हिंदी

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

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

Identify the regression equations of X on Y and Y on X from the following equations :
2x + 3y = 6 and 5x + 7y – 12 = 0 


Find the feasible solution for the following system of linear inequations:
0 ≤ x ≤ 3, 0 ≤ y ≤ 3, x + y ≤ 5, 2x + y ≥ 4


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.


Compute the product moment coefficient of correlation for the following data: 
n = 100, `bar x` = 62, `bary` = 53, `sigma_x` = 10, `sigma_y` = 12

`Sigma (x_i - bar x) (y_i - bary) = 8000`


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)


For the following bivariate data obtain the equations of two regression lines:

X 1 2 3 4 5
Y 5 7 9 11 13

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


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.


The equation of the line of regression of y on x is y = `2/9` x and x on y is x = `"y"/2 + 7/6`.
Find (i) r,  (ii) `sigma_"y"^2 if sigma_"x"^2 = 4`


Identify the regression equations of x on y and y on x from the following equations, 2x + 3y = 6 and 5x + 7y − 12 = 0


If for a bivariate data byx = – 1.2 and bxy = – 0.3 then find r.


From the two regression equations y = 4x – 5 and 3x = 2y + 5, find `bar x and bar y`.


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:

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


State whether the following statement is True or False:

y = 5 + 2.8x and x = 3 + 0.5y be the regression lines of y on x and x on y respectively, then byx = – 0.5


State whether the following statement is True or False:

If equation of regression lines are 3x + 2y – 26 = 0 and 6x + y – 31= 0, then mean of X is 7


State whether the following statement is True or False:

bxy is the slope of regression line of y on x


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


The age in years of 7 young couples is given below. Calculate husband’s age when wife’s age is 38 years.

Husband (x) 21 25 26 24 22 30 20
Wife (y) 19 20 24 20 22 24 18

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


If `(x - 1)/l = (y - 2)/m = (z + 1)/n` is the equation of the line through (1, 2, -1) and (-1, 0, 1), then (l, m, n) is ______ 


The management of a large furniture store would like to determine sales (in thousands of ₹) (X) on a given day on the basis of number of people (Y) that visited the store on that day. The necessary records were kept, and a random sample of ten days was selected for the study. The summary results were as follows:

`sumx_i = 370 , sumy_i = 580, sumx_i^2 = 17200 , sumy_i^2 = 41640, sumx_iy_i = 11500, n = 10`


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×