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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 (Given0.933=0.9667)

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प्रश्न

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)`

योग
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उत्तर

r = `+-  sqrt("b"_(xy) * "b"_(yx))`

= `+-  sqrt((-7)/5 xx (-2)/3)`

= `+-  sqrt(0.933)`

= 0.9667

Since the values of bXY and bYX are negative,

r is also negative.

∴ r = – 0.9667

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Properties of Regression Coefficients
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अध्याय 2.3: Linear Regression - Q.4

संबंधित प्रश्न

For bivariate data. `bar x = 53`, `bar y = 28`, byx = −1.2, bxy = −0.3. Find the correlation coefficient between x and y.


From the data of 7 pairs of observations on X and Y, following results are obtained.

∑(xi - 70) = - 35,  ∑(yi - 60) = - 7,

∑(xi - 70)2 = 2989,    ∑(yi - 60)2 = 476, 

∑(xi - 70)(yi - 60) = 1064

[Given: `sqrt0.7884` = 0.8879]

Obtain

  1. The line of regression of Y on X.
  2. The line regression of X on Y.
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Bring out the inconsistency in the following:

bYX + bXY = 1.30 and r = 0.75 


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Estimate the expenditure on food and entertainment when expenditure on accommodation is Rs 200.


The following data about the sales and advertisement expenditure of a firms is given below (in ₹ Crores)

  Sales Adv. Exp.
Mean 40 6
S.D. 10 1.5

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The equations of two regression lines are x − 4y = 5 and 16y − x = 64. Find means of X and Y. Also, find correlation coefficient between X and Y.


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4y − 15x + 500 = 0
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Find the mean height and weight of the group. Also, estimate the weight of a girl whose height is 70 inches.


Choose the correct alternative:

If for a bivariate data, bYX = – 1.2 and bXY = – 0.3, then r = ______


Choose the correct alternative:

|byx + bxy| ≥ ______


Choose the correct alternative:

bxy and byx are ______


Choose the correct alternative:

If r = 0.5, σx = 3, σy2 = 16, then bxy = ______


State whether the following statement is True or False: 

If bxy < 0 and byx < 0 then ‘r’ is > 0


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The following data is not consistent: byx + bxy =1.3 and r = 0.75


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


Corr(x, x) = 1


If n = 5, ∑xy = 76, ∑x2 = ∑y2 = 90, ∑x = 20 = ∑y, the covariance = ______


|bxy + byx| ≥ ______


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 ______


If u = `(x - 20)/5` and v = `(y - 30)/4`, then byx = ______


The geometric mean of negative regression coefficients is ______


byx is the ______ of regression line of y on x


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`2 square -  5 bary + 60` = 0

∴ `bary = square`

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∴ byx = `square/square`

∴ byx = `square/square`

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x y xy x2 y2
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2 11 22 4 121
10 5 50 100 25
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8 7 `square` 64 49
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byx = `square/square`

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