Question

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

Answer 1

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.