Question # 1

The multiplicative time series model is:

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Y = T + S + C + I

TSCI

Y = a + bX

Y = a + bX + cX²

ŷ=a+bx, this line will be called least squares line if it makes=Σ(y-a-bx)2

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maximum

constant

minimum

variable

For a least squares linear trend=ŷ= a + b x,

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Σy <Σŷ

Σŷ = 0

Σy =Σŷ

none of these

In a straight line equation Y = a + bX; a is the:

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X - intercept

Slope

Y- intercept

None of them

For a least squares linear trend Y = a + bx, the Σ(Y - Y)² = 0 when:

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All the Y-values are positive

All the Y-values lie on the line

All the Y-values lie above the line

None of these

Sum of squares of residuals is denoted by

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∑e

∑e²

∑e³

∑e⁴

The secular trend is measured by the method of semi-averages when:

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Time series contains yearly value

Trend is linear

Time series contains odd number of values

None of them

In the measurement of secular trend the moving averages

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give the trend in a straight line

measure the seasonal variations

smoothes out a time series

measure irregular fluctuations

The straight line is fitted to a time series when the movements in the time series are

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linear

quadratic

cubic

constant

The trend values in freehand curve method are obtained by:

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Equation of straight line

Second degree parabola

Signal

Graph

In moving average method, we cannot find the trend values of some:

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Middle periods

End periods

Starting periods

Between extreme periods

Which one is a rough and crude method for measuring secular trend ?

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free hand curve method

semi average method

moving averages method

least square method

The equation of the quadratic (parabolic) trend is

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ŷ=a+bx

ŷ=a+by

ŷ=a+bΣx+cΣx²

ŷ=a+bx+cx²

The rise and fall of a time series periods longer than one- year is called.

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Secular trend

Seasonal variation

Cyclical variation

Irregular variation

Methods of semi-averages gives an

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accurate result

objective result

authentic result

none of these

The basic components of a time series are:

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2

3

4

5

For a least squares linear trend ŷ = a + bx, the Σ(y-ŷ)² = 0 when

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all the y-values lie on the line

all the y-values are positive

all the y-+values lie above the line

none of these

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