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National Scan, Inc., sells ratio frequency inventory tags. Monthly sales for a 6-month period were as follows: Month: Sales Feb 56 Mar 52 Apr 61 May 65 Jun 71 Jul 68 Disregard the demand pattern of the given time series, You are asked to use the time series to derive a trend equation. In order to derive the trend equation is Ft = a + bt, you have to compute several components to compute the values for the variables a and b. Answer the following questions pertaining to information that are relevant to deriving the trend equation. a) The Σty = b) The Σy = c) The value for the b (slope of the trend line) = (in 3 decimal places) d) The value for the a (intercept of the trend line) = (in 3 decimal places)

The trend line equation is given as follows:
Y = a + bt
https://d2vlcm61l7u1fs.cloudfront.net/media%2F696%2F69647eca-67f5-4c9e-941f-06d58db7e6d6%2FphpEByFFb.png
Month
Period
Sales
t
y
ty
t*t
y*y
Feb
1
56
56
1
3,136
Mar
2
52
104
4
2,704
Apr
3
61
183
9
3,721
May
4
65
260
16
4,225
Jun
5
71
355
25
5,041
Jul
6
68
408
36
4,624
Total
21
373
1366
91
23451
Mean
3.5
62.17
a) The Σty = 1366
b) The Σy = 373
c) slope of trend line = b = (1366 – 6 x 3.5 x 62.17)/(91 – 6 x 3.5 x 3.5) = 3.457
d) Intercept of the trend line a = 62 – (3.46)(3.5) = 50.067
Trend Line Equation: Y = 50.067 + 3.457t
 
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