हिंदी

State whether the following statement is True or False: If u = x – a and v = y – b then bxy = buv

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प्रश्न

State whether the following statement is True or False: 

If u = x – a and v = y – b then bxy = buv 

विकल्प

  • True

  • False

MCQ
सत्य या असत्य
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उत्तर

True

shaalaa.com
Properties of Regression Coefficients
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 2.3: Linear Regression - Q.2

संबंधित प्रश्न

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

  1. Obtain the two regression equations.
  2. What is the likely sales when the advertising budget is ₹ 15 lakh?
  3. What should be the advertising budget if the company wants to attain sales target of ₹ 120 lakh?

Bring out the inconsistency in the following:

bYX = bXY = 1.50 and r = - 0.9 


Given the following information about the production and demand of a commodity obtain the two regression lines:

  X Y
Mean 85 90
S.D. 5 6

The coefficient of correlation between X and Y is 0.6. Also estimate the production when demand is 100.


An inquiry of 50 families to study the relationship between expenditure on accommodation (₹ x) and expenditure on food and entertainment (₹ y) gave the following results: 

∑ x = 8500, ∑ y = 9600, σX = 60, σY = 20, r = 0.6

Estimate the expenditure on food and entertainment when expenditure on accommodation is Rs 200.


From the two regression equations, find r, `bar x and bar y`. 4y = 9x + 15 and 25x = 4y + 17


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.


If the two regression lines for a bivariate data are 2x = y + 15 (x on y) and 4y = 3x + 25 (y on x), find

  1. `bar x`,
  2. `bar y`,
  3. bYX
  4. bXY
  5. r [Given `sqrt0.375` = 0.61]

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.


Regression equations of two series are 2x − y − 15 = 0 and 3x − 4y + 25 = 0. Find `bar x, bar y` and regression coefficients. Also find coefficients of correlation. [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`


If bYX = − 0.6 and bXY = − 0.216, then find correlation coefficient between X and Y. Comment on it.


Choose the correct alternative:

If for a bivariate data, bYX = – 1.2 and bXY = – 0.3, then r = ______


Choose the correct alternative:

|byx + bxy| ≥ ______


Choose the correct alternative:

bxy and byx are ______


Choose the correct alternative:

If r = 0.5, σx = 3, `σ_"y"^2` = 16, then byx = ______


Choose the correct alternative:

Both the regression coefficients cannot exceed 1


State whether the following statement is True or False:

Cov(x, x) = Variance of x


If u = `(x - "a")/"c"` and v = `(y - "b")/"d"`, then bxy = ______ 


The value of product moment correlation coefficient between x and x is ______


If u = `(x - 20)/5` and v = `(y - 30)/4`, then byx = ______


byx is the ______ of regression line of y on x


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


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


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`

bxy = `square/square`

byx = `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

∴ byx = `square/square`

∴ byx = `square/square`

∴ r = `square`


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