00:01
Hello students, in this problem given the two regression lines are obtained from y equal to x plus 5 and 16x is equal to 9y minus 94.
00:24
We have to find the variance of x and when the variance of y is 16 and consider this as equation number 1, this as equation number 2.
00:53
Now from equation number 1, we have x minus y plus 5 equal to 0 and this can be written as y equal to x plus 5 and this is regression line of y on x.
01:18
So this implies byx is equal to r sigma y divided by sigma x that is equal to 1 since the coefficient of x is 1.
01:30
So here i am taking 1 and from the equation number 2, we have x is equal to 9 by 16 y minus 94 by 16 and this is regression equation regression line of x on y which implies bxy is equal to r into sigma x divided by sigma y that is 9 by 16 and we know the formula that is the correlation coefficient r square is equal to bxy into byx that is equal to 1 into 9 by 16 that is 9 by 16.
02:24
Hence r square is equal to 9 by 16 which implies r is equal to plus or minus square root of 9 by 16 that is plus or minus 3 by 4 and also here both bxy and byx are positive.
02:47
Therefore, i am taking r equal to positive 3 by 4 that is 0 .75.
02:56
So r is equal to 0 .75...