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The geometric mean of negative regression coefficients is ______
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Solution
– r
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Mean | 25 | 20 |
S.D. | 4 | 3 |
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Choose the correct alternative:
If b_{yx} < 0 and b_{xy} < 0, then r is ______
Choose the correct alternative:
b_{xy} and b_{yx} are ______
Choose the correct alternative:
If r = 0.5, σ_{x} = 3, σ_{y}^{2} = 16, then b_{xy} = ______
State whether the following statement is True or False:
The following data is not consistent: b_{yx} + b_{xy} =1.3 and r = 0.75
State whether the following statement is True or False:
If u = x – a and v = y – b then b_{xy} = b_{uv}
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 the sign of the correlation coefficient is negative, then the sign of the slope of the respective regression line is ______
Arithmetic mean of positive values of regression coefficients is greater than or equal to ______
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)`
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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 = 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`
x | y | xy | x^{2} | y^{2} |
6 | 9 | 54 | 36 | 81 |
2 | 11 | 22 | 4 | 121 |
10 | 5 | 50 | 100 | 25 |
4 | 8 | 32 | 16 | 64 |
8 | 7 | `square` | 64 | 49 |
Total = 30 | Total = 40 | Total = `square` | Total = 220 | Total = `square` |
b_{xy} = `square/square`
b_{yx} = `square/square`
∴ Regression equation of x on y is `square`
∴ Regression equation of y on x is `square`
b_{xy} . b_{yx} = ______.
For a bivariate data:
`sum(x - overlinex)^2` = 1200, `sum(y - overliney)^2` = 300, `sum(x - overlinex)(y - overliney)` = – 250
Find:
- b_{yx}
- b_{xy}
- Correlation coefficient between x and y.