Q.State two reasons why the method of least squares is generally preferred over the method of moving averages for measuring the trend of a time series.

Contrast what each method delivers — a formula and full coverage versus gaps and no equation.

Both methods give an objective trend, but least squares has two clear advantages.

(1) It yields a definite equation that can forecast. Least squares produces a single trend line $Y_t = a + bX$. Substituting a future year's $X$ gives a forecast — something moving averages cannot do, because they produce only a smoothed series with no underlying formula.

(2) It covers every year. Least squares gives a trend value for each year of the data, including the first and last. A moving average of period $k$ leaves the first and last few periods blank (e.g. a 3-yearly average has no value for the two end years), losing information at exactly the points where forecasts are most wanted. …

Stating that moving averages are 'always wrong' — they are perfectly valid for smoothing and are objective; the point is only that they cannot f …