Advertisements
Advertisements
प्रश्न
Bring out the inconsistency in the following:
bYX + bXY = 1.30 and r = 0.75
Advertisements
उत्तर
Given, bYX + bXY = 1.30, r = 0.75
Consider, `("b"_"YX" + "b"_"XY")/2 = 1.30/2 = 0.65`
∴ `("b"_"YX" + "b"_"XY")/2 < "r"`
But, for consistent data `|("b"_"YX" + "b"_"XY")/2|` >|r|
∴ Given data is inconsistent.
APPEARS IN
संबंधित प्रश्न
For bivariate data. `bar x = 53`, `bar y = 28`, byx = −1.2, bxy = −0.3. Find the correlation coefficient between x and y.
Bring out the inconsistency in the following:
bYX = 2.6 and bXY = `1/2.6`
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 respective means is 136 and 150. The sum of the product of deviations from respective means is 123. Obtain the equation of the line of regression of X on Y.
The following data about the sales and advertisement expenditure of a firms is given below (in ₹ Crores)
| Sales | Adv. Exp. | |
| Mean | 40 | 6 |
| S.D. | 10 | 1.5 |
Coefficient of correlation between sales and advertisement expenditure is 0.9.
Estimate the likely sales for a proposed advertisement expenditure of ₹ 10 crores.
The following data about the sales and advertisement expenditure of a firms is given below (in ₹ Crores)
| Sales | Adv. Exp. | |
| Mean | 40 | 6 |
| S.D. | 10 | 1.5 |
Coefficient of correlation between sales and advertisement expenditure is 0.9.
What should be the advertisement expenditure if the firm proposes a sales target ₹ 60 crores?
From the two regression equations, find r, `bar x and bar y`. 4y = 9x + 15 and 25x = 4y + 17
The equations of two regression lines are
2x + 3y − 6 = 0
and 3x + 2y − 12 = 0 Find
- Correlation coefficient
- `sigma_"X"/sigma_"Y"`
If the two regression lines for a bivariate data are 2x = y + 15 (x on y) and 4y = 3x + 25 (y on x), find
- `bar x`,
- `bar y`,
- bYX
- bXY
- r [Given `sqrt0.375` = 0.61]
The equations of two regression lines are 10x − 4y = 80 and 10y − 9x = − 40 Find:
- `bar x and bar y`
- bYX and bXY
- If var (Y) = 36, obtain var (X)
- r
If bYX = − 0.6 and bXY = − 0.216, then find correlation coefficient between X and Y. Comment on it.
Choose the correct alternative:
If the regression equation X on Y is 3x + 2y = 26, then bxy equal to
Choose the correct alternative:
Find the value of the covariance between X and Y, if the regression coefficient of Y on X is 3.75 and σx = 2, σy = 8
Choose the correct alternative:
bxy and byx are ______
Choose the correct alternative:
If r = 0.5, σx = 3, σy2 = 16, then bxy = ______
Choose the correct alternative:
Both the regression coefficients cannot exceed 1
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
State whether the following statement is True or False:
If bxy < 0 and byx < 0 then ‘r’ is > 0
State whether the following statement is True or False:
The following data is not consistent: byx + bxy =1.3 and r = 0.75
State whether the following statement is True or False:
If u = x – a and v = y – b then bxy = buv
State whether the following statement is True or False:
Corr(x, x) = 0
|bxy + byx| ≥ ______
The geometric mean of negative regression coefficients is ______
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?
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`
Mean of x = 25
Mean of y = 20
`sigma_x` = 4
`sigma_y` = 3
r = 0.5
byx = `square`
bxy = `square`
when x = 10,
`y - square = square (10 - square)`
∴ y = `square`
The regression equation of y on x is 2x – 5y + 60 = 0
Mean of x = 18
`2 square - 5 bary + 60` = 0
∴ `bary = square`
`sigma_x : sigma_y` = 3 : 2
∴ byx = `square/square`
∴ byx = `square/square`
∴ r = `square`
|bxy + byz| ≥ ______.
