Advertisements
Advertisements
प्रश्न
Given the following information about the production and demand of a commodity obtain the two regression lines:
| X | Y | |
| Mean | 85 | 90 |
| S.D. | 5 | 6 |
The coefficient of correlation between X and Y is 0.6. Also estimate the production when demand is 100.
उत्तर
Given, `bar x = 85, bar y = 90, sigma_"X" = 5, sigma_"Y" = 6`, r =0.6
`"b"_"YX" = "r" sigma_"Y"/sigma_"X" = 0.6 xx 6/5 = 0.72`
`"b"_"XY" = "r" sigma_"X"/sigma_"Y" = 0.6 xx 5/6 = 0.5`
The regression equation of Y on X is
`("Y" - bar y) = "b"_"YX" ("X" - bar x)`
(Y - 90) = 0.72 (X - 85)
Y - 90 = 0.72 X - 61.2
Y = 0.72X - 61.2 + 90
Y = 28.8 + 0.72 X ....(i)
The regression equation of X on Y is
`("X" - bar x) = "b"_"XY" ("Y" - bar y)`
(X - 85) = 0.5(Y - 90)
X - 85 = 0.5 Y - 45
X = 0.5 Y - 45 + 85
X = 40 + 0.5Y ....(ii)
For Y = 100, from equation (ii) we get
X = 40 + 0.5(100) = 40 + 50 = 90
∴ The production is 90 when demand is 100.
Notes
The answer in the textbook is incorrect.
APPEARS IN
संबंधित प्रश्न
For bivariate data. `bar x = 53, bar y = 28, "b"_"YX" = - 1.2, "b"_"XY" = - 0.3` Find estimate of Y for X = 50.
From the data of 7 pairs of observations on X and Y, following results are obtained.
∑(xi - 70) = - 35, ∑(yi - 60) = - 7,
∑(xi - 70)2 = 2989, ∑(yi - 60)2 = 476,
∑(xi - 70)(yi - 60) = 1064
[Given: `sqrt0.7884` = 0.8879]
Obtain
- The line of regression of Y on X.
- The line regression of X on Y.
- The correlation coefficient between X and Y.
Bring out the inconsistency in the following:
bYX = 1.9 and bXY = - 0.25
Bring out the inconsistency in the following:
bYX = 2.6 and bXY = `1/2.6`
From the two regression equations, find r, `bar x and bar y`. 4y = 9x + 15 and 25x = 4y + 17
For bivariate data, the regression coefficient of Y on X is 0.4 and the regression coefficient of X on Y is 0.9. Find the value of the variance of Y if the variance of X is 9.
The two regression equations are 5x − 6y + 90 = 0 and 15x − 8y − 130 = 0. Find `bar x, bar y`, r.
Regression equations of two series are 2x − y − 15 = 0 and 3x − 4y + 25 = 0. Find `bar x, bar y` and regression coefficients. Also find coefficients of correlation. [Given `sqrt0.375` = 0.61]
Choose the correct alternative:
If byx < 0 and bxy < 0, then r is ______
State whether the following statement is True or False:
If byx = 1.5 and bxy = `1/3` then r = `1/2`, the given data is consistent
The following data is not consistent: byx + bxy =1.3 and r = 0.75
Arithmetic mean of positive values of regression coefficients is greater than or equal to ______
Given the following information about the production and demand of a commodity.
Obtain the two regression lines:
| ADVERTISEMENT (x) (₹ in lakhs) |
DEMAND (y) (₹ in lakhs) |
|
| Mean | 10 | 90 |
| Variance | 9 | 144 |
Coefficient of correlation between x and y is 0.8.
What should be the advertising budget if the company wants to attain the sales target of ₹ 150 lakhs?
For a certain bivariate data of a group of 10 students, the following information gives the internal marks obtained in English (X) and Hindi (Y):
| X | Y | |
| Mean | 13 | 17 |
| Standard Deviation | 3 | 2 |
If r = 0.6, Estimate x when y = 16 and y when x = 10
Mean of x = 53
Mean of y = 28
Regression coefficient of y on x = – 1.2
Regression coefficient of x on y = – 0.3
a. r = `square`
b. When x = 50,
`y - square = square (50 - square)`
∴ y = `square`
c. When y = 25,
`x - square = square (25 - square)`
∴ x = `square`
| x | y | xy | x2 | y2 |
| 6 | 9 | 54 | 36 | 81 |
| 2 | 11 | 22 | 4 | 121 |
| 10 | 5 | 50 | 100 | 25 |
| 4 | 8 | 32 | 16 | 64 |
| 8 | 7 | `square` | 64 | 49 |
| Total = 30 | Total = 40 | Total = `square` | Total = 220 | Total = `square` |
bxy = `square/square`
byx = `square/square`
∴ Regression equation of x on y is `square`
∴ Regression equation of y on x is `square`
For a bivariate data:
`sum(x - overlinex)^2` = 1200, `sum(y - overliney)^2` = 300, `sum(x - overlinex)(y - overliney)` = – 250
Find:
- byx
- bxy
- Correlation coefficient between x and y.
