English

Choose the correct alternative: u = x-205 and v = y-304, then bxy = - Mathematics and Statistics

Advertisements
Advertisements

Question

Choose the correct alternative:

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

Options

  • `4/5` bvu

  • `4/5` buv

  • `5/4` buv

  • `5/4` buv 

MCQ

Solution

`5/4` buv 

shaalaa.com
  Is there an error in this question or solution?
Chapter 2.3: Linear Regression - Q.1

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

If Σx1 = 56 Σy1 = 56, Σ`x_1^2` = 478,
Σ`y_1^2` = 476, Σx1y1 = 469 and n = 7, Find
(a) the regression equation of y on x.
(b) y, if x = 12.


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`


Information on v:ehicles [in thousands) passing through seven different highways during a day (X) and number of accidents reported (Y) is given as follows :   

`Sigmax_i` = 105, `Sigmay_i` = 409, n = 7, `Sigmax_i^2` = 1681, `Sigmay_i^2` = 39350 `Sigmax_iy_i` = 8075

  Obtain the linear regression of Y on X.


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.


Calculate the Spearman’s rank correlation coefficient for the following data and interpret the result: 

X 35 54 80 95 73 73 35 91 83 81
Y 40 60 75 90 70 75 38 95 75 70

From the data of 20 pairs of observations on X and Y, following results are obtained.

`barx` = 199, `bary` = 94,

`sum(x_i - barx)^2` = 1200, `sum(y_i - bary)^2` = 300,

`sum(x_i - bar x)(y_i - bar y)` = –250

Find:

  1. The line of regression of Y on X.
  2. The line of regression of X on Y.
  3. Correlation coefficient between X and Y.

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.


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.


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`


Regression equation of X on Y 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:

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


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 ______


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

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


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


If n = 5, Σx = Σy = 20, Σx2 = Σy2 = 90, Σxy = 76 Find 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 `(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 ______ 


For certain bivariate data on 5 pairs of observations given:

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


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`


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)`


Out of the two regression lines x + 2y – 5 = 0 and 2x + 3y = 8, find the line of regression of y on x.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×