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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

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प्रश्न

Bring out the inconsistency in the following:

bYX = 1.9 and bXY = - 0.25

बेरीज
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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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बालभारती Mathematics and Statistics 2 (Commerce) [English] Standard 12 Maharashtra State Board
पाठ 3 Linear Regression
Exercise 3.2 | Q 5.3 | 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.

You are given the following information about advertising expenditure and sales.

  Advertisement expenditure
(₹ in lakh) (X)
Sales (₹ in lakh) (Y)
Arithmetic Mean 10 90
Standard Mean 3 12

Correlation coefficient between X and Y is 0.8

  1. Obtain the two regression equations.
  2. What is the likely sales when the advertising budget is ₹ 15 lakh?
  3. What should be the advertising budget if the company wants to attain sales target of ₹ 120 lakh?

Bring out the inconsistency in the following:

bYX = bXY = 1.50 and r = - 0.9 


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.


In a partially destroyed record, the following data are available: variance of X = 25, Regression equation of Y on X is 5y − x = 22 and regression equation of X on Y is 64x − 45y = 22 Find

  1. Mean values of X and Y
  2. Standard deviation of Y
  3. Coefficient of correlation between X and Y.

If the two regression lines for a bivariate data are 2x = y + 15 (x on y) and 4y = 3x + 25 (y on x), find

  1. `bar x`,
  2. `bar y`,
  3. bYX
  4. bXY
  5. r [Given `sqrt0.375` = 0.61]

Two lines of regression are 10x + 3y − 62 = 0 and 6x + 5y − 50 = 0. Identify the regression of x on y. Hence find `bar x, bar y` and r.


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.


Regression equations of two series are 2x − y − 15 = 0 and 3x − 4y + 25 = 0. Find `bar x, bar y` and regression coefficients. Also find coefficients of correlation. [Given `sqrt0.375` = 0.61]


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.


Choose the correct alternative:

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


Choose the correct alternative:

Both the regression coefficients cannot exceed 1


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:

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


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 ______


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


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`


Mean of x = 53

Mean of y = 28

Regression coefficient of y on x = – 1.2

Regression coefficient of x on y = – 0.3

a. r = `square`

b. When x = 50,

`y - square = square (50 - square)`

∴ y = `square`

c. When y = 25,

`x - square = square (25 - square)`

∴ x = `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`


For a bivariate data:

`sum(x - overlinex)^2` = 1200, `sum(y - overliney)^2` = 300, `sum(x - overlinex)(y - overliney)` = – 250

Find: 

  1. byx
  2. bxy
  3. Correlation coefficient between x and y.

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