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

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प्रश्न

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

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उत्तर

6x + y – 31 = 0

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अध्याय 2.3: Linear Regression - Q.3

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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 the equation of the regression line of y on x, if the observations (x, y) are as follows : 
(1,4),(2,8),(3,2),(4,12),(5,10),(6,14),(7,16),(8,6),(9,18)
Also, find the estimated value of y when x = 14.


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


Compute the product moment coefficient of correlation for the following data: 
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`Sigma (x_i - bar x) (y_i - bary) = 8000`


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.


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`


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`.


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

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

Regression equation of X on Y is ______


Regression equation of X on Y is_________


In the regression equation of Y on X, byx represents slope of the line.


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


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


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 ______ 


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:


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


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


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


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