Measurement of Secular Trend

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Mathematical Logic
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Management Mathematics
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- Assignment Problem
- Sequencing in Management Mathematics

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Method of Freehand Curve ( Graphical Method)
Method of Moving Averages
Method of Least Squares

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Related QuestionsVIEW ALL [18]

The simplest method of measuring trend of time series is ______

The method of measuring trend of time series using only averages is ______

State whether the following statement is True or False:

The secular trend component of time series represents irregular variations

State whether the following statement is True or False:

Least squares method of finding trend is very simple and does not involve any calculations

Following table shows the all India infant mortality rates (per ‘000) for years 1980 to 2010

Year	1980	1985	1990	1995
IMR	10	7	5	4
Year	2000	2005	2010
IMR	3	1	0

Fit a trend line by the method of least squares

Solution: Let us fit equation of trend line for above data.

Let the equation of trend line be y = a + bx .....(i)

Here n = 7(odd), middle year is `square` and h = 5

Year	IMR (y)	x	x²	x.y
1980	10	– 3	9	– 30
1985	7	– 2	4	– 14
1990	5	– 1	1	– 5
1995	4	0	0	0
2000	3	1	1	3
2005	1	2	4	2
2010	0	3	9	0
Total	30	0	28	– 44

The normal equations are

Σy = na + bΣx

As, Σx = 0, a = `square`

Also, Σxy = aΣx + bΣx²

As, Σx = 0, b =`square`

∴ The equation of trend line is y = `square`

Fit equation of trend line for the data given below.

Year	Production (y)	x	x²	xy
2006	19	– 9	81	– 171
2007	20	– 7	49	– 140
2008	14	– 5	25	– 70
2009	16	– 3	9	– 48
2010	17	– 1	1	– 17
2011	16	1	1	16
2012	18	3	9	54
2013	17	5	25	85
2014	21	7	49	147
2015	19	9	81	171
Total	177	0	330	27

Let the equation of trend line be y = a + bx .....(i)

Here n = `square` (even), two middle years are `square` and 2011, and h = `square`

The normal equations are Σy = na + bΣx

As Σx = 0, a = `square`

Also, Σxy = aΣx + bΣx²

As Σx = 0, b = `square`

Substitute values of a and b in equation (i) the equation of trend line is `square`

To find trend value for the year 2016, put x = `square` in the above equation.

y = `square`

Obtain the trend values for the following data using 5 yearly moving averages:

Year	2000	2001	2002	2003	2004
Production x_i	10	15	20	25	30
Year	2005	2006	2007	2008	2009
Production x_i	35	40	45	50	55

Following table shows the amount of sugar production (in lakh tonnes) for the years 1931 to 1941:

Year	Production	Year	Production
1931	1	1937	8
1932	0	1938	6
1933	1	1939	5
1934	2	1940	1
1935	3	1941	4
1936	2

Complete the following activity to fit a trend line by method of least squares:

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Measurement of Secular Trend

Topics

Mathematical Logic

Mathematical Logic

Matrices

Differentiation

Applications of Derivatives

Integration

Definite Integration

Applications of Definite Integration

Differential Equation and Applications

Matrices

Commission, Brokerage and Discount

Insurance and Annuity

Linear Regression

Time Series

Index Numbers

Linear Programming

Assignment Problem and Sequencing

Probability Distributions

Continuity

Differentiation

Applications of Derivative

Indefinite Integration

Definite Integrals

Ratio, Proportion and Partnership

Commission, Brokerage and Discount

Insurance and Annuity

Demography

Bivariate Data and Correlation

Regression Analysis Introduction

Random Variable and Probability Distribution

Management Mathematics

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Related QuestionsVIEW ALL [18]

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