Advertisements
Advertisements
Question
If the two regression lines for a bivariate data are 2x = y + 15 (x on y) and 4y = 3x + 25 (y on x), find
- `bar x`,
- `bar y`,
- bYX
- bXY
- r [Given `sqrt0.375` = 0.61]
Solution
Given,
regression equation of X on Y is 2x = y + 15,
i.e., 2x - y = 15 …(i)
regression equation of Y on X is 4y = 3x + 25,
i.e., - 3x + 4y = 25 …(ii)
By (i) × 4 + (ii) we get
8x - 4y = 60
+ - 3x + 4y = 25
5x = 85
∴ x = 17
Substituting the value of x = 17 in (i), we get
2(17) – y = 15
∴ 34 y = 15
∴ y = 34 – 15 = 19
Since the point of intersection of two regression lines is `(bar x, bar y)`,
(i) `bar x` = 17
(ii) `bar y` = 19
(iii) Regression equation of Y on X is 4y = 3x + 25
i.e., 4Y = 3X + 25
i.e., Y = `3/4 "X" + 25/4`
Comparing it with Y = bYX X + a, we get
`"b"_"YX" = 3/4`
(iv) Regression equation of X on Y is 2x = y + 15
i.e., 2X = Y + 15
i.e., X = `"Y"/2 + 15/2`
Comparing it with X = bXY Y + a' we get,
`"b"_"XY" = 1/2`
(v) r = `+-sqrt("b"_"XY" * "b"_"YX")`
`= +- sqrt((1/2) * (3/4)) = +- sqrt0.375 = +- 0.61`
Since bYX and bXY both are positive,
r is also positive.
∴ r = 0.61
APPEARS IN
RELATED QUESTIONS
For bivariate data. `bar x = 53, bar y = 28, "b"_"YX" = - 1.2, "b"_"XY" = - 0.3` Find estimate of Y for X = 50.
Bring out the inconsistency in the following:
bYX + bXY = 1.30 and r = 0.75
The following data about the sales and advertisement expenditure of a firms is given below (in ₹ Crores)
| Sales | Adv. Exp. | |
| Mean | 40 | 6 |
| S.D. | 10 | 1.5 |
Coefficient of correlation between sales and advertisement expenditure is 0.9.
Estimate the likely sales for a proposed advertisement expenditure of ₹ 10 crores.
For bivariate data, the regression coefficient of Y on X is 0.4 and the regression coefficient of X on Y is 0.9. Find the value of the variance of Y if the variance of X is 9.
The equations of two regression lines are x − 4y = 5 and 16y − x = 64. Find means of X and Y. Also, find correlation coefficient between X and Y.
For certain X and Y series, which are correlated the two lines of regression are 10y = 3x + 170 and 5x + 70 = 6y. Find the correlation coefficient between them. Find the mean values of X and Y.
Choose the correct alternative:
If byx < 0 and bxy < 0, then r is ______
Choose the correct alternative:
Find the value of the covariance between X and Y, if the regression coefficient of Y on X is 3.75 and σx = 2, σy = 8
State whether the following statement is True or False:
If byx = 1.5 and bxy = `1/3` then r = `1/2`, the given data is consistent
The following data is not consistent: byx + bxy =1.3 and r = 0.75
State whether the following statement is True or False:
If u = x – a and v = y – b then bxy = buv
Corr(x, x) = 1
State whether the following statement is True or False:
Regression coefficient of x on y is the slope of regression line of x on y
If n = 5, ∑xy = 76, ∑x2 = ∑y2 = 90, ∑x = 20 = ∑y, the covariance = ______
If u = `(x - "a")/"c"` and v = `(y - "b")/"d"`, then bxy = ______
If u = `(x - 20)/5` and v = `(y - 30)/4`, then byx = ______
The equations of the two lines of regression are 2x + 3y − 6 = 0 and 5x + 7y − 12 = 0. Find the value of the correlation coefficient `("Given" sqrt(0.933) = 0.9667)`
The equations of the two lines of regression are 6x + y − 31 = 0 and 3x + 2y – 26 = 0. Find the value of the correlation coefficient
Mean of x = 53
Mean of y = 28
Regression coefficient of y on x = – 1.2
Regression coefficient of x on y = – 0.3
a. r = `square`
b. When x = 50,
`y - square = square (50 - square)`
∴ y = `square`
c. When y = 25,
`x - square = square (25 - square)`
∴ x = `square`
