Question

Demand for stereo headphones and music players for joggers has caused Nina Industries to grow almost 50 percent over the past year. The number of joggers continues to expand, so Nina expects demand for headsets to also expand, because, as yet, no safety laws have been passed to prevent joggers from wearing them. Demand for the players for this year was as follows: MONTH DEMAND (UNITS)January 4,110 February 4,210 March 3,910 April 4,310 May 4,910 June 4,610 July 5,210 August 4,810 September 5,310 October 5,610 November 6,210 December 5,910Using linear regression analysis, what would you estimate demand to be for each month next year

Answer 1

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

Step-by-step 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)