Advertisements
Advertisements
प्रश्न
The equations of the two lines of regression are 3x + 2y − 26 = 0 and 6x + y − 31 = 0 Find
- Means of X and Y
- Correlation coefficient between X and Y
- Estimate of Y for X = 2
- var (X) if var (Y) = 36
Advertisements
उत्तर
(i) Given equations of regression are
3x + 2y - 26 = 0
i.e., 3x + 2y = 26 ….(i)
and 6x + y - 31 = 0
i.e., 6x + y = 31 ….(ii)
By (i) - 2 × (ii), we get
3x + 2y = 26
12x + 2y = 62
- - -
- 9x = - 36
∴ x = `(-36)/-9 = 4`
Substituting x = 4 in (ii), we get
6 × 4 + y = 31
∴ 24 + y = 31
∴ y = 31 - 24
∴ y = 7
Since the point of intersection of two regression lines is `(bar x, bar y)`,
`bar x` = mean of X = 4, and
`bar y` = mean of Y = 7
(ii) Let 3x + 2y 26 = 0 be the regression equation of Y on X.
∴ The equation becomes 2Y = 3X + 26
i.e., Y = `(-3)/2"X" + 26/2`
Comparing it with Y = bYX X + a, we get
`"b"_"YX" = (- 3)/2`
Now, the other equation 6x + y - 31 = 0 is the regression equation of X on Y.
∴ The equation becomes 6X = - Y + 31
i.e., X = `(-1)/6 "Y" + 31/6`
Comparing it with X = bXY Y+ a', we get
`"b"_"XY" = (-1)/6`
∴ r = `+-sqrt("b"_"XY" * "b"_"YX")`
`= +- sqrt((- 1)/6 xx (- 3)/2) = +- sqrt(1/4) = +- 1/2 = +- 0.5`
Since the values of bXY and bYX are negative,
r is also negative.
∴ r = - 0.5
(iii) The regression equation of Y on X is
Y = `(- 3)/2 "X" + 26/2`
For X = 2, we get
Y = `(- 3)/2 xx 2 + 26/2 = - 3 + 13 = 10`
(iv) Given, Var (Y) = 36, i.e., `sigma_"Y"^2` = 36
∴ `sigma_"Y" = 6`
Since `"b"_"XY" = "r" xx sigma_"X"/sigma_"Y"`
`(- 1)/6 = - 0.5 xx sigma_"X"/6`
∴ `sigma_"X" = (-6)/(- 6 xx 0.5) = 2`
∴ `sigma_"X"^2` = Var(X) = 4
APPEARS IN
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.
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.
If Σx1 = 56 Σy1 = 56, Σ`x_1^2` = 478,
Σ`y_1^2` = 476, Σx1y1 = 469 and n = 7, Find
(a) the regression equation of y on x.
(b) y, if x = 12.
Find graphical solution for following system of linear inequations :
3x + 2y ≤ 180; x+ 2y ≤ 120, x ≥ 0, y ≥ 0
Hence find co-ordinates of corner points of the common region.
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)
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 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`
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:
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:
bxy is the slope of regression line of y on x
Among the given regression lines 6x + y – 31 = 0 and 3x + 2y – 26 = 0, the regression line of x on y is ______
If the regression equations are 8x – 10y + 66 = 0 and 40x – 18y = 214, the mean value of y is ______
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. 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
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 = 5, Σx = Σy = 20, Σx2 = Σy2 = 90, Σxy = 76 Find 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 `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 = ______.
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`
Out of the two regression lines x + 2y – 5 = 0 and 2x + 3y = 8, find the line of regression of y on x.
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?
