Bxy . byx = ______. - Mathematics and Statistics

Question

b_xy . b_yx = ______.

Options

V(X)
σ_x
r²
$σ_{y}^{2}$

MCQ

Fill in the Blanks

Solution

b_xy . b_yx = r².

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Properties of Regression Coefficients

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Q 4.A.ii Q 4.A.i Q 4.A.iii

2021-2022 (March) Set 1

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2021-2022 (March) Set 1 (with solutions)

Q 4.A.ii | 1 mark

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From the data of 7 pairs of observations on X and Y, following results are obtained.

∑(x_i - 70) = - 35, ∑(y_i - 60) = - 7,

∑(x_i - 70)² = 2989, ∑(y_i - 60)² = 476,

∑(x_i - 70)(y_i - 60) = 1064

[Given: $\sqrt{0.7884}$ = 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.

You are given the following information about advertising expenditure and sales.

	Advertisement expenditure (₹ in lakh) (X)	Sales (₹ in lakh) (Y)
Arithmetic Mean	10	90
Standard Mean	3	12

Correlation coefficient between X and Y is 0.8

Obtain the two regression equations.
What is the likely sales when the advertising budget is ₹ 15 lakh?
What should be the advertising budget if the company wants to attain sales target of ₹ 120 lakh?

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

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 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 ${(\frac{9}{16})}^{th}$ of the variance of marks in accountancy. Find the correlation coefficient between marks in two subjects.

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.

In a partially destroyed record, the following data are available: variance of X = 25, Regression equation of Y on X is 5y − x = 22 and regression equation of X on Y is 64x − 45y = 22 Find

Mean values of X and Y
Standard deviation of Y
Coefficient of correlation between X and 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

$\bar{x}$ ,
$\bar{y}$ ,
b_YX
b_XY
r [Given $\sqrt{0.375}$ = 0.61]

For certain X and Y series, which are correlated the two lines of regression are 10y = 3x + 170 and 5x + 70 = 6y. Find the correlation coefficient between them. Find the mean values of X and Y.

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

$\bar{x} and \bar{y}$
b_YX and b_XY
If var (Y) = 36, obtain var (X)
r

If b_YX = − 0.6 and b_XY = − 0.216, then find correlation coefficient between X and Y. Comment on it.

Choose the correct alternative:

If b_yx < 0 and b_xy < 0, then r is ______

The following data is not consistent: b_yx + b_xy =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

|b_xy + b_yx| ≥ ______

If u = $\frac{x - a}{c}$ and v = $\frac{y - b}{d}$ , then b_xy = ______

The value of product moment correlation coefficient between x and x is ______

The equations of two lines of regression are 3x + 2y – 26 = 0 and 6x + y – 31 = 0. Find variance of x if variance of y is 36

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?

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

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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 = 25

Mean of y = 20

$σ_{x}$ = 4

$σ_{y}$ = 3

r = 0.5

b_yx = $□$

b_xy = $□$

when x = 10,

$y - □ = □ (10 - □)$

∴ y = $□$

The regression equation of y on x is 2x – 5y + 60 = 0

Mean of x = 18

$2 □ - 5 \bar{y} + 60$ = 0

∴ $\bar{y} = □$

$σ_{x} : σ_{y}$ = 3 : 2

∴ b_yx = $\frac{□}{□}$

∴ r = $□$

For a bivariate data:

$\sum {(x - \bar{x})}^{2}$ = 1200, $\sum {(y - \bar{y})}^{2}$ = 300, $\sum (x - \bar{x}) (y - \bar{y})$ = – 250

Find:

b_yx
b_xy
Correlation coefficient between x and y.

Bxy . byx = ______. - Mathematics and Statistics

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