(b) Fit a straight line trend to the following data and estimate the expected profit for the year 2020. What is the average annual change in profit?
Year 2014 2015 2016 2017 2018 2019
Sales (in ‘000 of Rs.) 15 17 20 21 23 24
Answers
Given : Data Showing sale data
Year 2014 2015 2016 2017 2018 2019
Sales (in ‘000 of Rs.) 15 17 20 21 23 24
To find : average annual change in profit & estimate the expected profit for the year 2020.
Solution:
YEAR Sales in'000 Rs Sales Line of Best Fit y = 2x - 4013
2014 15 15 ( Actual Data on line)
2015 17 17 (Actual Data on line)
2016 20 19 (Actual Data Above line)
2017 21 21 (Actual Data on line)
2018 23 23 (Actual Data on line)
2019 24 25 (Actual Data Below line)
2020 - 27
Let say Line going through (2015 , 17) & (2018 , 23)
Slope = 6/3 = 2
y - 17 = 2(x - 2015)
=> y = 2x - 4013
This is correct line of Best fit as Equal number of points are below & above Best Fit line .
As per Best fir line Average annual Change = 2000
average annual change in profit = 2000
expected profit for the year 2020 = 25000 + 20000 = Rs 27000
y = 2x - 4013 = 2*2020 - 4013 = 27 in thousands
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