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Given the data for the sales of a product in a state is as follows:

Year20052006200720082009
Sales (In lakh Rs)150130160170200

The equation of the straight-line trend by method of least squares is:

Solution

✅ Correct Option: 4

Take origin at 2007. Then xx values: −2,−1,0,1,2-2, -1, 0, 1, 2, with ∑x=0\sum x = 0, ∑x2=10\sum x^2 = 10.

∑y=810\sum y = 810, mean yˉ=162\bar{y} = 162.

∑xy=−300−130+0+170+400=140\sum xy = -300 - 130 + 0 + 170 + 400 = 140.

Slope b=140/10=14b = 140/10 = 14. Intercept a=162a = 162.

Trend: y=162+14xy = 162 + 14x.

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