Two lines of regression are given by 5x+7y-22=0 and 6x+2y-22=0if the variance of y is 15 find the standard deviation of x
Answers
Answer:
6x +2y-22=0 is the line of xon y
if the variance of y is 15 then variance of x is given as follows
(2/6)^2 *15 = 4/36*15 =1.66666
and sd is 1.29099
Answer:
The standard deviation of is .
Step-by-step explanation:
Consider the equations of lines of regression as follows:
. . . . . (1)
. . . . . (2)
Rewrite equation (1) as follows:
⇒
⇒
⇒
⇒ . . . . . (3) (Regression equation of on )
Then, the regression equation of on is
,
where = correlation coefficient and = variance of and respectively.
⇒ . . . . . (4)
Rewrite equation (2) as follows:
⇒
⇒
⇒
⇒ . . . . . (5) (Regression equation of on )
Then, the regression equation of on is
,
⇒ . . . . . (6)
Multiply (4) and (6), we get
⇒
⇒
⇒ (As both are negative so will also be negative)
From (4),
⇒ (Since and )
⇒
⇒
As we know,
The Standard deviation of =
S.D =
= 4.5
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