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For bivariate data. x¯=53,y¯=28,bYX=-1.2,bXY=-0.3 Find estimate of X for Y = 25. - Mathematics and Statistics

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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.

बेरीज
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उत्तर

Here, `bar x = 53, bar y = 28, "b"_"YX" = - 1.2, "b"_"XY" = - 0.3`

The regression equation of X on Y is

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

∴ (X - 53) = (- 0.3)(Y - 28)

∴ X - 53 = - 0.3 Y + 8.4

∴ X = - 0.3 Y + 8.4 + 53

∴ X = - 0.3 Y + 61.4

For Y = 25

∴ X = - 0.3(25) + 61.4 = - 7.5 + 61.4 = 53.9

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Properties of Regression Coefficients
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पाठ 3: Linear Regression - Exercise 3.2 [पृष्ठ ४७]

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बालभारती Mathematics and Statistics 2 (Commerce) [English] Standard 12 Maharashtra State Board
पाठ 3 Linear Regression
Exercise 3.2 | Q 1.3 | पृष्ठ ४७

संबंधित प्रश्‍न

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


Given the following information about the production and demand of a commodity obtain the two regression lines:

  X Y
Mean 85 90
S.D. 5 6

The coefficient of correlation between X and Y is 0.6. Also estimate the production when demand is 100.


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?


For certain bivariate data the following information is available.

  X Y
Mean 13 17
S.D. 3 2

Correlation coefficient between x and y is 0.6. estimate x when y = 15 and estimate y when x = 10.


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.
  3. Standard deviation of Y.

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.


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"`

The two regression lines between height (X) in inches and weight (Y) in kgs of girls are,
4y − 15x + 500 = 0
and 20x − 3y − 900 = 0
Find the mean height and weight of the group. Also, estimate the weight of a girl whose height is 70 inches.


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`


If bYX = − 0.6 and bXY = − 0.216, then find correlation coefficient between X and Y. Comment on it.


Choose the correct alternative:

|byx + bxy| ≥ ______


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


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


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


Corr(x, x) = 1


State whether the following statement is True or False:

Cov(x, x) = Variance of x


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


The value of product moment correlation coefficient between x and x is ______


Arithmetic mean of positive values of regression coefficients is greater than or equal to ______


The geometric mean of negative regression coefficients is ______


byx is the ______ of regression line of y on x


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)`


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


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`


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