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

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

$y=9.4x-18940.6$

The correct answer is Option (2) → $y=9.4x-18940.6$ **

Given data:

Years (x): 2019, 2020, 2021, 2022, 2023

Profit (y): 38, 40, 65, 72, 69

Mean of x:
x̄ = (2019 + 2020 + 2021 + 2022 + 2023) / 5 = 2021

Mean of y:
ȳ = (38 + 40 + 65 + 72 + 69) / 5 = 56.8

The slope (m) represents the rate at which profit changes with time, i.e., how much profit increases per year. In this question, the slope is not directly given, but it is embedded in the options as the coefficient of x. By observing the options, we can identify possible slope values like 9.4, 6.4, etc., and select the correct one. Here, the correct slope is 9.4, which means profit increases by 9.4 units per year on average.

Intercept:
c = ȳ − m×x̄
c = 56.8 − 9.4×2021
c = −18940.6

The required trend equation is:

$y = -18940.6 + 9.4x$