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Bring out the inconsistency in the following: bYX = bXY = 1.50 and r = - 0.9

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प्रश्न

Bring out the inconsistency in the following:

bYX = bXY = 1.50 and r = - 0.9 

योग
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उत्तर

Given, bYX = bXY = 1.50 and r = - 0.9 

Here, the coefficient of regressions is positive and the coefficient of correlation is negative.

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

∴ The given data is inconsistent.

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Properties of Regression Coefficients
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 3: Linear Regression - Exercise 3.2 [पृष्ठ ४७]

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बालभारती Mathematics and Statistics 2 (Commerce) [English] Standard 12 Maharashtra State Board
अध्याय 3 Linear Regression
Exercise 3.2 | Q 5.2 | पृष्ठ ४७

संबंधित प्रश्न

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


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.
  3. The correlation coefficient between X and Y.

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


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

Coefficient of correlation between sales and advertisement expenditure is 0.9.

Estimate the likely sales for a proposed advertisement expenditure of ₹ 10 crores.


The equations of two regression lines are
2x + 3y − 6 = 0
and 3x + 2y − 12 = 0 Find 

  1. Correlation coefficient
  2. `sigma_"X"/sigma_"Y"`

For a bivariate data, `bar x = 53`, `bar y = 28`, byx = −1.5 and bxy = −0.2. Estimate y when x = 50.


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`


Choose the correct alternative:

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


Choose the correct alternative:

If the regression equation X on Y is 3x + 2y = 26, then bxy equal to 


Choose the correct alternative:

|byx + bxy| ≥ ______


Choose the correct alternative:

Find the value of the covariance between X and Y, if the regression coefficient of Y on X is 3.75 and σx = 2, σy = 8


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:

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


State whether the following statement is True or False:

Corr(x, x) = 0


State whether the following statement is True or False:

Cov(x, x) = Variance of x


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 ______


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)`


The equations of the two lines of regression are 6x + y − 31 = 0 and 3x + 2y – 26 = 0. Find the value of the correlation coefficient


If n = 5, Σx = Σy = 20, Σx2 = Σy2 = 90 , Σxy = 76 Find Covariance (x,y) 


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`

bxy = `square/square`

byx = `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`


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

∴ byx = `square/square`

∴ byx = `square/square`

∴ r = `square`


x y xy x2 y2
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`

bxy = `square/square`

byx = `square/square`

∴ Regression equation of x on y is `square`

∴ Regression equation of y on x is `square`


|bxy + byz| ≥ ______.


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