Target Exam

CUET

Subject

-- Applied Mathematics - Section B2

Chapter

Question:

Let $y = 138.86 + 7.64(x-2021)$ be a straight line of best fit by using least square method to the following data:

Year(x)

2018

2019

2020

2021

2022

2023

2024

Profit(y) (in Rs. '000)

114

130

126

144

138

156

164

Then the trend value for the year 2024 is:

Options:

164

154.14

161.78

162.86

Correct Answer:

161.78

Explanation:

The correct answer is Option (3) → 161.78

Given trend line: $y = 138.86 + 7.64(x - 2021)$

For the year 2024, $x = 2024$

Substitute $x = 2024$:

$y = 138.86 + 7.64(2024 - 2021)$

$y = 138.86 + 7.64 \times 3$

$y = 138.86 + 22.92$

$y = 161.78$

Therefore, the trend value for the year 2024 is Rs. 161.78 thousand