Worked Examples · Example 5
Q.
Fit a straight-line trend by the method of least squares to the following data and write down the trend value for each year.
| Year | 2013 | 2014 | 2015 | 2016 | 2017 |
|---|---|---|---|---|---|
| Sales (Rs lakh) | 12 | 18 | 20 | 23 | 27 |
Maharashtra MsbshseTextbookSubjectiveImportance★★★★★
40% · 10/25 Questions
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Start your 14-day free trial to unlock the full solution →There are years (odd), so we take the middle year 2015 as origin and let be the deviation in years: . Then and the normal equations reduce to and .
| Year | ||||
|---|---|---|---|---|
| 2013 | 12 | 4 | ||
| 2014 | 18 | 1 | ||
| 2015 | 20 | 0 | 0 | 0 |
| 2016 | 23 | 1 | 23 | 1 |
| 2017 | 27 | 2 | 54 | 4 |
| Total | 100 | 0 | 35 | 10 |
Hence
The trend line is (origin 2015, unit of = 1 year).
Trend values (substitute each ):
| Year | ||
|---|---|---|
| 2013 | ||
| 2014 | ||
| 2015 | 0 | |
| 2016 | 1 | |
| 2017 | 2 |
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