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State whether the following statement is True or False:
If b_{yx} = 1.5 and b_{xy} = `1/3` then r = `1/2`, the given data is consistent
Options
True
False
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Solution
False
RELATED QUESTIONS
From the data of 7 pairs of observations on X and Y, following results are obtained.
∑(x_{i} - 70) = - 35, ∑(y_{i} - 60) = - 7,
∑(x_{i} - 70)^{2} = 2989, ∑(y_{i} - 60)^{2} = 476,
∑(x_{i} - 70)(y_{i} - 60) = 1064
[Given: `sqrt0.7884` = 0.8879]
Obtain
- The line of regression of Y on X.
- The line regression of X on Y.
- The correlation coefficient between X and 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,` b_{YX} = - 1.5 and b_{XY} = - 0.2. Estimate Y when X = 50.
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.
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.
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`
Choose the correct alternative:
If for a bivariate data, b_{YX} = – 1.2 and b_{XY} = – 0.3, then r = ______
Choose the correct alternative:
If b_{yx} < 0 and b_{xy} < 0, then r is ______
Choose the correct alternative:
If r = 0.5, σ_{x} = 3, σ_{y}^{2} = 16, then b_{xy} = ______
Choose the correct alternative:
Both the regression coefficients cannot exceed 1
Corr(x, x) = 1
If the sign of the correlation coefficient is negative, then the sign of the slope of the respective regression line is ______
If u = `(x - 20)/5` and v = `(y - 30)/4`, then b_{yx} = ______
b_{yx} is the ______ of regression line of y on x
The equations of two lines of regression are 3x + 2y – 26 = 0 and 6x + y – 31 = 0. Find variance of x if variance of y is 36
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
If n = 5, Σx = Σy = 20, Σx^{2} = Σy^{2} = 90 , Σxy = 76 Find Covariance (x,y)
For a certain bivariate data of a group of 10 students, the following information gives the internal marks obtained in English (X) and Hindi (Y):
X | Y | |
Mean | 13 | 17 |
Standard Deviation | 3 | 2 |
If r = 0.6, Estimate x when y = 16 and y when x = 10
x | y | `x - barx` | `y - bary` | `(x - barx)(y - bary)` | `(x - barx)^2` | `(y - bary)^2` |
1 | 5 | – 2 | – 4 | 8 | 4 | 16 |
2 | 7 | – 1 | – 2 | `square` | 1 | 4 |
3 | 9 | 0 | 0 | 0 | 0 | 0 |
4 | 11 | 1 | 2 | 2 | 4 | 4 |
5 | 13 | 2 | 4 | 8 | 1 | 16 |
Total = 15 | Total = 45 | Total = 0 | Total = 0 | Total = `square` | Total = 10 | Total = 40 |
Mean of x = `barx = square`
Mean of y = `bary = square`
b_{xy} = `square/square`
b_{yx} = `square/square`
Regression equation of x on y is `(x - barx) = "b"_(xy) (y - bary)`
∴ Regression equation x on y is `square`
Regression equation of y on x is `(y - bary) = "b"_(yx) (x - barx)`
∴ Regression equation of y on x is `square`
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`
Mean of x = 25
Mean of y = 20
`sigma_x` = 4
`sigma_y` = 3
r = 0.5
b_{yx} = `square`
b_{xy} = `square`
when x = 10,
`y - square = square (10 - square)`
∴ y = `square`
The regression equation of y on x is 2x – 5y + 60 = 0
Mean of x = 18
`2 square - 5 bary + 60` = 0
∴ `bary = square`
`sigma_x : sigma_y` = 3 : 2
∴ b_{yx} = `square/square`
∴ b_{yx} = `square/square`
∴ r = `square`