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प्रश्न
State whether the following statement is True or False:
Corr(x, x) = 0
विकल्प
True
False
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उत्तर
False
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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.
Bring out the inconsistency in the following:
bYX + bXY = 1.30 and r = 0.75
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
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.
From the two regression equations, find r, `bar x and bar y`. 4y = 9x + 15 and 25x = 4y + 17
The two regression equations are 5x − 6y + 90 = 0 and 15x − 8y − 130 = 0. Find `bar x, bar y`, r.
Two lines of regression are 10x + 3y − 62 = 0 and 6x + 5y − 50 = 0. Identify the regression of x on y. Hence find `bar x, bar y` and r.
Find the line of regression of X on Y for the following data:
n = 8, `sum(x_i - bar x)^2 = 36, sum(y_i - bar y)^2 = 44, sum(x_i - bar x)(y_i - bar y) = 24`
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
Choose the correct alternative:
If byx < 0 and bxy < 0, then r is ______
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:
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:
Cov(x, x) = Variance of x
If u = `(x - "a")/"c"` and v = `(y - "b")/"d"`, then bxy = ______
If the sign of the correlation coefficient is negative, then the sign of the slope of the respective regression line is ______
The value of product moment correlation coefficient between x and x is ______
If u = `(x - 20)/5` and v = `(y - 30)/4`, then byx = ______
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?
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
If n = 5, Σx = Σy = 20, Σx2 = Σy2 = 90 , Σxy = 76 Find Covariance (x,y)
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`
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`
