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Sample of Statistics Assignment Help Illustrations and Solutions:

Illustration: 1 Convert the following annual trend equation into a monthly one:

Yc = 24 + 1.8X

Given X unit = 1 Year, and Y unit = annual production.

Solution:

By the formula of conversion of an annual trend to a monthly one we have :

Yc = 𝒂

𝟏𝟐 +

𝒃𝑿

𝟏𝟐 ×𝟏𝟐

Substituting the respective values in the above we get,

Yc = 𝟐𝟒

𝟏𝟐 +

𝟏.𝟖𝑿

𝟏𝟒𝟒

Or Yc = 2 + 0.0125X

Where, X unit = 1 month and Y unit = monthly prodn.

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Illustration: 2 Convert the following monthly trend equation into the annual one :

Yc = 2 + 0.0125X

Where, X unit = 1 month, and Y unit = monthly sales

Solution:

By the formula of conversion of a monthly trend into an annual one we have,

Yc = a × 12 + bX (12 × 12)


Yc = 2 × 12 × 0.0125 × 144 or

Yc = 24 + 1.8X

Where, X unit = 1 Year, and Y unit = annual sales.

Note. The above answer may be compared with the respective values of the annual

equation given in the illustration 1.

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Illustration: 3 Convert the following annual trend equation into a monthly order:

Yc = 60 + 3.6X + 2.4𝑋2

Solution:

By the formula of conversion of an annual equation of second degree parabola into a

monthly one we have :

Yc = 𝒂

𝟏𝟐 +

𝒃𝑿

𝟏𝟐 ×𝟏𝟐 +

𝒄𝑿𝟐

𝟏𝟐 ×𝟏𝟐 ×𝟏𝟐


Yc = 𝟔𝟎

𝟏𝟐 +

𝟑.𝟔𝑿

𝟏𝟒𝟒 +

𝟐.𝟒𝑿𝟐

𝟏𝟕𝟐𝟖 ,

= 5 + 0.025X + 0.0014 𝑋2

Where, X unit = 1 month, and Y unit = monthly value.

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Illustration: 4 Convert the following annual trend equation into a quarterly one:

Yc = 32 + 4.8X

Solution:

By the formula of conversion of an annual trend into a quarterly, one we have,

Yc = 𝒂

𝟒 +

𝒃𝑿

𝟒 ×𝟏𝟐


Yc = 𝟑𝟐

𝟒 +

𝟒.𝟖𝑿

𝟒𝟖

= 8 + 0.1 X

Where, X unit = 1 quarter, and Y unit = quarterly value of a variable.

Illustration: 5

Given the trend equation, Yc = 240 – 1.8X, where X unit = 6 months, and Y unit =

annual production. Convert the equation into a monthly trend.

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Solution:

Here, Y unit = annual production, and X unit is 6 months, So to convert the given

equation into a monthly trend, we have to divide a by 12, but bX by 12 × 6. Thus the

required equation will be :

Yc = 𝒂

𝟏𝟐 -

𝒃𝑿

𝟏𝟐 ×𝟔

= 20 – 0.025X

Where, X unit = 1 month, and Y unit = monthly production.

Illustration: 6

Convert the following trend equation into an annual basis:

Yc = 50 + 0.5X

Where, the point of origin is Jan 2004, X unit = one month and Y unit = monthly sales

(in ’000 $)

Solution:

Here, the origin of the equation is 15th ’04 (i.e. the midpoint of January) which needs to

be shifted first to the 1st July ’04 (i.e. the midpoint of the yr. ’04) by 5.5 months

forward.

Hence, K = 5.5

By the formula of shifting a trend we have,

Yc = a + b (X + K)

= 50 + 0.5 (X + 5.5)

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= 50 + 0.5X + 2.75

= 52.75 + 0.5X

Now, by the formula of conversion of a monthly equation into an annual trend we have,

Yc = a × 12 × bX (12 × 12)


Yc = 52.75 × 12 + 0.5 × (144)

= 633 + 72X

Where, the point of origin = 2004, X unit = 1 year and Y unit = annual sales (in ’000 $).

Note. The above problems required both shifting of the trend origin, and conversion of

the trend equation. Since, the conversion was to be made from a lower time basis (i.e.

monthly) to a higher time basis (i.e. annual) shifting, was made first and the conversion

at the last.

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