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Choose the correct alternative:
b_{xy} and b_{yx} are ______
Options
Independent of change of origin and scale
Independent of change of origin but not of scale
Independent of change of scale but not of origin
Affected by change of origin and scale
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Solution
Independent of change of origin but not of scale
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RELATED QUESTIONS
For bivariate data. `bar x = 53, bar y = 28, "b"_"YX" =  1.2, "b"_"XY" =  0.3` Find Correlation coefficient between X and Y.
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.
You are given the following information about advertising expenditure and sales.
Advertisement expenditure (₹ in lakh) (X) 
Sales (₹ in lakh) (Y)  
Arithmetic Mean  10  90 
Standard Mean  3  12 
Correlation coefficient between X and Y is 0.8
 Obtain the two regression equations.
 What is the likely sales when the advertising budget is ₹ 15 lakh?
 What should be the advertising budget if the company wants to attain sales target of ₹ 120 lakh?
Bring out the inconsistency in the following:
b_{YX} + b_{XY} = 1.30 and r = 0.75
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.
The equations of two regression lines are
2x + 3y − 6 = 0
and 3x + 2y − 12 = 0 Find
 Correlation coefficient
 `sigma_"X"/sigma_"Y"`
Two lines of regression are 10x + 3y − 62 = 0 and 6x + 5y − 50 = 0. Identify the regression of x on y. Hence find `bar x, bar y` and r.
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`
If b_{YX} = − 0.6 and b_{XY} = − 0.216, then find correlation coefficient between X and Y. Comment on it.
Choose the correct alternative:
If the regression equation X on Y is 3x + 2y = 26, then b_{xy} equal to
Choose the correct alternative:
b_{yx} + b_{xy} ≥ ______
Choose the correct alternative:
If r = 0.5, σ_{x} = 3, `σ_"y"^2` = 16, then b_{yx} = ______
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
If u = `(x  "a")/"c"` and v = `(y  "b")/"d"`, then b_{xy} = ______
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
Given the following information about the production and demand of a commodity.
Obtain the two regression lines:
ADVERTISEMENT (x) (₹ in lakhs) 
DEMAND (y) (₹ in lakhs) 

Mean  10  90 
Variance  9  144 
Coefficient of correlation between x and y is 0.8.
What should be the advertising budget if the company wants to attain the sales target of ₹ 150 lakhs?
If n = 5, Σx = Σy = 20, Σx^{2} = Σy^{2} = 90 , Σxy = 76 Find Covariance (x,y)
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`
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`
If b_{yx} > 1 then b_{xy} is _______.