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State whether the following statement is True or False:
Cov(x, x) = Variance of x
Options
True
False
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Solution
True
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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.
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
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 What is the likely sales when the advertising budget is ₹ 15 lakh?
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2x + 3y − 6 = 0
and 3x + 2y − 12 = 0 Find
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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.
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 b_{yx} < 0 and b_{xy} < 0, then r is ______
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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
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b_{xy} and b_{yx} are ______
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If r = 0.5, σ_{x} = 3, `σ_"y"^2` = 16, then b_{yx} = ______
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If r = 0.5, σ_{x} = 3, σ_{y}^{2} = 16, then b_{xy} = ______
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
State whether the following statement is True or False:
If u = x – a and v = y – b then b_{xy} = b_{uv}
Corr(x, x) = 1
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
b_{xy} + b_{yx} ≥ ______
If u = `(x  "a")/"c"` and v = `(y  "b")/"d"`, then b_{xy} = ______
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If u = `(x  20)/5` and v = `(y  30)/4`, then b_{yx} = ______
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:
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?
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.
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
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`
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`
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`
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.