Time Series - 12 Conversion of Annual Trend Equation to Monthly - Quarterly - Half Yearly

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Converting the annual trend equation to monthly or quarterly or half-yearly
If an annual linear trend is y = a + bx,
(1) The monthly trend with same origin month, x units of one year and y units of average monthly values will be y = a/12 + (b/12)x
(2) The monthly trend having origin in same month, x units of one month and y units of average monthly values will be y = a/12 + (b/12x12)x. So, y = a/12 + (b/144)x
(3) The Quarterly trend with the origin in same month, x units of one quarter and y units of average quarterly values will be
y = a/4 + (b/12x4)x
So, y = a/4 + (b/48)x
(4) The half-yearly trend with the origin in the same month, x units of half year and y units of average half-yearly values will be
y = a/2 + (b/2x12)x
So, y = a/2 + (b/24)x
Time Series, Business Forecasting, Method of Least Squares, Linear Trend, Conversion of Annual Trend Equation to Monthly or Quarterly, Statistics, MBA, MCA, BE, CA, CS, CWA, CMA, CPA, CFA, BBA, BCom, MCom, BTech, MTech, CAIIB, FIII, Graduation,Post Graduation, BSc, MSc, BA, MA, Diploma, Production, Finance, Management, Commerce, Engineering , Grade-11, Grade- 12
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[@subhrajitdasgupta3868]

I was so confused between those two cases! Thanks again sir(2) I got to know about you last year while I was searching about problems of LPP

[@yeeeyeee3449]

They way you teach is awesome.
Thankyou sir ! , For these videos.
Your lectures are really helpful.
Thnkyou much so.

[@reshmi6912]

It helps a lot, thank you so much sir.

[@xxSpartax]

Sir, why the bx is not divided by (4x4) during conversion into quarterly trend. ( As both constants and x units should be divided by 4?) ?

[@PUAARAcademy]

In the converted trend directly the quarterly 'x' is substituted...
Keep watching keep learning... There are playlists on various topics on my channel so don't forget to visit and subscribe my channel and also recommend it to others... There will be more new lectures soon... :)

[@croraf]

Very good explainations on couple of videos of yours that I watched. Here I doubt why for quarterly are not b/(4x4) and half yearly b/(2x2)?

[@amritkumar1950]

You are right same here.

[@SreyasiDey]

If question is
Reduce T = 1560+84t, (origin is at 1998, unit of t is 6 months) for yearly totals to monthly trend eq.
What will be the answer ? Sir, please answer my question.

[@prernachandak2649]

what does Origin = I-II quarter 1986 means in quarterly trend equation