Advertisements
Advertisements
प्रश्न
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.
उत्तर
Given equations of regression lines are
x - 4y = 5 …(i)
16y - x = 64
i.e., - x + 16y = 64 …(ii)
Adding (i) and (ii), we get
x - 4y = 5
- x + 16y = 64
12y = 69
∴ y = `69/12 = 5.75`
Substituting y = 5.75 in (i), we get
x - 4(5.75) = 5
∴ x - 23 = 5
∴ x = 5 + 23 = 28
Since the point of intersection of two regression lines is `(bar x, bar y)`,
∴ `bar x = 28 and bar y = 5.75`
Let, x - 4y = 5 be the regression equation of X on Y
∴ The equation becomes X = 4Y + 5
Comparing it with X = bXY Y + a', we get
bXY = 4
Now, the other equation i.e. 16y - x = 64 is regression equation of Y on X
∴ The equation becomes 16Y = X + 64
i.e., Y = `1/16 "X" + 64/16`
Comparing it with Y = bYX X + a, we get
`"b"_"YX" = 1/16`
r = `+-sqrt("b"_"XY" * "b"_"YX")`
`= +- sqrt(4 xx 1/16) = +- sqrt(1/4) = +- 1/2 = +- 0.5`
Since bXY and bYX both are positive,
r is also positive.
∴ r = 0.5
APPEARS IN
संबंधित प्रश्न
For bivariate data. `bar x = 53, bar y = 28, "b"_"YX" = - 1.2, "b"_"XY" = - 0.3` Find Correlation coefficient between X and Y.
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 = 2.6 and bXY = `1/2.6`
Two samples from bivariate populations have 15 observations each. The sample means of X and Y are 25 and 18 respectively. The corresponding sum of squares of deviations from respective means is 136 and 150. The sum of the product of deviations from respective means is 123. Obtain the equation of the line of regression of X on Y.
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.
What should be the advertisement expenditure if the firm proposes a sales target ₹ 60 crores?
In a partially destroyed laboratory record of an analysis of regression data, the following data are legible:
Variance of X = 9
Regression equations:
8x − 10y + 66 = 0
and 40x − 18y = 214.
Find on the basis of above information
- The mean values of X and Y.
- Correlation coefficient between X and Y.
- Standard deviation of Y.
For 50 students of a class, the regression equation of marks in statistics (X) on the marks in accountancy (Y) is 3y − 5x + 180 = 0. The variance of marks in statistics is `(9/16)^"th"` of the variance of marks in accountancy. Find the correlation coefficient between marks in two subjects.
For a bivariate data: `bar x = 53, bar y = 28,` bYX = - 1.5 and bXY = - 0.2. Estimate Y when X = 50.
In a partially destroyed record, the following data are available: variance of X = 25, Regression equation of Y on X is 5y − x = 22 and regression equation of X on Y is 64x − 45y = 22 Find
- Mean values of X and Y
- Standard deviation of Y
- Coefficient of correlation between X and Y.
The two regression equations are 5x − 6y + 90 = 0 and 15x − 8y − 130 = 0. Find `bar x, bar y`, r.
Two lines of regression are 10x + 3y − 62 = 0 and 6x + 5y − 50 = 0. Identify the regression of x on y. Hence find `bar x, bar y` and r.
Find the line of regression of X on Y for the following data:
n = 8, `sum(x_i - bar x)^2 = 36, sum(y_i - bar y)^2 = 44, sum(x_i - bar x)(y_i - bar y) = 24`
If bYX = − 0.6 and bXY = − 0.216, then find correlation coefficient between X and Y. Comment on it.
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:
Cov(x, x) = Variance of x
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
|bxy + byx| ≥ ______
If u = `(x - 20)/5` and v = `(y - 30)/4`, then byx = ______
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`
