3 Production for last 7 years of XYZ ltd is given in following table
3 Production for last 7 years of XYZ ltd is given in following table
| Year | 2009 | 2010 | 2011 | 2012 | 2013 | 2014 | 2015 |
| Production(in Tons) | 8 | 12 | 13 | 17 | 25 | 22 | 30 |
Based on above data forecast the production for year 2016 & 2017.
A Fitting of straight line
Production for year 2016
Production for year 2017
Answer: The trend line can be fitted by using the method of least squares for the given data.
| Year | Production
y |
X= Year – 2012 | XY | X^2 |
| 2009 | 8 | -3 | -24 | 9 |
| 2010 | 12 | -2 | -24 | 4 |
| 2011 | 13 | -1 | -13 | 1 |
| 2012 | 17 | 0 | 0 | 0 |
| 2013 | 25 | 1 | 25 | 1 |
| 2014 | 22 | 2 | 44 | 4 |
| 2015 | 30 | 3 | 90 | 9 |
| 127 | 0 | 98 | 28 |
When å X = 0, then normal equations reduce to:
åY = Na , therefore,
a = SY/N
= 127/7
= 18.14
å XY = bå X^2 , therefore, b = S XY/ SX
= 98/28
= 3.5
The estimated equation of the trend line is given by
Y = a + bX =18.14 + 3.5 X
for 2016, X = 4
Y = 18.14 + (3.5 *4)
= 79.65 – 7.44
= 32.14
Hence the price for 2016 is Rs 32.14
for 2017, X = 5
Y = 18.14 + (3.5 * 5)
= 79.65 – 7.44
= 35.64
Hence the price for 2017 is Rs 35.64
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