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
Fill in the Blanks
Sum

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`

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

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

RELATED QUESTIONS

Bring out the inconsistency in the following:

bYX = 1.9 and bXY = - 0.25


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.


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
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.


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.

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.


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`


Choose the correct alternative:

bxy and byx are ______


Choose the correct alternative:

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


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:

Corr(x, x) = 0


State whether the following statement is True or False:

Cov(x, x) = Variance of x


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


|bxy + byx| ≥ ______


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


The geometric mean of negative regression coefficients is ______


Given the following information about the production and demand of a commodity.

Obtain the two regression lines:

  Production
(X)
Demand
(Y)
Mean 85 90
Variance 25 36

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


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


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`


bxy . byx = ______.


Share
Notifications



      Forgot password?
Use app×