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Do My Statistics Assignment
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Do My Statistics Homework | Do My Statistics Assignment
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Do My Statistics Homework Illustrations and Solutions
Illustration 1.
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 par4abol,a into a
monthly one we have:
Yc =
𝑎
12
+
𝑏𝑋
12 ×12
+
𝑐𝑋 2
12 ×12 ×12
Substituting the respective values in the above we get,
Yc =
60
12
+
3.6𝑋
144
+
2.4𝑋2
1728
,

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= 5 + 0.025X + 0.0014 X2
Where, X unit = 1 month, and Y unit = monthly value.
Illustration 2.
Convert the following annual trend equation into a quarterly one:
Ye = 31 + 4.8 X
Solution
By the formula of conversion of an annual trend into a quarterly one we have,
Yc =
𝑎
4
+
𝑏𝑋
4 ×12
Substitution the respective values in the above we get,
Yc =
32
4
+
4.8 𝑋
48
= 8 + 0.1X
Where, X unit = 1 quarter and Y unit = quarterly value of a variable.
Illustration 3.
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.
Solution
Here, Y unit = annual production, and X unit is 6 months. And Y unit = annual production.
Convert the 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

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= 20 – 0.025X
Where, X unit = 1 month, and Y unit = monthly production.
Illustration 4.
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 Rs.)
Solution
Here, the origin of the equation is 15th Jan’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.

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Hence, K = 5.5
By the formula of shifting a trend we have,
Yc = a + b (X + K)
= 50 + 0.5 (X +5.5)
= 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)
Substitution the respective values in the above we get,
Yc = 52.75 × 12 + 0.5 × (144)
= 633 + 72X
Where, the point of origin = 2004, X unit = 1 Year and unit = annual sales (in ’000 Rs.)
Illustration 5.
The equation for yearly sales (in ’000 Rs.) for a commodity with the year, 2003 as origin is
Yc = 91.6 + 28.8X. Determine the trend equation to give the monthly trend values with Jan
’04 as the origin, and calculate the trend value for March ’04.

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Solution
Here, the problem involves both conversion of the trend equation form annual to monthly
basis, and shifting of the trend origin from 1st July 03 to 15tyh Jan ’03 to 15th Jan ’04.
Since, the conversion is required to be made from a higher periodical base (annual) to a
lower periodical base (monthly), it is necessary to attempt on the conversion first, and then
on shifting of end origin as follows:
(ii) Conversion of the trend
By the formula of conversion of an annual trend into a monthly one we have,
Yc =
𝑎
12
+
𝑏𝑋
12 ×12
Substituting the respective values, in the above we get,
Yc =
91.6
12
+
28.8 𝑋
12 ×𝑋
= 7.63 + 0.2 X
Thus, Yc = 7.63 + 0.2 y
When X unit = 1 month, and Y unit = monthly sales
(ii) Shifting of the Trend Origin
Here, it is required to shift forward the trend origin by 6.5 months i.e. from 1st July, 03 (the
midpoint of the year, 03) to the 15th Jan, 04 (the midpoint of the month).
Thus, K = 5.5
By the formula of shifting a trend we have,
Yc = a + b (X + K)
Substituting the respective values in the above we get,
Yc = 7.63 + 0.2 (X + 6.5)
= 7.63 + 0.2X + 1.3
= 8.93 + 0.2 Y
Thus, Yc = 8.93 + 0.2 X
Where, the point of origin is Jan ’03, X unit = 1 month, and Y unit monthly sales.
(ii) Calculation of the trend value for March ’04
The time deviation of March ’04 from the trend origin Jan ’04, or X = 2
Thus, when X = 2, Yc = 8.93 + 0.2 (2)
= 8.93 + 0.4 = 9.33

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Hence, the trend value for March ’04 will be 9.33.
Illustration 6.
Convert the annual trend equation Yc = 48 + 1.2 X into monthly trend equation, and shift
the origin from 2003 to Jan 1, 2004.
Solution
Here, conversion is to be made first as it is required to be made from a higher period
(annual) to a lower period (monthly) basis.
(i) Conversion of the trend equation
By the formula of conversion of an annual trend to a monthly one we have,
Yc =
𝑎
12
+
𝑏𝑋
12 ×12

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