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Arithmetic mean of positive values of regression coefficients is greater than or equal to ______
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Solution
r
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RELATED QUESTIONS
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.
Two samples from bivariate populations have 15 observations each. The sample means of X and Y are 25 and 18 respectively. The corresponding sum of squares of deviations from respective means is 136 and 150. The sum of the product of deviations from respective means is 123. Obtain the equation of the line of regression of X on Y.
The equations of two regression lines are
2x + 3y − 6 = 0
and 3x + 2y − 12 = 0 Find
 Correlation coefficient
 `sigma_"X"/sigma_"Y"`
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.
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:
If b_{yx} < 0 and b_{xy} < 0, then r is ______
Choose the correct alternative:
Find the value of the covariance between X and Y, if the regression coefficient of Y on X is 3.75 and σ_{x} = 2, σ_{y} = 8
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_{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_{yx} = 1.5 and b_{xy} = `1/3` then r = `1/2`, the given data is consistent
Corr(x, x) = 1
If n = 5, ∑xy = 76, ∑x^{2} = ∑y^{2} = 90, ∑x = 20 = ∑y, the covariance = ______
If u = `(x  "a")/"c"` and v = `(y  "b")/"d"`, then b_{xy} = ______
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 ______
If u = `(x  20)/5` and v = `(y  30)/4`, then b_{yx} = ______
The geometric mean of negative regression coefficients is ______
b_{yx} is the ______ of regression line of y on x
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.
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 = 25
Mean of y = 20
`sigma_x` = 4
`sigma_y` = 3
r = 0.5
b_{yx} = `square`
b_{xy} = `square`
when x = 10,
`y  square = square (10  square)`
∴ y = `square`
The regression equation of y on x is 2x – 5y + 60 = 0
Mean of x = 18
`2 square  5 bary + 60` = 0
∴ `bary = square`
`sigma_x : sigma_y` = 3 : 2
∴ b_{yx} = `square/square`
∴ b_{yx} = `square/square`
∴ r = `square`
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`