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Business Statistics Homework Help Service
Alex Gerg

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Business Statistics Homework Help Service
About Business Statistics: Business statistics is a science
that deals with the process of taking good decisions under
the condition of uncertainty. It is used in many business
fields such as banking, finance, stock market, econometrics,
production process, quality control, and marketing research.
It is a well-known fact that business environment is always
more complex as it deals with money and direct/indirect
communication with people. This makes the process of
decision-making more difficult in any type of Business Statistics Homework Help
Service. Due to this reason, the businessman or the decision-maker do not have confidence
on his decision that was taken simply based on his observation and own experience in his
business.
Business Statistics Homework Illustrations and Solutions
Illustration 1.
The trend equation for a time series is fitted as Yc = 60 + 1.5X
Shift the trend origin from 2004 to 1998, given that the time unit is 1 year.
Solution:
Here, the trend origin is to be shifted back by 5 years i.e. from 2004 to 1999.
Thus K = -5
By the formula of trend shifting we have, Yc = a + b (X – K)
= 60 + 1.5 (X – 5)
= 60 + 1.5X – 7.5
= 52.5 + 1.5X, where the origin of X = 1999.

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Illustration 2.
Shift the trend origin from 2002 to 2004 in the following trend equation:
Yc = 20.3 + 0.4X + 0.5𝑋2
Given that the time unit = 1 Year.
Solution:
Here, the trend origin is to be shifted forward by 2 years i.e. from 2002 to 2004. Hence, k =
2. By the formula of trend shifting we have, Yc = a +b (X + K) + c (X + K )2
(∵ it is a parabolic equation of second degree)
Substituting the respective values in the above, we get Yc = 20.3 + 0.4 (X + 2) + 0.5 (X +
2)2
= 20.3 + 0.4X + 0.8 + 0.5 (𝑋2
+ 4X + 4)
= 20.3 + 0.4X + 0.8 + 0.5𝑋2
+ 2X + 2
= Yc = 23.1 + 2.4X + 0.5𝑋2

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In the above equation, it must be seen that the values of both a and b have been changed,
whereas the value of c has remained unchanged This is because, it was the case of shifting
a parabolic equation of second degree.
Illustration 3.
The parabolic trend equation for the sales (’000 $) of a company is given below :
Yc = 20.4 – 1.5X + 0.6𝑋2
Shift the trend origin from 1999 to 2004 given that the time unit is 1 Year.
Solution:
Here, the trend origin is to be shifted forward by 5 years i.e. from 1999 to 2004. Hence, k =
5
By the formula of shifting a trend we have,
Yc = a –b (X + K) + c(X + K)2
(∵ it is a parabolic equation of the given order.)

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Substituting the respective values in the above we have,
Yc = 20.4 – 1.5 X +5) + 0.6 (X + 5)2
= 20.4 – 1.5X – 7.5 + 0.6 (𝑋2
+ 10X + 25)
= 20.4 – 1.5X – 7.5 + 0.6𝑋2
+ 6X + 15
= 27.9 + 4.5X + 0.6𝑋2
Hence, the shifted trend equation is Yc = 27.9 + 4.5X + 0.6𝑋2
given that the trend origin is
shifted to 2004.
Illustration 4
Shift the trend origin from 2003 to 1st Jan ’04 in the linear equation,
Yc = 14.5 + 0.4X, given that unit of time = 1 Year.
Solution:
Here, the origin 2003 means 1st July ’03 (the middle part of the year).
Hence, the origin is to be shifted forward by only
1
2
year i.e. from 1st July ’03 to 1st
Jan ’04.
Thus ,k = ½
By the formula of shifting a trend we have,
Yc = a + b (X + k)
Substituting the given values we have,

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Yc = 14.5 + 0.4 (X + ½)
= 14.5 + 0.4X + 0.2
= 14.7 + 0.4X
Hence Yc = 14.7 + 0.4X
Where the trend origin is shifted to 1st Jan ’04.
Conversion of a Trend Equation.
By conversion of a trend equation, we mean the change of a trend equation formulated on
one type of time basis into a trend equation on another type of time basis. Thus, if a trend
equation of yearly period, is transformed into a trend equation of monthly or quarterly
period, or vice versa, it will be called conversion of a trend equation.
Method of Conversion.
The following methods are to be adopted for converting a given trend equation into a
required trend equation :
(i) To convert an annual trend equation into a monthly trend equation : Divide a
by 12, bX, by 12 × (or 144), c𝑋2
, by 12 × 12 × 12 (or 1728) and so on.
(ii) To convert a monthly trend equation into an annual trend equation. Multiply a
by 12, bX by 12 × 12 (or 144), c𝑋2
by 12 × 12 × 12 (or 1728) and so on.
(iii) To convert an annual trend equation into a Quarterly trend equation : Divide a
by 4, bX by 4 × 12 (or 48), c𝑋2
,by 4 × 12 × 12 × 12 (or 576) and so on.
(iv) To convert a quarterly trend equation into an annual trend equation : Multiply
a by 4, bX by 4 × 12 and c𝑋2
by 4 ×12 × 12 and so on.
Notes: 1. Under (i) above, the constant a is divided by 12 because the trend value of the
origin would now relate to a month instead of a year. The factor bX is divided by 12 × 12
because the slope of the change i.e. b and the time deviation i.e. X would now relate to a
month instead of a year.
2. Under (iii) above, the constant a is divided by 4, so that it may relate to a quarters and
the factor bX is divided by 4 × 12, so that the slope of change i.e. b may relate to a
quarters, and the time deviation i.e. X may relate to a month.
3. The problem of conversion of a trend may be clubbed with a problem of shifting the trend
origin as well. In such cases, the shifting is to be made first, and then the conversion, if it is
desired to convert a trend equation from a lower periodical base to a higher periodical base
viz: from monthly to annual equation. In the reverse case, the conversion is to be made
first, and then the shifting.

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