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Bring out the inconsistency in the following: bYX = 2.6 and bXY = 12.6 - Mathematics and Statistics

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प्रश्न

Bring out the inconsistency in the following:

bYX = 2.6 and bXY = `1/2.6`

बेरीज
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उत्तर

Given, bYX = 2.6 and bXY = `1/2.6`

Here, bYX and bXY have the same signs.

Also, bYX > 1 and bXY < 1

Also, for consistent data, the signs of bYX and bXY are same and bYX > 1, bXY < 1

Here, bYX. bXY = 1

∴ The given data is consistent.

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Properties of Regression Coefficients
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 3: Linear Regression - Exercise 3.2 [पृष्ठ ४७]

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बालभारती Mathematics and Statistics 2 (Commerce) [English] Standard 12 Maharashtra State Board
पाठ 3 Linear Regression
Exercise 3.2 | Q 5.4 | पृष्ठ ४७

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

  1. The line of regression of Y on X.
  2. The line regression of X on Y.
  3. The correlation coefficient between X and Y.

Bring out the inconsistency in the following:

bYX + bXY = 1.30 and r = 0.75 


Bring out the inconsistency in the following:

bYX = bXY = 1.50 and r = - 0.9 


Bring out the inconsistency in the following:

bYX = 1.9 and bXY = - 0.25


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.


An inquiry of 50 families to study the relationship between expenditure on accommodation (₹ x) and expenditure on food and entertainment (₹ y) gave the following results: 

∑ x = 8500, ∑ y = 9600, σX = 60, σY = 20, r = 0.6

Estimate the expenditure on food and entertainment when expenditure on accommodation is Rs 200.


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


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

  1. The mean values of X and Y.
  2. Correlation coefficient between X and Y.
  3. Standard deviation of Y.

For 50 students of a class, the regression equation of marks in statistics (X) on the marks in accountancy (Y) is 3y − 5x + 180 = 0.  The variance of marks in statistics is `(9/16)^"th"` of the variance of marks in accountancy. Find the correlation coefficient between marks in two subjects.


If the two regression lines for a bivariate data are 2x = y + 15 (x on y) and 4y = 3x + 25 (y on x), find

  1. `bar x`,
  2. `bar y`,
  3. bYX
  4. bXY
  5. r [Given `sqrt0.375` = 0.61]

The following results were obtained from records of age (X) and systolic blood pressure (Y) of a group of 10 men.

  X Y
Mean 50 140
Variance 150 165

and `sum (x_i - bar x)(y_i - bar y) = 1120`. Find the prediction of blood pressure of a man of age 40 years.


The equations of two regression lines are 10x − 4y = 80 and 10y − 9x = − 40 Find:

  1. `bar x and bar y`
  2. bYX and bXY
  3. If var (Y) = 36, obtain var (X)
  4. r

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:

If r = 0.5, σx = 3, `σ_"y"^2` = 16, then byx = ______


The following data is not consistent: byx + bxy =1.3 and r = 0.75


State whether the following statement is True or False:

Corr(x, x) = 0


State whether the following statement is True or False:

Cov(x, x) = Variance of x


|bxy + byx| ≥ ______


If u = `(x - "a")/"c"` and v = `(y - "b")/"d"`, then bxy = ______ 


If u = `(x - 20)/5` and v = `(y - 30)/4`, then byx = ______


The equations of the two lines of regression are 2x + 3y − 6 = 0 and 5x + 7y − 12 = 0. Find the value of the correlation coefficient `("Given"  sqrt(0.933) = 0.9667)`


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`


If byx > 1 then bxy is _______.


The following results were obtained from records of age (x) and systolic blood pressure (y) of a group of 10 women.

  x y
Mean 53 142
Variance 130 165

`sum(x_i - barx)(y_i - bary)` = 1170


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