Question

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

Answer 1

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 fit 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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