto | 3.2 | 3.0 | 2.8 | 3.0 | 2.7 | 3.7 | 9.8 | 4.36 |
Septiembre | 2.4 | 2.3 | 2.0 | 2.2 | 2.5 | 3.6 | 7.9 | 3.58 |
Octubre | 3.0 | 2.9 | 2.7 | 3.5 | 2.8 | 2.9 | 9.5 | 4.27 |
Noviembre | 2.8 | 2.7 | 2.5 | 2.6 | 2.4 | 3.0 | 8.5 | 3.80 |
Diciembre | 3.1 | 3.0 | 2.9 | 3.0 | 3.1 | 3.6 | 9.9 | 1.40 |
Totales | 33.2 | 29.5 | 27.5 | 32.6 | 30.4 | 36.1 | 100 | 44.84 |
98/03 = 18.7 Enero
Totales 98/03 = 189.3
18.7 = % = 9.87
189.3
44.84 X 0.0987 = 4.42
Ventas para el 2004
RD $ 28.26
Enero – Diciembre
Meses | 98 | 99 | 00 | 01 | 02 | 03 | % | 2004 |
Enero | 2.0 | 1.9 | 1.8 | 2.0 | 2.1 | 2.5 | 9.3 | 2.63 |
Febrero | 1.5 | 1.3 | 1.2 | 1.3 | 1.2 | 2.6 | 9.1 | 2.52 |
Marzo | 2.1 | 2.0 | 1.9 | 1.8 | 1.7 | 2.9 | 9.2 | 2.64 |
Abril | 1.3 | 1.1 | 1.0 | 1.1 | 1.0 | 2.5 | 6.0 | 1.62 |
Mayo | 2.1 | 1.8 | 1.5 | 2.7 | 2.4 | 2.3 | 9.3 | 2.70 |
Junio | 1.5 | 1.2 | 1.1 | 1.4 | 1.3 | 2.4 | 6.5 | 1.90 |
Julio | 1.2 | 1.1 | 1.0 | 1.2 | 1.1 | 2.5 | 6.1 | 1.71 |
Agosto | 1.7 | 2.3 | 2.0 | 2.2 | 2.0 | 2.4 | 9.3 | 2.63 |
Septiembre | 2.0 | 1.8 | 1.6 | 1.9 | 1.8 | 2.9 | 9.0 | 2.54 |
Octubre | 1.7 | 1.4 | 2.0 | 2.1 | 1.9 | 2.0 | 8.2 | 2.33 |
Noviembre | 1.0 | 1.6 | 1.4 | 2.6 | 2.4 | 2.6 | 8.5 | 2.44 |
Diciembre | 2.0 | 1.9 | 1.6 | 2.0 | 2.1 | 3.4 | 9.5 | 2.60 |
Totales | 20.1 | 19.4 | 18.1 | 22.3 | 21.0 | 31.0 | 109.50.0 | 28.26 |
98/03 = 12.3 Enero
Totales 98/03 = 131.9
12.3 = % = 9.32
131.9
28.26 X 0.0932 = 2.63
Cuota De Ventas
Año 2004
Territorio
Zonas | % | Vendedor | Enero | Febrero | Marzo | Abril | Mayo |
Santo Domingo | 35 | 101=11% 102=9% 103=4% 104=6% 105=5% | 44,135 | 39,550 | 36,190 | 33,530 | 38,570 |
Cibao | 30 | 201=9% 202=8% 203=4% 204=6% 205=3% | 37,830 | 33,900 | 31,020 | 28,740 | 33,060 |
Este | 20 | 301=4% 302=8% 303=4% 304=3% | 25,220 | 22,600 | 20,680 | 19,160 | 22,040 |
Sur | 15 | 401=7% 402=4% 403=4% | 18,915 | 16,950 | 15,510 | 14,370 | 16,530 |
Totales | 100 | 106.380.00 | 126.100 | 113.000 | 103.400 | 95,8000 | 100.2000 |
Junio | Julio | Agosto | Septiembre | Octubre | Noviembre | Diciembre |
33,635 | 30,975 | 41,160 | 39,375 | 42,980 | 42,630 | 48,930 |
28,830 | 26,550 | 35,280 | 33,750 | 36,840 | 36,540 | 41,940 |
19,220 | 17,700 | 23,520 | 22,500 | 24,560 | 24,360 | 27,960 |
14,415 | 13,275 | 17,640 | 16,875 | 18,420 | 18,270 | 20,970 |
96,100 | 88,500 | 117,600 | 112,500 | 122,800 | 121,800 | 139,800 |
Variación Anual
I Galón
Años | Ventas | Incremento | Variación Anual |
98 99 00 01 02 03 | 31.4 26.6 25.3 30.5 28.0 34.2 | (4.8) (1.3) 5.2 (2.5) 6.2 |
0.0 (4) (0.4) (2.4) |
04 | 31.5 | ∑ = 15 / 5 = 3 | (2.2) |
Años | Ventas | Incremento | Variación Anual |
98 99 00 01 02 03 | 28.2 22.5 21.2 27.4 25.1 33.0 | (5.7) 1.3 (6.2) 2.3 (7.9) |
0.2 (4.7) (0.3) (3.4) |
04 | 22.5 | ∑ = 16.2 / 5 = 3.24 = 1.0324 | ∑ (8.2) |
16 onz
Años | Ventas | Incremento | Variación Anual |
98 99 00 01 02 03 | 33.2 29.5 27.5 32.6 30.4 36.1 | (3.7) (2) (5.1) 2.2 (5.7) |
(0.5) (0.3) (0.4) (2.5) |
04 | 44.84 | ∑ = 10.3 = 1.0103 | ∑ = 2.7 |
Años | Ventas | Incremento | Variación Anual |
98 99 00 01 02 03 | 20.1 19.4 18.1 22.3 21.0 31.0 | 0.7 1.3 (4.2) 1.3 (10) |
1.8 (3.2) (0.3) (7.6) |
04 | 28.26 | ∑ = 10.9 = 1.0109 | ∑ 9.3 |
José Berroa
Lic. En Informática