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

Bring out the inconsistency in the following: bYX = 1.9 and bXY = - 0.25 - Mathematics and Statistics

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प्रश्न

Bring out the inconsistency in the following:

bYX = 1.9 and bXY = - 0.25

बेरीज

उत्तर

Given, bYX = 1.9 and bXY = - 0.25

Here, bYX and bXY have different signs.

But, for consistent data, they must have the same signs.

∴ The given data is inconsistent.

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Properties of Regression Coefficients
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 3: Linear Regression - Exercise 3.2 [पृष्ठ ४७]

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संबंधित प्रश्‍न

For bivariate data. `bar x = 53, bar y = 28, "b"_"YX" = - 1.2, "b"_"XY" = - 0.3` Find estimate of Y for X = 50.


For bivariate data. `bar x = 53, bar y = 28, "b"_"YX" = - 1.2, "b"_"XY" = - 0.3` Find estimate of X for Y = 25.


For a certain bivariate data

  X Y
Mean 25 20
S.D. 4 3

And r = 0.5. Estimate y when x = 10 and estimate x when y = 16


From the two regression equations, find r, `bar x and bar y`. 4y = 9x + 15 and 25x = 4y + 17


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

  1. The mean values of X and Y.
  2. Correlation coefficient between X and Y.
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The equations of two regression lines are
2x + 3y − 6 = 0
and 3x + 2y − 12 = 0 Find 

  1. Correlation coefficient
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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`


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

  1. `bar x and bar y`
  2. bYX and bXY
  3. If var (Y) = 36, obtain var (X)
  4. r

Choose the correct alternative:

bxy and byx are ______


Choose the correct alternative:

If r = 0.5, σx = 3, `σ_"y"^2` = 16, then byx = ______


State whether the following statement is True or False: 

If u = x – a and v = y – b then bxy = buv 


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Regression coefficient of x on y is the slope of regression line of x on y


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byx 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


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`sigma_y` = 3

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∴ byx = `square/square`

∴ byx = `square/square`

∴ r = `square`


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