हिंदी

If the two regression lines for a bivariate data are 2x = y + 15 (x on y) and 4y = 3x + 25 (y on x), find x¯, y¯, bYX bXY r [Given 0.375 = 0.61]

Advertisements
Advertisements

प्रश्न

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]
योग
Advertisements

उत्तर

Given,

regression equation of X on Y is 2x = y + 15,

i.e., 2x - y = 15           …(i)

regression equation of Y on X is 4y = 3x + 25,

i.e., - 3x + 4y = 25       …(ii)

By (i) ×  4 + (ii) we get

    8x - 4y = 60
+ - 3x + 4y = 25 
   5x    = 85

∴ x = 17

Substituting the value of x = 17 in (i), we get

2(17) – y = 15

∴ 34  y = 15

∴ y = 34 – 15 = 19

Since the point of intersection of two regression lines is `(bar x, bar y)`,

(i) `bar x` = 17

(ii) `bar y` = 19

(iii) Regression equation of Y on X is 4y = 3x + 25

i.e., 4Y = 3X + 25

i.e., Y = `3/4 "X" + 25/4`

Comparing it with Y = bYX X + a, we get

`"b"_"YX" = 3/4`

(iv) Regression equation of X on Y is 2x = y + 15

i.e., 2X = Y + 15

i.e., X = `"Y"/2 + 15/2`

Comparing it with X = bXY Y + a' we get,

`"b"_"XY" = 1/2`

(v) r = `+-sqrt("b"_"XY" * "b"_"YX")`

`= +- sqrt((1/2) * (3/4)) = +- sqrt0.375 = +- 0.61`

Since bYX and bXY both are positive,

r is also positive.

∴ r = 0.61

shaalaa.com
Properties of Regression Coefficients
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 3: Linear Regression - Exercise 3.3 [पृष्ठ ५०]

APPEARS IN

बालभारती Mathematics and Statistics 2 (Commerce) [English] Standard 12 Maharashtra State Board
अध्याय 3 Linear Regression
Exercise 3.3 | Q 9 | पृष्ठ ५०

संबंधित प्रश्न

For bivariate data. `bar x = 53, bar y = 28, "b"_"YX" = - 1.2, "b"_"XY" = - 0.3` Find estimate of Y for X = 50.


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 = bXY = 1.50 and r = - 0.9 


Bring out the inconsistency in the following:

bYX = 1.9 and bXY = - 0.25


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.


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 50 students of a class, the regression equation of marks in statistics (X) on the marks in accountancy (Y) is 3y − 5x + 180 = 0.  The variance of marks in statistics is `(9/16)^"th"` of the variance of marks in accountancy. Find the correlation coefficient between marks in two subjects.


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.


The two regression equations are 5x − 6y + 90 = 0 and 15x − 8y − 130 = 0. Find `bar x, bar y`, r.


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.


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.


The equations of two regression lines are 10x − 4y = 80 and 10y − 9x = − 40 Find:

  1. `bar x and bar y`
  2. bYX and bXY
  3. If var (Y) = 36, obtain var (X)
  4. r

Choose the correct alternative:

If r = 0.5, σx = 3, `σ_"y"^2` = 16, then byx = ______


Choose the correct alternative:

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


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


|bxy + byx| ≥ ______


If the sign of the correlation coefficient is negative, then the sign of the slope of the respective regression line is ______


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


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`


bXY . bYX = ______.


|bxy + byz| ≥ ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×