Which of the following statements are correct?
(A) In the method of moving averages, a trend value is obtained for every year, including the first and the last year.
(B) In the method of least squares, the sum of the squares of the deviations of the actual values from the trend values is least.
(C) In 4-year moving averages, centring is needed to place the trend values against actual years.
(D) The method of least squares depends on the personal judgement of the person fitting the line.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (B) and (C) only
A moving average uses values on both sides of a year, so the years at the two ends get no trend value. A 4-year average falls between two years and must be centred. The method of least squares is a fixed calculation that makes \(\sum (y - y_t)^2\) least, so it leaves no room for personal bias.
So the end years get no moving average, an even period needs centring, and least squares minimises the sum of squared deviations without personal bias.
Checking the statements
(A) In the method of moving averages, a trend value is obtained for every year, including the first and the last year. — Incorrect. The beginning and ending years get no moving average.
(B) In the method of least squares, the sum of the squares of the deviations of the actual values from the trend values is least. — Correct. This is the principle of least squares.
(C) In 4-year moving averages, centring is needed to place the trend values against actual years. — Correct. Each 4-year average lies between two years until centred.
(D) The method of least squares depends on the personal judgement of the person fitting the line. — Incorrect. It is a fixed calculation and eliminates personal bias.