Question

The sales of a company in million of rupees for the years 1994-2001 are given below:

Year: 1994 1995 1996 1997 1998 1999 2000 2001

Sales: 550 560 555 585 540 525 545 585

Fit a trend Line

Estimate the sales for the year 1993.

Answer 1

The regression equation will be y = a + bx

Constants a and b can be obtained by

Σy = ax + bΣx and Σxy = aΣx + bΣx²

At 1994

$4445 = 1994a + 15980b \\ 8878905 = 15980a + 31920092b$

Solving equations:

$a = -1.146 \times 10^{-6} \\ b = 0.278 \\ y = -1.146 \times 10^{-6} + 0.278x$

At 1993

$y = -1.146 \times 10^{-6} + 0.278 \times 1993 \\ ≈ 554$

The sales for the year 1993 is 554 million of rupees.