Advertisements
Advertisements
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
APPEARS IN
RELATED QUESTIONS
Bring out the inconsistency in the following:
b_{YX} = 1.9 and b_{XY} =  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
 Correlation coefficient
 `sigma_"X"/sigma_"Y"`
For a bivariate data: `bar x = 53, bar y = 28,` b_{YX} =  1.5 and b_{XY} =  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
 Mean values of X and Y
 Standard deviation of Y
 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:
b_{xy} and b_{yx} are ______
Choose the correct alternative:
If r = 0.5, σ_{x} = 3, σ_{y}^{2} = 16, then b_{xy} = ______
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 b_{xy} = b_{uv}
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, ∑x^{2} = ∑y^{2} = 90, ∑x = 20 = ∑y, the covariance = ______
b_{xy} + b_{yx} ≥ ______
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  x^{2}  y^{2} 
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` 
b_{xy} = `square/square`
b_{yx} = `square/square`
∴ Regression equation of x on y is `square`
∴ Regression equation of y on x is `square`
b_{xy} . b_{yx} = ______.