Let x and y be the year and production
From the normal equation na + bΣx + cΣx2
= Σy; 5a + b.0 + c. 10 = 115
5a + 10c = 115 … (1) From: aΣx + bΣx2 + cΣx3 = Σxy
a.0 + b. 10 + c.0 = -25; b = -2.5 and From: aΣx2 + bΣx3 + cΣx4 = Σx2y ;
a. 10 + b.0 + c.34 = 237; 10a + 34c = 237 … (2)
from(1) and (2) 5a + 10c =115 × 2
0 – 14c = -7;
∴ c = 0.5; Put c = 0.5 in (1)
5a + 10(0.5)= 115; a = 22
The fitted parabolic trend equation is:-
y = a + bx + cx2 ; y =22 – 2.5x + 0.5x2
