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Assuming the same rate of change continues for the following data:

Year (x)20192020202120222023
Profit(in Percentage) (y)3840657269

The equation of the straight line trend using the least square method is:

Solution

✅ Correct Option: 2

The equation needs to be in the form y=mx+cy = mx + c where mm is the slope and cc is the y-intercept.

Given that the slope is 9.49.4, we need to find the y-intercept cc.


Year (x)Profit (y)
201938
202040
202165
202272
202369

Number of data points: n=5n = 5


The least squares line passes through the point (xˉ,yˉ)(\bar{x}, \bar{y}).

xˉ=2019+2020+2021+2022+20235\bar{x} = \dfrac{2019 + 2020 + 2021 + 2022 + 2023}{5}

xˉ=101155\bar{x} = \dfrac{10115}{5}

xˉ=2021\bar{x} = 2021


yˉ=38+40+65+72+695\bar{y} = \dfrac{38 + 40 + 65 + 72 + 69}{5}

yˉ=2845\bar{y} = \dfrac{284}{5}

yˉ=56.8\bar{y} = 56.8


Using the formula c=yˉ−m×xˉc = \bar{y} - m \times \bar{x}:

c=56.8−9.4×2021c = 56.8 - 9.4 \times 2021

c=56.8−18997.4c = 56.8 - 18997.4

c=−18940.6c = -18940.6


The equation of the straight line trend is:

y=9.4x−18940.6y = 9.4x - 18940.6

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