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

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प्रश्न

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

बेरीज
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उत्तर

Given, bYX = − 0.6, bXY = − 0.216

∴ r = `+-sqrt("b"_"XY" * "b"_"YX")`

`= +- sqrt(- 0.216 * (- 0.6)) = +- sqrt(0.1296)`

∴ r = ± 0.36

Since bXY and bYX are negative,

r is also negative.

∴ r = - 0.36

∴ X and Y negatively correlated.

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Properties of Regression Coefficients
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पाठ 3: Linear Regression - Miscellaneous Exercise 3 [पृष्ठ ५४]

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बालभारती Mathematics and Statistics 2 (Commerce) [English] Standard 12 Maharashtra State Board
पाठ 3 Linear Regression
Miscellaneous Exercise 3 | Q 4.12 | पृष्ठ ५४

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.

Bring out the inconsistency in the following:

bYX = 2.6 and bXY = `1/2.6`


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.


Two samples from bivariate populations have 15 observations each. The sample means of X and Y are 25 and 18 respectively. The corresponding sum of squares of deviations from respective means is 136 and 150. The sum of the product of deviations from respective means is 123. Obtain the equation of the line of regression of X on Y.


An inquiry of 50 families to study the relationship between expenditure on accommodation (₹ x) and expenditure on food and entertainment (₹ y) gave the following results: 

∑ x = 8500, ∑ y = 9600, σX = 60, σY = 20, r = 0.6

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


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.


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


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.

The following results were obtained from records of age (X) and systolic blood pressure (Y) of a group of 10 men.

  X Y
Mean 50 140
Variance 150 165

and `sum (x_i - bar x)(y_i - bar y) = 1120`. Find the prediction of blood pressure of a man of age 40 years.


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:

bxy and byx are ______


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:

Regression coefficient of x on y is the slope of regression line of x on y


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


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)`


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


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`


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`


The following results were obtained from records of age (x) and systolic blood pressure (y) of a group of 10 women.

  x y
Mean 53 142
Variance 130 165

`sum(x_i - barx)(y_i - bary)` = 1170


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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