Advertisements
Advertisements
Choose the correct alternative:
Both the regression coefficients cannot exceed 1
Options
True
False
Advertisements
Solution
True
APPEARS IN
RELATED QUESTIONS
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`
For a certain bivariate data
X  Y  
Mean  25  20 
S.D.  4  3 
And r = 0.5. Estimate y when x = 10 and estimate x when y = 16
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 a bivariate data: `bar x = 53, bar y = 28,` b_{YX} =  1.5 and b_{XY} =  0.2. Estimate Y when X = 50.
If the two regression lines for a bivariate data are 2x = y + 15 (x on y) and 4y = 3x + 25 (y on x), find
 `bar x`,
 `bar y`,
 b_{YX}
 b_{XY}
 r [Given `sqrt0.375` = 0.61]
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 following results were obtained from records of age (X) and systolic blood pressure (Y) of a group of 10 men.
X  Y  
Mean  50  140 
Variance  150  165 
and `sum (x_i  bar x)(y_i  bar y) = 1120`
Find the prediction of blood pressure of a man of age 40 years.
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:
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} = ______
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 the sign of the correlation coefficient is negative, then the sign of the slope of the respective regression line 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?
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 = 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`
b_{xy} . b_{yx} = ______.
If b_{yx} > 1 then b_{xy} is _______.