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Choose the correct alternative: y = 5 – 2.8x and x = 3 – 0.5 y be the regression lines, then the value of byx is - Mathematics and Statistics

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प्रश्न

Choose the correct alternative:

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

विकल्प

  • – 0.5

  • – 2.8

  • 0.5

  • – 2

MCQ
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उत्तर

– 2

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अध्याय 2.3: Linear Regression - Q.1

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संबंधित प्रश्न

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.


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)


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

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

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

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.


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`.


Choose the correct alternative:

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


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


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


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


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)`


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`


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