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महाराष्ट्र राज्य शिक्षण मंडळएचएससी वाणिज्य (इंग्रजी माध्यम) इयत्ता १२ वी

Find the line of regression of X on Y for the following data: n = 8, ∑(xi-x¯)2=36,∑(yi-y¯)2=44,∑(xi-x¯)(yi-y¯)=24

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प्रश्न

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`

बेरीज
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उत्तर

Given, 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`

∴ `"b"_"XY" = (sum(x_i - bar x)(y_i - bar y))/(sum(y_i - bar y)^2) = 24/44 = 6/11`

Now, the regression equation of X on Y is

`("X" - bar x) = "b"_"XY" ("Y" - bar y)`

i.e., `("X" - bar x) = 6/11 ("Y" - bar y)`

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Properties of Regression Coefficients
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पाठ 3: Linear Regression - Miscellaneous Exercise 3 [पृष्ठ ५४]

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बालभारती Mathematics and Statistics 2 (Commerce) [English] Standard 12 Maharashtra State Board
पाठ 3 Linear Regression
Miscellaneous Exercise 3 | Q 4.08 | पृष्ठ ५४

संबंधित प्रश्‍न

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Variance of X = 9
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8x − 10y + 66 = 0
and 40x − 18y = 214.
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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 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.


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and 3x + 2y − 12 = 0 Find 

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The equations of two regression lines are 10x − 4y = 80 and 10y − 9x = − 40 Find:

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Both the regression coefficients cannot exceed 1


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