Advertisements
Advertisements
प्रश्न
If for bivariate data `bar x = 10, bar y = 12,` v(x) = 9, σy = 4 and r = 0.6 estimate y, when x = 5.
उत्तर
Given, `bar x = 10, bar y = 12,` v(x) = 9, σy = 4, r = 0.6
∴ σx = 3
To estimate y, we should first find the regression equation of Y on X.
∴ `"b"_"YX" = "r" sigma_y/sigma_x = 0.6 xx 4/3 = 0.8`
Also, `"a" = bar "y" - "b"_"YX" bar"x"`
= 12 - 0.8(10) = 12 - 8 = 4
The regression equation of Y on X is
Y = a + bYX X
∴ Y = 4 + 0.8 X
For X = 5,
Y = 4 + 0.8 (5) = 4 + 4 = 8
APPEARS IN
संबंधित प्रश्न
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.
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)
For the following bivariate data obtain the equations of two regression lines:
| X | 1 | 2 | 3 | 4 | 5 |
| Y | 5 | 7 | 9 | 11 | 13 |
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
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`.
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.
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:
u = `(x - 20)/5` and v = `(y - 30)/4`, then bxy =
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
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 |
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
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:
For certain bivariate data on 5 pairs of observations given:
∑x = 20, ∑y = 20, ∑x2 = 90, ∑y2 = 90, ∑xy = 76 then bxy = ______.
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`
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?
