Let $y_t=a+b(x_i-2021)$ be the straight line trend for the following data by least squares method:

Year($x_i$)	2018	2019	2020	2021	2022	2023	2024
Production in Lakh tonnes($y_i$)	32	34	30	35	38	39	42

the trend value for the year 2025 approximately is:

The number of letters posted in a certain city on each day for a week is given as follows: 40, 55, 28, 25, 31, 52, 43. Which of the following is not an entry in the three-day moving averages?

A fire in a factory delaying production for some time is:

The pattern and behavior of the data in any time series are based on which of the following components:

(A) Secular trend component

(B) Seasonal component

(C) Cyclical component

(D) Irregular component

Choose the correct answer from the options given below:

Based on the data available for the production ($y_i$ in thousand tons) of a cloth factory for 7 years ($x_i$) using the method of least squares, the straight line trend is given by $y - a + bx$ with $\sum y_i = 608, \sum x_i = 0, \sum x_iy_i = 116, \sum x_i^2 = 28$. Then, the increase in production per year is:

Which of the following statement(s) mentioned below do/does not specify the concept of time series analysis:-

A. Time series analysis comprises methods for analysing time series data in order to extract meaningful statistics and other characteristics of the data.

B. Time series analysis provides good forecasts or predictions of further values of the time series.

C. The time series analysis does not derive conclusions after arranging the time series in a systematic manner.

D. The measurement analysis and study of components of time series is called time series analysis.

Choose the correct answer from the options given below:

For the given five values $16, 25, 19, 34, 46$, the three years moving averages are