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प्रश्न
If the regression equations are 8x – 10y + 66 = 0 and 40x – 18y = 214, the mean value of y is ______
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उत्तर
17
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`
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.
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
bYX is ______.
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`
Identify the regression equations of x on y and y on x from the following equations, 2x + 3y = 6 and 5x + 7y − 12 = 0
Regression equation of X on Y is ______
Regression equation of X on Y is_________
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
Choose the correct alternative:
y = 5 – 2.8x and x = 3 – 0.5 y be the regression lines, then the value of byx 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:
If equation of regression lines are 3x + 2y – 26 = 0 and 6x + y – 31= 0, then mean of X is 7
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
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 ______
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)`
XYZ company plans to advertise some vacancies. The Manager is asked to suggest the monthly salary for these vacancies based on the years of experience. To do so, the Manager studies the years of service and the monthly salary drawn by the existing employees in the company.
Following is the data that the Manager refers to:
| Years of service (X) | 11 | 7 | 9 | 5 | 8 | 6 | 10 |
| Monthly salary (in ₹ 1000)(Y) | 10 | 8 | 6 | 5 | 9 | 7 | 11 |
- Find the regression equation of monthly salary on the years of service.
- If a person with 13 years of experience applies for a job in this company, what monthly salary will be suggested by the Manager?
