| Year (t) | 2010 | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | |---|---|---|---|---|---|---|---| | Sales (in Rs. crores) (y) | 6 | 8 | 9 | 11 | 13 | 17 | 20 | 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 $\sum(y - y_t) = 0$. Choose the correct answer from the options given below:
(A), (B) and (D) only
(A) and (D) only
(A), (B) and (C) only
(B), (C) and (D) only

Question

| Year (t) | 2010 | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | |---|---|---|---|---|---|---|---| | Sales (in Rs. crores) (y) | 6 | 8 | 9 | 11 | 13 | 17 | 20 | 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 $\sum(y - y_t) = 0$. Choose the correct answer from the options given below:

(A), (B) and (D) only

(A) and (D) only

(A), (B) and (C) only

(B), (C) and (D) only

Option 1: (A), (B) and (D) only

Option 2: (A) and (D) only

Option 3: (A), (B) and (C) only

Option 4: (B), (C) and (D) only

AfterBoards · Accepted Answer

The answer is '(A) and (D) only'. View full solution:

List-I	List-II
Time Series Component	Example
(A) Secular Variation	(I) Pandemic
(B) Seasonal Variation	(II) Recession in business
(C) Cyclic Variation	(III) Monthly sale of woolen cloths
(D) Irregular variation	(IV) Data regarding National income

List-I	List-II
Example	Time-series component
(A) Labour strike	(I) Secular-trend
(B) Continuous decline in death rate	(II) Seasonal
(C) Rise in prices before Diwali	(III) Cyclical
(D) Rise and fall of the share-market	(IV) Irregular