Get Started
Start Free Mocks
CUETMOCK

Ace Your

CUET Preparation Today

Start Free Mocks
Home Questions DNN9CT3U5U
Target Exam

CUET

Subject

-- Applied Mathematics - Section B2

Chapter

Index Numbers and Time Based Data

Question:

Given below are the consumer price index numbers (CPI) of the industrial workers.

Year

2014

2015

2016

2017

2018

2019

2020

Index Number

145

140

150

190

200

220

230

Find the best fitted trend line by the method of least squares and tabulate the trend values.

Options:

$y_t=152.1+16.6x$

$y_t = 155.20 + 12.45x$

$y_t = 190.0 + 10.5x$

$y_t = 175.5 + 20.15x$

Correct Answer:

$y_t=152.1+16.6x$

Explanation:

The correct answer is Option (1) → $y_t=152.1+16.6x$

Year ($x_i$)

Index number ($y$)

$X = x_i – A = x_i – 2017$

$X^2$

$XY$

Trend value $y_t = a + bx$

2014

145

-3

9

-435

$152.1+ (-3)×16.6 = 102.3$

2015

140

-2

4

-280

$152.1+ (-2)×16.6 = 118.9$

2016

150

-1

1

-150

$152.1+ (-1)×16.6 = 135.5$

2017

190

0

0

0

$152.1+ (0)×16.6 = 152.1$

2018

200

1

1

200

$152.1+ (1)×16.6 = 168.7$

2019

220

2

4

440

$152.1+ (2)×16.6 = 185.3$

2020

230

3

9

690

$152.1+ (3)×16.6 = 201.9$

$n = 7$

$∑Y = 1065$

$∑X = 0$

$∑X^2 = 28$

$∑XY = 465$

$∑Y_t = 1064.7$

 

$a=\frac{∑y}{n}=\frac{1065}{7}=152.14$

and $b=\frac{∑xy}{∑x^2}=\frac{465}{28}=16.6$

Therefore, the required equation of the straight-line trend is given by

$y_t=a+bc⇒y_t=152.1+16.6x$

CUET Questions