Advertisements
Advertisements
Question
The equations of the two lines of regression are 2x + 3y − 6 = 0 and 5x + 7y − 12 = 0. Identify the regression lines
Advertisements
Solution
Let 2x + 3y − 6 = 0 be the regression equation of Y on X
∴ The equation becomes 3Y = −2X + 6
i.e., Y = `(-2)/3 "X" + 2`
Comparing it with Y = bYX X + a, we get
bYX = `(-2)/3`
Now, the other equation 5x + 7y − 12 = 0 is the regression equation of X on Y.
∴ The equation becomes 5X = − 7Y + 12
i.e., X = `(-7)/5 "Y" + 12/5`
Comparing it with X = bXY Y+ a', we get
bxy = `(-7)/5`
APPEARS IN
RELATED QUESTIONS
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.
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`
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 |
bYX is ______.
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`
Identify the regression equations of x on y and y on x from the following equations, 2x + 3y = 6 and 5x + 7y − 12 = 0
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_________
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:
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
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
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`
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 ______
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`
