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प्रश्न
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
पर्याय
`1/6`
0
`- 1/4`
`- 1/6`
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उत्तर
`1/6`
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.
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 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
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.
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:
- The line of regression of Y on X.
- The line of regression of X on Y.
- 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.
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`
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 ______
Regression equation of X on Y is_________
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:
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:
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
If the regression equations are 8x – 10y + 66 = 0 and 40x – 18y = 214, the mean value of y is ______
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 |
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
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`
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)`
