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प्रश्न
If the sign of the correlation coefficient is negative, then the sign of the slope of the respective regression line is ______
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उत्तर
negative
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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.
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.
For a certain bivariate data
| X | Y | |
| Mean | 25 | 20 |
| S.D. | 4 | 3 |
And r = 0.5. Estimate y when x = 10 and estimate x when y = 16
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.
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.
For certain bivariate data the following information is available.
| X | Y | |
| Mean | 13 | 17 |
| S.D. | 3 | 2 |
Correlation coefficient between x and y is 0.6. estimate x when y = 15 and estimate y when x = 10.
From the two regression equations, find r, `bar x and bar y`. 4y = 9x + 15 and 25x = 4y + 17
In a partially destroyed laboratory record of an analysis of regression data, the following data are legible:
Variance of X = 9
Regression equations:
8x − 10y + 66 = 0
and 40x − 18y = 214.
Find on the basis of above information
- The mean values of X and Y.
- Correlation coefficient between X and Y.
- Standard deviation of Y.
For a bivariate data, `bar x = 53`, `bar y = 28`, byx = −1.5 and bxy = −0.2. Estimate y when x = 50.
The two regression equations are 5x − 6y + 90 = 0 and 15x − 8y − 130 = 0. Find `bar x, bar y`, r.
Choose the correct alternative:
If byx < 0 and bxy < 0, then r is ______
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:
The following data is not consistent: byx + bxy =1.3 and r = 0.75
Corr(x, x) = 1
State whether the following statement is True or False:
Regression coefficient of x on y is the slope of regression line of x on y
|bxy + byx| ≥ ______
If u = `(x - "a")/"c"` and v = `(y - "b")/"d"`, then bxy = ______
The value of product moment correlation coefficient between x and x is ______
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:
| Production (X) |
Demand (Y) |
|
| Mean | 85 | 90 |
| Variance | 25 | 36 |
Coefficient of correlation between X and Y is 0.6. Also estimate the demand when the production is 100 units.
The equations of the two lines of regression are 6x + y − 31 = 0 and 3x + 2y – 26 = 0. Find the value of the correlation coefficient
| x | y | `x - barx` | `y - bary` | `(x - barx)(y - bary)` | `(x - barx)^2` | `(y - bary)^2` |
| 1 | 5 | – 2 | – 4 | 8 | 4 | 16 |
| 2 | 7 | – 1 | – 2 | `square` | 1 | 4 |
| 3 | 9 | 0 | 0 | 0 | 0 | 0 |
| 4 | 11 | 1 | 2 | 2 | 4 | 4 |
| 5 | 13 | 2 | 4 | 8 | 1 | 16 |
| Total = 15 | Total = 45 | Total = 0 | Total = 0 | Total = `square` | Total = 10 | Total = 40 |
Mean of x = `barx = square`
Mean of y = `bary = square`
bxy = `square/square`
byx = `square/square`
Regression equation of x on y is `(x - barx) = "b"_(xy) (y - bary)`
∴ Regression equation x on y is `square`
Regression equation of y on x is `(y - bary) = "b"_(yx) (x - barx)`
∴ Regression equation of y on x is `square`
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 . bYX = ______.
