Question

calculate the trend values by the method of least squares from the following data year: 1995-1996 1996-97 1997-98 1998-99 1999-2000 production: 83 92 71 90 169

Answer 1

Step-by-step explanation:

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.

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Answer 2

Answer: 1995- 1996- 97-1997-98-99-1999-2000 is 6291

Step-by-step explanation: