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प्रश्न
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 means are 136 and 148 respectively. The sum of product of deviations from respective means is 122. Obtain the regression equation of x on y
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उत्तर
Given, n = 15, `barx` = 25, `bary` = 18,
`sum(x_"i" - barx)^2` = 136, `sum(y_"i" - bary)^2` = 148,
`sum(x_"i" - barx)(y_"i" - bary)` = 122
Now, bxy = `(sum(x_"i" - barx)(y_"i" - bary))/(sum(y_"i" - bary)^2`
= `122/148`
= 0.82
Also, a' = `barx - "b"_(xy) bary`
= 25 – 0.82 × 18
= 25 – 14.76
= 10.24
∴ The regression equation of X on Y is
X = a' + bxyY
∴ X = 10.24 + 0.82Y
संबंधित प्रश्न
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| X | 1 | 2 | 3 | 4 | 1 | 3 | 1 | 2 | 3 | 4 | 2 | 4 |
| Y | 10 | 10 | 18 | 20 | 11 | 15 | 12 | 15 | 17 | 19 | 13 | 16 |
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Regression equation of X on Y is_________
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Choose the correct alternative:
The slope of the line of regression of y on x is called the ______
Choose the correct alternative:
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State whether the following statement is True or False:
y = 5 + 2.8x and x = 3 + 0.5y be the regression lines of y on x and x on y respectively, then byx = – 0.5
State whether the following statement is True or False:
If equation of regression lines are 3x + 2y – 26 = 0 and 6x + y – 31= 0, then mean of X is 7
State whether the following statement is True or False:
bxy is the slope of regression line of y on x
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The equations of the two lines of regression are 2x + 3y − 6 = 0 and 5x + 7y − 12 = 0. Identify the regression lines
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The regression equation of y on x is 8x – 10y + 66 = 0 ......(ii)
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`bary = square`
∴ byx = `square/square`
∴ bxy = `square/square`
∴ r = `square`
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