English

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 = □ b. When x = 50, y-□=□(50-□) ∴ y = □ c. When y = 25, x-□=□(25-□) ∴ x = □ - Mathematics and Statistics

Advertisements
Advertisements

Question

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`

Fill in the Blanks
Sum
Advertisements

Solution

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 = `+- sqrt("b"_(xy)*"b"_(yx))`

= `+- sqrt((-0.3)(-1.2))`

= `+-  0.6`

Since bYX and bXY both are – negative,

r is also negative.

∴ r = – 0.6

b.  When x = 50,

`(y - bary) = "b"_(yx)  (x- barx)`

∴ `(y - 28) = - 1.2 (50 - 53)`

∴ y = 28 – 60 + 63.6

∴ y = 31.6

c. When y = 25,

`(x - 53) = - 0.3 (25 - 28)`

∴ X = 53 – 7.5 + 8.4

∴ X = 53.9

shaalaa.com
Properties of Regression Coefficients
  Is there an error in this question or solution?
Chapter 2.3: Linear Regression - Q.5

RELATED QUESTIONS

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 = 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.


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.


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?


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"`

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.


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]

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


Choose the correct alternative:

If byx < 0 and bxy < 0, then r is ______


Choose the correct alternative:

bxy and byx are ______


Choose the correct alternative:

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


State whether the following statement is True or False: 

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


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 = ______


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)`


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


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 _______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×