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State whether the following statement is True or False:
Regression coefficient of x on y is the slope of regression line of x on y
Options
True
False
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Solution
False
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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
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Arithmetic Mean  10  90 
Standard Mean  3  12 
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Bring out the inconsistency in the following:
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Bring out the inconsistency in the following:
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For a certain bivariate data
X  Y  
Mean  25  20 
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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.
For bivariate data, the regression coefficient of Y on X is 0.4 and the regression coefficient of X on Y is 0.9. Find the value of the variance of Y if the variance of X is 9.
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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.
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4y − 15x + 500 = 0
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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`
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If the regression equation X on Y is 3x + 2y = 26, then b_{xy} equal to
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
State whether the following statement is True or False:
The following data is not consistent: b_{yx} + b_{xy} =1.3 and r = 0.75
If n = 5, ∑xy = 76, ∑x^{2} = ∑y^{2} = 90, ∑x = 20 = ∑y, the covariance = ______
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} = ______
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Given the following information about the production and demand of a commodity.
Obtain the two regression lines:
Production (X) 
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Mean  85  90 
Variance  25  36 
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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
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`
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`
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Mean  53  142 
Variance  130  165 
`sum(x_i  barx)(y_i  bary)` = 1170