Advertisements
Advertisements
If n = 5, Σx = Σy = 20, Σx^{2} = Σy^{2} = 90 , Σxy = 76 Find Covariance (x,y)
Advertisements
Solution
Given, Σx = 20, Σy = 20, Σx^{2} = 90, Σy^{2} = 90, Σxy = 76, n = 5
Now,
`barx = (sumx)/"n" = 20/5` = 4
`bary = (sumy)/"n" = 20/5` = 4
cov(X, Y) = `1/"n" sumxy  bar(x) bar(y)`
= `1/5 xx 76  4 xx 4`
= 15.2 – 16
= – 0.8
APPEARS IN
RELATED QUESTIONS
Bring out the inconsistency in the following:
b_{YX} = 2.6 and b_{XY} = `1/2.6`
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"`
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.
The two regression equations are 5x − 6y + 90 = 0 and 15x − 8y − 130 = 0. Find `bar x, bar y`, r.
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.
The equations of two regression lines are 10x − 4y = 80 and 10y − 9x = − 40 Find:
 `bar x and bar y`
 `"b"_"YX" and "b"_"XY"`
 If var (Y) = 36, obtain var (X)
 r
Choose the correct alternative:
If b_{yx} < 0 and b_{xy} < 0, then r is ______
Choose the correct alternative:
b_{yx} + b_{xy} ≥ ______
Choose the correct alternative:
b_{xy} and b_{yx} are ______
State whether the following statement is True or False:
If b_{xy} < 0 and b_{yx} < 0 then ‘r’ is > 0
If n = 5, ∑xy = 76, ∑x^{2} = ∑y^{2} = 90, ∑x = 20 = ∑y, the covariance = ______
b_{xy} + b_{yx} ≥ ______
If u = `(x  20)/5` and v = `(y  30)/4`, then b_{yx} = ______
The geometric mean of negative regression coefficients 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)`
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.
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
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
b_{xy} . b_{yx} = ______.
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:
 b_{yx}
 b_{xy}
 Correlation coefficient between x and y.