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
Answers
Answer: 1992:13 1993:16.5 1994:20 1995:23.5 1996:27
Explanation:
The trend values are 13, 16.5, 20, 23.5, 27
Explanation:
Given that,
Years Sales ∑x ∑x^2 ∑xy
1992 12 -2 4 -24
1993 18 -1 1 -18
1994 20 0 0 0
1995 23 1 1 23
1996 27 2 4 54
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N = 5 ∑y = 100 ∑x = 0 ∑x^2 ∑xy = 35
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To find the trend values:
To find the value of a,
∑y = Na + b∑x
by putting the values,
100 = 5a + 0
a = 100/5
∵ a = 20
To find the value of b,
∑xy = a∑x + b∑x^2
35 = 0 + b * 10
35/10 = b
∵ b = 3.5
Therefore, the equation for Yc = 20 + 3.5x
Now the trend values,
Y = a + b * ∑x
= (20 + 3.5) * -2
= 13
Y = (20 + 3.5) * -1
= 16.5
Y = (20 + 3.5) * 0
= 20
Y = (20 + 3.5) * 1
= 23.5
Y = (20 + 3.5) * 2
= 27
Thus, the trend values are 13, 16.5, 20, 23.5, 27.
Learn more: Trend Values
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