Statistics & Applications

Trends & Data

Medium

applied

Data available for profit (₹ Thousands) of a company as

Year 2004 2005 2006 2007 2008 2009 2010
Profit(₹ 000) 114 130 126 144 138 156 164

Based on the above data using least square method the trend value for the year '2007' is

Year	2004	2005	2006	2007	2008	2009	2010
Profit(₹ 000)	114	130	126	144	138	156	164

147.64

138.86

130.57

131.22

✅ Correct Option: 2

For the least squares method, coded values (X) are assigned to years, centered around the middle year (2007 = 0):

Year	X	Y (Profit in ₹ 000)
2004	-3	114
2005	-2	130
2006	-1	126
2007	0	144
2008	1	138
2009	2	156
2010	3	164

Centering at 0 makes calculations easier because $\Sigma X = 0$ .

Calculate the required sums:

Year	X	Y	XY	X²
2004	-3	114	-342	9
2005	-2	130	-260	4
2006	-1	126	-126	1
2007	0	144	0	0
2008	1	138	138	1
2009	2	156	312	4
2010	3	164	492	9
Total	0	972	214	28

The trend equation is $Y = a + bX$

Since $\Sigma X = 0$ :

$b = \dfrac{\Sigma XY}{\Sigma X^2}$

$b = \dfrac{214}{28}$

$b = 7.643$

Since $\Sigma X = 0$ :

$a = \dfrac{\Sigma Y}{n}$

$a = \dfrac{972}{7}$

$a = 138.857$

Trend Equation: $Y = 138.857 + 7.643X$

For year 2007, $X = 0$ :

$Y = 138.857 + 7.643(0)$

$Y = 138.857$

$Y \approx 138.86$

The trend value for the year 2007 is 138.86 (₹ Thousands).

The actual profit in 2007 was 144, but the trend value is 138.86, representing the smoothed pattern based on the overall data.

2025: 15 May Shift 2

The pattern and behavior of the data in any time series are based on which of the following components:

(A) Secular trend component

(B) Seasonal component

(D) Irregular component

Choose the correct answer from the options given below:

2025: 19 May Shift 1

For the given five values, 15, 24, 18, 33, 42, the three-year moving averages are

2026: 22 May Shift 2

For the given five values 15, 24, 18, 33, 45, which of the following is not the three years moving average?

2025: 30 May Shift 1

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

2025: 21 May Shift 1

If for the following data:

Year (x)	2000	2001	2002	2003	2004	2005	2006
Production(in tonnes) (y)	40	45	46	42	47	50	46

the equation of the straight line trend is $y = 45.143 + 1.036(x - 2003)$ , then the trend value for the year 2004 is

2026: 18 May Shift 2

The pattern of data in the time series is influenced by a large variety of factors. Which of the following are not the components of the time series?

A. Regional component

B. Irregular component

C. Cyclone component

D. Seasonal component

Choose the correct answer from the options given below:

Data available for profit (₹ Thousands) of a company as Year2004200520062007200820092010Profit(₹ 000)114130126144138156164 Based on the above data using least square method the trend value for the year '2007' is

Solution

Related questions:

Keyboard Shortcuts

CUET Mathematics Past Year Questions (Topic-Wise)

Data available for profit (₹ Thousands) of a company as

Year 2004 2005 2006 2007 2008 2009 2010
Profit(₹ 000) 114 130 126 144 138 156 164

Based on the above data using least square method the trend value for the year '2007' is