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Choose the correct alternative:
b_{yx} + b_{xy} ≥ ______
Options
r
2r
r
– r
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Solution
2r
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RELATED QUESTIONS
For bivariate data. `bar x = 53, bar y = 28, "b"_"YX" =  1.2, "b"_"XY" =  0.3` Find estimate of Y for X = 50.
For bivariate data. `bar x = 53, bar y = 28, "b"_"YX" =  1.2, "b"_"XY" =  0.3` Find estimate of X for Y = 25.
From the data of 7 pairs of observations on X and Y, following results are obtained.
∑(x_{i}  70) =  35, ∑(y_{i}  60) =  7,
∑(x_{i}  70)^{2} = 2989, ∑(y_{i}  60)^{2} = 476,
∑(x_{i}  70)(y_{i}  60) = 1064
[Given: `sqrt0.7884` = 0.8879]
Obtain
 The line of regression of Y on X.
 The line regression of X on Y.
 The correlation coefficient between X and Y.
Bring out the inconsistency in the following:
b_{YX} = 1.9 and b_{XY} =  0.25
Bring out the inconsistency in the following:
b_{YX} = 2.6 and b_{XY} = `1/2.6`
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?
From the two regression equations, find r, `bar x and bar y`. 4y = 9x + 15 and 25x = 4y + 17
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
 The mean values of X and Y.
 Correlation coefficient between X and Y.
 Standard deviation of Y.
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 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`
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 for a bivariate data, b_{YX} = – 1.2 and b_{XY} = – 0.3, then r = ______
Choose the correct alternative:
If the regression equation X on Y is 3x + 2y = 26, then b_{xy} equal to
Choose the correct alternative:
If r = 0.5, σ_{x} = 3, `σ_"y"^2` = 16, then b_{yx} = ______
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 b_{xy} < 0 and b_{yx} < 0 then ‘r’ is > 0
State whether the following statement is True or False:
Corr(x, x) = 0
b_{xy} + b_{yx} ≥ ______
If the sign of the correlation coefficient is negative, then the sign of the slope of the respective regression line is ______
The value of product moment correlation coefficient between x and x 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
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
If n = 5, Σx = Σy = 20, Σx^{2} = Σy^{2} = 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
x  y  `x  barx`  `y  bary`  `(x  barx)(y  bary)`  `(x  barx)^2`  `(y  bary)^2` 
1  5  – 2  – 4  8  4  16 
2  7  – 1  – 2  `square`  1  4 
3  9  0  0  0  0  0 
4  11  1  2  2  4  4 
5  13  2  4  8  1  16 
Total = 15  Total = 45  Total = 0  Total = 0  Total = `square`  Total = 10  Total = 40 
Mean of x = `barx = square`
Mean of y = `bary = square`
b_{xy} = `square/square`
b_{yx} = `square/square`
Regression equation of x on y is `(x  barx) = "b"_(xy) (y  bary)`
∴ Regression equation x on y is `square`
Regression equation of y on x is `(y  bary) = "b"_(yx) (x  barx)`
∴ Regression equation of y on x is `square`
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`