Statistics & Applications

Trends & Data

Medium

applied

Consider the following data

Year (x) 2014 2016 2018 2020 2022 2024
Profit (in Rs. Thousand) (y) 7 9 10 12 14 14

Then for the above data the equation of straight line trend by method of least square is given by:

Year (x)	2014	2016	2018	2020	2022	2024
Profit (in Rs. Thousand) (y)	7	9	10	12	14	14

17y = 13x + 285

13y = 17x + 285

35y = 26(x - 2019) + 385

26y = 35(x - 2019) + 385

✅ Correct Option: 3

The task is to find the equation of a straight line that best fits the given profit data using the method of least squares.

Using a change of variable to simplify calculations with large year values.

Let $u = x - 2019$

Year (x)	u = x - 2019	Profit (y)
2014	-5	7
2016	-3	9
2018	-1	10
2020	1	12
2022	3	14
2024	5	14

Calculate the required sums:

$n = 6$

$\sum u = -5 + (-3) + (-1) + 1 + 3 + 5 = 0$

$\sum y = 7 + 9 + 10 + 12 + 14 + 14 = 66$

$\sum u^2 = 25 + 9 + 1 + 1 + 9 + 25 = 70$

$\sum uy = (-5 \times 7) + (-3 \times 9) + (-1 \times 10) + (1 \times 12) + (3 \times 14) + (5 \times 14)$

$\sum uy = -35 - 27 - 10 + 12 + 42 + 70 = 52$

The equation of the line is $y = a + bu$

Since $\sum u = 0$ :

$b = \dfrac{\sum uy}{\sum u^2}$

$b = \dfrac{52}{70}$

$b = \dfrac{26}{35}$

$a = \dfrac{\sum y}{n}$

$a = \dfrac{66}{6}$

$a = 11$

The equation becomes:

$y = 11 + \dfrac{26}{35}u$

Substituting $u = x - 2019$ :

$y = 11 + \dfrac{26}{35}(x - 2019)$

$35y = 385 + 26(x - 2019)$

$35y = 26(x - 2019) + 385$

Therefore, the equation of straight line trend is $35y = 26(x - 2019) + 385$

2025: 2 June Shift 1

Match List-I with List-II

List-I	List-II
(A) A fire in a factory causing production delay for some time is	(I) Secular trend
(B) Technological progress is	(II) Seasonal trend
(C) The rise in prices before big festival is example of	(III) Irregular trend
(D) Rise and fall of share market is	(IV) Cyclic trend

Choose the correct answer from the options given below:

2025: 15 May Shift 1

Year (t)	2010	2011	2012	2013	2014	2015	2016
Sales (in Rs. crores) (y)	6	8	9	11	13	17	20

In reference to the above data, which of the following statements are correct? (where $x = t - 2013$ )

(A) If the equation of the straight line trend is $y = 12 + 2.29 x$ , then the trend value for the year 2017 is 21.16.

(B) If the equation of the straight line trend is $y = 12 + 2.29 x$ , then the trend value for the year 2013 is 11.

(D) If $(t_1, y_2),(t_2, y_2),(t_3, y_3),......,(t_n, y_n)$ denote the time series and $y_t$ are the trend values of the variable y, then $\sum(y - y_t) = 0$ .

Choose the correct answer from the options given below:

2025: 15 May Shift 2

Year (x)	2011	2012	2013	2014	2015	2016	2017
Sales (in lakh Rs.) (y)	65	68	70	72	75	67	73

If $y = 70 + 0.964(x - 2014)$ be a straight line trend fitted by the method of the least squares to the above data, then the trend value for the year 2015 is:

2025: 3 June Shift 1

Components of Time Series are

(A) Secular Trend Component

(B) Seasonal Component

(D) Cyclical Component

Choose the correct answer from the options given below:

2025: 27 May Shift 1

Match List-I with List-II

List-I	List-II
(Example)	(Components of Time Series)
(A) Lockouts and strikes	(I) Secular trend
(B) Rise and fall of share market	(II) Seasonal trend
(C) Continuous decline in death rate	(III) Irregular trend
(D) The rise in prices before Diwali	(IV) Cyclical trend

Choose the correct answer from the options given below:

2025: 30 May Shift 1

Increase in the number of patients in the hospitals due to heat stroke is:

Consider the following data Year (x)201420162018202020222024Profit (in Rs. Thousand) (y)7910121414 Then for the above data the equation of straight line trend by method of least square is given by:

Solution

Related questions:

Keyboard Shortcuts

CUET Mathematics Past Year Questions (Topic-Wise)

Consider the following data

Year (x) 2014 2016 2018 2020 2022 2024
Profit (in Rs. Thousand) (y) 7 9 10 12 14 14

Then for the above data the equation of straight line trend by method of least square is given by: