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There are two series of index numbers : P for price index and S for stock o

There are two series of index numbers : P for price index and S for stock of a commodity.The mean and standard deviation of P are 100 and 8 and of S are 103 and 4 respectively.The correlation coefficient between the two series is 0.4,with these data,obtain the regression lines of P on S and S on P.

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A)

Correlation coefficient (r) = 0.4.

Therefore,       byx = (rσy)/σx = (0.4×4)/8 = 0.2 ,

And                 bxy = (rσx)/σy = (0.4×8)/4 = 0.8 .

Therefore, regression line of P on S is,

(x – Mx) = bxy(y – My)

Or,                                     (x – 100) = 0.8(y – 103)

Or,                                    x – 100 = 0.8y – 82.4

Or,                                   x – 0.8y = 17.6      [Ans.]

And regression line of S on P is

(y – My) = byx(x – Mx)

Or,                                      (y – 103) = 0.2(x – 100)

Or,                                   y – 103 = 0.2x – 20

Or,                                  0.2x – y + 83 = 0  

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