CMA Foundation · Fundamentals of Business Mathematics and Statistics · Index Numbers and Time Series
A firm's sales trend is Y = 50 + 4X with origin 2019 (X in years). If the origin is shifted to 2021 with the same unit of X, what is the new equation?
The new equation is Y = 58 + 4X. Shifting the origin from 2019 to 2021 makes the intercept the trend value at X = 2, which is 50 + 8 = 58, while the slope stays 4 because the unit is unchanged.
- AY = 58 + 4XCorrect
- BY = 50 + 4X
- CY = 42 + 4X
- DY = 58 + 8X
Explanation
At the new origin 2021, the old X is 2, so the trend value is 50 + 4×2 = 58. The slope stays 4 because the unit is unchanged. Option 42 subtracts instead of adds, a sign error.
Did you get it right without looking?
One question tells you little. A timed set on Index Numbers and Time Series shows your real accuracy, how long you take and where you lose marks.
More Index Numbers and Time Series questions
- Annual output (in thousand units) of a plant for 5 successive years is 10, 14, 18, 22 and 26. Fitting a straight-line trend by the method of…
- A company's employee earned ₹24,000 per month when the cost of living index was 120. The index has now risen to 180. By how much must the mo…
- Using the ratio-to-trend method, the actual sales of a shop in a quarter were ₹ 66,000 while the trend value for that quarter was ₹ 60,000. …
- For a firm's quarterly sales, the average sales of each quarter over several years are: Quarter I ₹96 lakh, Quarter II ₹104 lakh, Quarter II…
- Which component of a time series is best illustrated by a sharp fall in a company's production caused by an unexpected flood?
- The prices of three items in the base year and the current year are: Rice Rs 40 to Rs 50, Oil Rs 100 to Rs 130, Sugar Rs 20 to Rs 30. Using …