Question

64. In the method of Least Square if the summation of Y is 1856 and N is 9, then a in a time
series is
O A. 201.8
O B. 204.5
O C. 206.22.
D. 209

Answer 1

Answer:

The sum of the deviations of the actual values of Y and the computed values of Y is zero.

The sum of the squares of the deviations of the actual values and the computed values is least.

This method gives the line which is the line of best fit. This method is applicable to give results either to fit a straight line trend or a parabolic trend.

The method of least squares as studied in time series analysis is used to find the trend line of best fit to a time series data.

Secular Trend Line

The secular trend line (Y) is defined by the following equation:

Y = a + b X

Where, Y = predicted value of the dependent variable

a = Y-axis intercept i.e. the height of the line above origin (when X = 0, Y = a)

b = slope of the line (the rate of change in Y for a given change in X)

When b is positive the slope is upwards, when b is negative, the slope is downwards

X = independent variable (in this case it is time)

To estimate the constants a and b, the following two equations have to be solved simultaneously:

ΣY = na + b ΣX

ΣXY = aΣX + bΣX2

 To simplify the calculations, if the midpoint of the time series is taken as origin, then the negative values in the first half of the series balance out the positive values in the second half so that ΣX = 0. In this case, the above two normal equations will be as follows:

ΣY = na

ΣXY = bΣX2

Step-by-step explanation:

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