Answer:
Y = 3,676.67 + 192.31(X)
In January = 3,676.67 + 192.31(1) = 3,868.98 units
In February = 3,676.67 + 192.31(2) = 4,061.29 units
In March = 3,676.67 + 192.31(3) = 4,253.6 units
In April = 3,676.67 + 192.31(4) = 4,445.91 units
In May = 3,676.67 + 192.31(5) = 4,638.22 units
In June = 3,676.67 + 192.31(6) = 4,830.53 units
In July = 3,676.67 + 192.31(7) = 5,022.84 units
In August = 3,676.67 + 192.31(8) = 5,215.15 units
In September = 3,676.67 + 192.31(9) = 5,407.46 units
In October = 3,676.67 + 192.31(10) = 5,599.77 units
In November = 3,676.67 + 192.31(11) = 5,792.08 units
In December = 3,676.67 + 192.31(12) = 5,984.39 units
Explanation:
Month(x) Demand (y) xy x² y²
1 4,110 4,110 1 16,892,100
2 4,210 8,420 4 17,724,100
3 3,910 11,730 9 15,288,100
4 4,310 17,240 16 18,576,100
5 4,910 24,550 25 24,108,100
6 4,610 27,660 36 21,252,100
7 5,210 36,470 49 27,144,100
8 4,810 38,480 64 23,136,100
9 5,310 47,790 81 28,196,100
10 5,610 56,100 100 31,472,100
11 6,210 68,310 121 38,564,100
12 5,910 70,920 144 34,928,100
∑ 78 59,120 411,780 650 297,281,200
Y = a + bX
Where a = {(∑y)(∑x²) - (∑x)(∑xy)} / {n(∑x²) - (∑x)²}
b = {n(∑xy) - (∑x)(∑y)} / {n(∑x²) - (∑x)²}
a = {(59120*650) - (78*411780)} / {(12*650) - 78²}
= {38,428,000 - 32,118,840} / {7,800 - 6,084}
= 6,309,160 / 1,716
= 3,676.67
b = {(12*411780) - (78*59120)} / 1,716
= {4,941,360 - 4,611,360} / 1,716
= 330,000 / 1,716
= 192.31
putting the equation together:
Y = 3,676.67 + 192.31(X)
