Question

calculate the trend values by the method of least squares from the following data year:1992 1993 1994 1995 1996 sales 12 18 20 23 27​

Answer 1

Solution:

There are five years. So, the value of N=5

The sum of sale, that is, sum of Y = 100

Now, x -1994, sum of x = 0, as the values of x for five years are  -2, -1, 0, +1, +2.

Now, sum of xY = 35

The x² values are 4,1,0,1,4 and their sum is 10.

To calculate trend values,

Equation of straight line = Yc = a + b(X -1994)

sum of x =0, therefore,

Value of a = sum of Y/N = 100/5 = 20

Value of b = sum of xY/ sum of x² = 25/10 = 3.5

therefore, the equation of Yc = 20 + 3.5x

When x = 1992, then Yc = 20 + (3.5 * -2) = 13

and calculate the values for 1993, 1994, 1995 and 1996,

The values come out to be 16.5, 20, 23.5, 27.

So, the final answer is 13, 16.5, 20, 23.5, 27.

Answer 2

Answer:

Fit a straight the trend by the method of least squares to

the following data :

Year : 1991 1992 1993 1994 1995 1996

Production (tones) : 24 25 29 26 22 24