Question

Demand for stereo headphones and MP3 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 last year was as follows:
MONTH DEMAND (UNITS)
January 4,130
February 4,230
March 3,930
April 4,330
May 4,930
June 4,630
July 5,230
August 4,830
September 5,330
October 5,630
November 6,230
December 5,930

Required:
Using linear regression technique, what would you estimate demand to be for each month next year?

Answer 1

Answer:

First month of next month ( x = 13)   = 6170

second month ( x = 14 ) = 6389

Explanation:

Determine the estimate demand for each month next year ( use Linear regression )

Linear regression equation: y = a + bx

a = intercept between regression line and y-axis

b = slope of regression

x = month

y = demand

Using excel table attached below

∑x = 78

∑xy = 413340

∑y = 59360

∑(x)^2 = 650

N = 12

(∑x )^2 = 6084

next we will calculate the slope and intercept value

b ( slope ) = ( 12 * 413340 ) - ( 78 * 59360 ) / ( 12 * 650 - 6084 )

                = 330,000 / 1716 = 192.31

intercept ( a ) = 59360 - ( 192.31 * 78 ) / 12 = 3696.65

Back to equation 1 :

Linear regression equation = Y = 3696.65 + 192.31 x

where x = number of month ( i.e. 13 , 14 ….. 24 )

To determine the estimate demand for each month next month

Linear regression equation : Y = 3696.65 + 192.31 x

first month of next month ( x = 13)  = 3696.65 + 192.31 * ( 13 )

second month ( x = 14 ) = 3696.65 + 192.31 * ( 14 )

Note : apply same equation to every month ( i.e. from x = 15 to 24 ) to determine the estimate demand for each month