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Bring out the inconsistency in the following: bYX + bXY = 1.30 and r = 0.75

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प्रश्न

Bring out the inconsistency in the following:

bYX + bXY = 1.30 and r = 0.75 

योग
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उत्तर

Given, bYX + bXY = 1.30, r = 0.75

Consider, `("b"_"YX" + "b"_"XY")/2 = 1.30/2 = 0.65`

∴ `("b"_"YX" + "b"_"XY")/2 < "r"`

But, for consistent data `|("b"_"YX" + "b"_"XY")/2|` >|r|

∴ 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 5.1 | पृष्ठ ४७

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.
  3. The correlation coefficient between X and Y.

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 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.

What should be the advertisement expenditure if the firm proposes a sales target ₹ 60 crores?


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.


For certain X and Y series, which are correlated the two lines of regression are 10y = 3x + 170 and 5x + 70 = 6y. Find the correlation coefficient between them. Find the mean values of X and Y.


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:

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


Choose the correct alternative:

Both the regression coefficients cannot exceed 1


State whether the following statement is True or False:

If byx = 1.5 and bxy = `1/3` then r = `1/2`, the given data is consistent


State whether the following statement is True or False: 

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


State whether the following statement is True or False: 

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


State whether the following statement is True or False:

Corr(x, x) = 0


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


If u = `(x - "a")/"c"` and v = `(y - "b")/"d"`, then bxy = ______ 


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 = ______


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


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)`


For a certain bivariate data of a group of 10 students, the following information gives the internal marks obtained in English (X) and Hindi (Y):

  X Y
Mean 13 17
Standard Deviation 3 2

If r = 0.6, Estimate x when y = 16 and y when x = 10


Mean of x = 25

Mean of y = 20

`sigma_x` = 4

`sigma_y` = 3

r = 0.5

byx = `square`

bxy = `square`

when x = 10,

`y - square = square (10 - square)`

∴ y = `square`


If byx > 1 then bxy is _______.


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