The following data related with the prices of
items in Jabalpur and Narsinghpur are available.
Estimate the price of item in Narsinghpur when
the price in Jabalpur is 15:
Jabalpur Narsinghpur
Mean of the prices
of the item
10
12
Standard Deviation of
the prices of the item 4.2
4.5
The correlation coefficient between the prices
of item in Jabalpur and Narsinghpur = +0.8
Answers
Given : Jabalpur Narsinghpur
Mean of the prices of the item 10 12
SD of the prices of the item 4.2 4.5
To Find : Estimate the price of item in Narsinghpur when the price in Jabalpur is 15
Solution:
x Jabalpur Mean = 10 , SD = 4.2
y Narsinghpur Mean = 12 , SD = 4.5
y = (byx ).x + c
byx = r σy/σx = 0.8 (4.5)/4.2 = 6/7
y - ymean = (byx ) (x - xmean)
y - 12 = (6/7)(x - 10)
=> 7y - 84 = 6x - 60
=> 7y = 6x + 25
=> y = 6x/7 + 24/7
x = 15
=> y = 6(15)/7 + 24/7
=> y = 114/7 = 16.2857
the price of item in Narsinghpur is 16.2857 when the price in Jabalpur is 15
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