The five month moving averages for the following data | Month ($r^{th}$) | 43 | 44 | 45 | 46 | 47 | 48 | 49 | 50 | 51 | |---|---|---|---|---|---|---|---|---|---| | Actual Demand | 105 | 106 | 110 | 110 | 114 | 121 | 130 | 128 | 137 | is:

The pattern of data in the time series is influenced by a large variety of factors. Which of the following are not the components of the time series?

A. Regional component

B. Irregular component

C. Cyclone component

D. Seasonal component

Choose the correct answer from the options given below:

Let $y = 138.86 + 7.64(x - 2021)$ be a straight line of best fit by using least square method to the following data:

Then the trend value for the year 2024 is:

Irregular trends in a time series are caused by

(A) Epidemics

(B) Strikes

(C) Festival season

(D) Floods

Choose the correct answer from the options given below:

For the given 5 values, 15, 18, 21, 27,39; the three year moving averages are:

Which of the following statements are correct?

A. If $x_1,x_2,x_3,\dots,x_n$ is the given annual time series, then 3-yearly moving averages are $\dfrac{x_1+x_2+x_3}{3},\dfrac{x_2+x_3+x_4}{3},\dots\dots$

B. In the method of the least squares, if $(t_1,y_1),(t_2,y_2),\dots(t_n,y_n)$ denote the time series and $y_t$ are trend values of $y$, then $\sum(y-y_t)=0$

C. In the method of the least squares, the sum of squares of the deviations of the values of $y$ from their corresponding trend values is least.

D. The rise in prices before Diwali is an example of a cyclical trend.

Choose the correct answer from the options given below:

For a straight line trend $y_t = a+bx$ for $n$ data by the method of least squares if, $n=8, \sum y=47.8, \sum xy=4.3$ and $\sum x^2=42$, then $y_t$ at $x=-3.5$ is _____.

[where $y_t$ represents trend value of y]