Target Exam

CUET

Subject

-- Applied Mathematics - Section B2

Chapter

Linear Programming

Question:

Consider the following data

Year 2012 2013 2014 2015 2016
Production (in tonnes) 15 20 25 30 35

The equation of straight line trend by method of least squares is :

Options:

$y = 5 + 25x$

$y = 10 + 15x$

$y = 25 + 5x$

$y = 15 + 5x$

Correct Answer:

$y = 25 + 5x$

Explanation:

The correct answer is Option (3) → $y = 25 + 5x$

The general form of the trend line equation is,

$y=a+bx$

x = year - 2014

$⇒x=-2,-1,0,1,2$

∴ The product values (y) remain the same,

$y=15,20,25,30,35$

$∑x=(-2)+(-1)+0+1+2=0$

$∑y=15+20+25+30+35=125$

$b=\frac{∑xy}{∑x^2}=\frac{50}{10}=5$

$a=\frac{∑y}{n}=\frac{125}{5}=25$

$y=25+5x$