Skip to main contentSkip to solution

If for the following data:

Year (xix_i)2010201120122013201420152016
Sales (in ₹ crores) (yiy_i)68911131720

If the equation of the straight line trend is y=a+b(xi−2013)y=a+b(x_i-2013), then the trend value for the year 2018 is

Solution

✅ Correct Option: 3

Taking X=xi−2013X = x_i-2013 gives ∑X=0\sum X = 0, so a=∑y7=847=12a = \frac{\sum y}{7} = \frac{84}{7} = 12 and b=∑Xy∑X2=6428=167b = \frac{\sum Xy}{\sum X^2} = \frac{64}{28} = \frac{16}{7}.

For 2018, X=5X=5: y=12+5×167≈23.43y = 12+5\times\frac{16}{7} \approx 23.43.

Note: The computed trend value is about 23.43, while the nearest option reads 23.45; we have taken that option as intended.

Keyboard Shortcuts

  • Left arrow: Previous question
  • Right arrow: Next question
  • S key: Jump to solution
  • Q key: Jump to question