If $y = 38.85 + 7.64(x - 2020)$ is the equation of the straight line trend for the following data:

Year $(x)$	2017	2018	2019	2020	2021	2022	2023
Profit (Rs. '000) $(y)$	14	30	26	44	38	56	64

The trend value for the year 2021 by least square method is:

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:

If 18, Q, 19.2, T, 19.8 are the 5-year moving averages of the following series of observations:

16, P, 20, 18, R, 17, 19, S, 20, then

Match List-I with List-II

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In reference to the above data, which of the following statements are correct? (where $x = t - 2013$)

(A) If the equation of the straight line trend is $y = 12 + 2.29 x$, then the trend value for the year 2017 is 21.16.

(B) If the equation of the straight line trend is $y = 12 + 2.29 x$, then the trend value for the year 2013 is 11.

(C) If the equation of the straight line trend is $y = 12 + 2.29 x$, then the trend value for the year 2015 is 17.

(D) If $(t_1, y_2),(t_2, y_2),(t_3, y_3),......,(t_n, y_n)$ denote the time series and $y_t$ are the trend values of the variable y, then $\sum(y - y_t) = 0$.

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Match List-I with List-II

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Which of the following are examples of irregular trends in a time series?

(A) Decrease in production due to a sudden strike.

(B) The rise in prices before festivals

(C) Unusual rise in income of the printing press due to the announcement of an election.

(D) Fall in crop yield due to floods.

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For the given five values 18, 25, 20, 36, 49, the three years moving averages are