हिंदी

The equations of the two lines of regression are 6x + y − 31 = 0 and 3x + 2y – 26 = 0. Identify the regression lines - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

The equations of the two lines of regression are 6x + y − 31 = 0 and 3x + 2y – 26 = 0. Identify the regression lines

योग
Advertisements

उत्तर

Let 3x + 2y – 26 = 0 be the regression equation of Y on X

∴ The equation becomes 2Y = −3X + 26

i.e., Y = `(-3)/2 "X" + 26/2`

Comparing it with Y = bYX X + a, we get

bYX = `(-3)/2`

Now, the other equation 6x + y − 31 = 0 is the regression equation of X on Y.

∴ The equation becomes 6X = − Y + 31

i.e., X = `(-1)/6 "Y" + 31/6`

Comparing it with X = bXY Y+ a', we get

bxy = `(-1)/6`

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 2.3: Linear Regression - Q.4

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

The equations given of the two regression lines are 2x + 3y - 6 = 0 and 5x + 7y - 12 = 0.

Find:

(a) Correlation coefficient

(b) `sigma_x/sigma_y`


Given that the observations are: (9, -4), (10, -3), (11, -1), (12, 0), (13, 1), (14, 3), (15, 5), (16, 8). Find the two lines of regression and estimate the value of y when x = 13·5.


Find graphical solution for following system of linear inequations :
3x + 2y ≤ 180; x+ 2y ≤ 120, x ≥ 0, y ≥ 0
Hence find co-ordinates of corner points of the common region.


The two lines of regressions are x + 2y – 5 = 0 and 2x + 3y – 8 = 0 and the variance of x is 12. Find the variance of y and the coefficient of correlation.


For the given lines of regression, 3x – 2y = 5 and x – 4y = 7, find:
(a) regression coefficients byx and bxy
(b) coefficient of correlation r (x, y)


Given the following data, obtain a linear regression estimate of X for Y = 10, `bar x = 7.6, bar y = 14.8, sigma_x = 3.2, sigma_y = 16` and r = 0.7


bYX is ______.


The data obtained on X, the length of time in weeks that a promotional project has been in progress at a small business, and Y, the percentage increase in weekly sales over the period just prior to the beginning of the campaign.

X 1 2 3 4 1 3 1 2 3 4 2 4
Y 10 10 18 20 11 15 12 15 17 19 13 16

Find the equation of the regression line to predict the percentage increase in sales if the campaign has been in progress for 1.5 weeks.


If for bivariate data `bar x = 10, bar y = 12,` v(x) = 9, σy = 4 and r = 0.6 estimate y, when x = 5.


The equations of the two lines of regression are 3x + 2y − 26 = 0 and 6x + y − 31 = 0 Find

  1. Means of X and Y
  2. Correlation coefficient between X and Y
  3. Estimate of Y for X = 2
  4. var (X) if var (Y) = 36

Find the equation of the line of regression of Y on X for the following data:

n = 8, `sum(x_i - barx).(y_i - bary) = 120, barx = 20, bary = 36, sigma_x = 2, sigma_y = 3`


Choose the correct alternative:

The slope of the line of regression of y on x is called the ______


Choose the correct alternative:

If the lines of regression of Y on X is y = `x/4` and X on Y is x = `y/9 + 1` then the value of r is


Choose the correct alternative:

y = 5 – 2.8x and x = 3 – 0.5 y be the regression lines, then the value of byx is 


State whether the following statement is True or False:

The equations of two regression lines are 10x – 4y = 80 and 10y – 9x = 40. Then bxy = 0.9


State whether the following statement is True or False:

bxy is the slope of regression line of y on x


Among the given regression lines 6x + y – 31 = 0 and 3x + 2y – 26 = 0, the regression line of x on y is ______


If the regression equations are 8x – 10y + 66 = 0 and 40x – 18y = 214, the mean value of y is ______


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 means are 136 and 148 respectively. The sum of product of deviations from respective means is 122. Obtain the regression equation of x on y


If n = 6, Σx = 36, Σy = 60, Σxy = –67, Σx2 = 50, Σy2 =106, Estimate y when x is 13


The regression equation of x on y is 40x – 18y = 214  ......(i)

The regression equation of y on x is 8x – 10y + 66 = 0  ......(ii)

Solving equations (i) and (ii),

`barx = square`

`bary = square`

∴ byx = `square/square`

∴ bxy = `square/square`

∴ r = `square`

Given variance of x = 9

∴ byx = `square/square`

∴ `sigma_y = square`


If `bar"X"` = 40, `bar"Y"` = 6, σx = 10, σy = 1.5 and r = 0.9 for the two sets of data X and Y, then the regression line of X on Y will be:


For certain bivariate data on 5 pairs of observations given:

∑x = 20, ∑y = 20, ∑x2 = 90, ∑y2 = 90, ∑xy = 76 then bxy = ______.


Complete the following activity to find, the equation of line of regression of Y on X and X on Y for the following data:

Given:`n=8,sum(x_i-barx)^2=36,sum(y_i-bary)^2=40,sum(x_i-barx)(y_i-bary)=24`

Solution:

Given:`n=8,sum(x_i-barx)=36,sum(y_i-bary)^2=40,sum(x_i-barx)(y_i-bary)=24`

∴ `b_(yx)=(sum(x_i-barx)(y_i-bary))/(sum(x_i-barx)^2)=square`

∴ `b_(xy)=(sum(x_i-barx)(y_i-bary))/(sum(y_i-bary)^2)=square`

∴ regression equation of Y on :

`y-bary=b_(yx)(x-barx)` `y-bary=square(x-barx)`

`x-barx=b_(xy)(y-bary)`  `x-barx=square(y-bary)`


For a bivariate data `barx = 10`, `bary = 12`, V(X) = 9, σy = 4 and r = 0.6
Estimate y when x = 5

Solution: Line of regression of Y on X is

`"Y" - bary = square ("X" - barx)`

∴ Y − 12 = `r.(σ_y)/(σ_x)("X" - 10)`

∴ Y − 12 = `0.6 xx 4/square ("X" - 10)`

∴ When x = 5

Y − 12 = `square(5 - 10)`

∴ Y − 12 = −4

∴ Y = `square`


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×