SCERT Maharashtra solutions for Mathematics and Statistics (Commerce) [English] 12 Standard HSC chapter 2.3 - Linear Regression [Latest edition]

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If for a bivariate data, b_YX = – 1.2 and b_XY = – 0.3, then r = ______

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If the regression equation X on Y is 3x + 2y = 26, then b_xy equal to 

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

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|b_yx + b_xy| ≥ ______

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Find the value of the covariance between X and Y, if the regression coefficient of Y on X is 3.75 and σ_x = 2, σ_y = 8

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The slope of the line of regression of y on x is called the ______

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Regression analysis is the theory of

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We can estimate the value of one variable with the help of other known variable only if they are

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There are ______ types of regression equations

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In the regression equation of X on Y

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b_xy and b_yx are ______

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If the lines of regression of Y on X is y = `x/4` and X on Y is x = `y/9 + 1` then the value of r is

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If r = 0.5, σ_x = 3, `σ_"y"^2` = 16, then b_yx = ______

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The regression line is obtained by

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

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y = 5 – 2.8x and x = 3 – 0.5 y be the regression lines, then the value of b_yx is 

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If r = 0.5, σ_x = 3, σ_y² = 16, then b_xy = ______

State whether the following statement is True or False:

The equations of two regression lines are 10x – 4y = 80 and 10y – 9x = 40. Then b_xy = 0.9

State whether the following statement is True or False:

y = 5 + 2.8x and x = 3 + 0.5y be the regression lines of y on x and x on y respectively, then b_yx = – 0.5

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Both the regression coefficients cannot exceed 1

State whether the following statement is True or False:

If b_yx = 1.5 and b_xy = `1/3` then r = `1/2`, the given data is consistent

State whether the following statement is True or False:

Correlation analysis is the theory of games

State whether the following statement is True or False: 

If b_xy < 0 and b_yx < 0 then ‘r’ is > 0

The following data is not consistent: b_yx + b_xy =1.3 and r = 0.75

State whether the following statement is True or False: 

If u = x – a and v = y – b then b_xy = b_uv 

State whether the following statement is True or False:

If equation of regression lines are 3x + 2y – 26 = 0 and 6x + y – 31= 0, then mean of X is 7

State whether the following statement is True or False:

b_xy is the slope of regression line of y on x

State whether the following statement is True or False:

Corr(x, x) = 0

Corr(x, x) = 1

State whether the following statement is True or False:

Cov(x, x) = Variance of x

State whether the following statement is True or False:

Regression analysis is used for measuring the degree of the relationship between the variables

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

State whether the following statement is True or False: 

The variable used for predicting the response is called the independent variable

If n = 5, ∑xy = 76, ∑x² = ∑y² = 90, ∑x = 20 = ∑y, the covariance = ______

|b_xy + b_yx| ≥ ______

Among the given regression lines 6x + y – 31 = 0 and 3x + 2y – 26 = 0, the regression line of x on y is ______

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

If the regression equations are 8x – 10y + 66 = 0 and 40x – 18y = 214, the mean value of y is ______

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 ______

Arithmetic mean of positive values of regression coefficients is greater than or equal to ______

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

The geometric mean of negative regression coefficients is ______

Dependent variables are also known as ______

b_yx is the ______ of regression line of y on x

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:

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 2x + 3y − 6 = 0 and 5x + 7y − 12 = 0. Identify the regression lines

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)`

The age in years of 7 young couples is given below. Calculate husband’s age when wife’s age is 38 years.

Given the following information about the production and demand of a commodity.

Obtain the two regression lines:

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. Identify the regression lines

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

The equations of the two lines of regression are 6x + y − 31 = 0 and 3x + 2y – 26 = 0. Calculate the mean values of x and y

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 means are 136 and 148 respectively. The sum of product of deviations from respective means is 122. Obtain the regression equation of x on 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 n = 5, Σx = Σy = 20, Σx² = Σy² = 90 , Σxy = 76 Find Covariance (x,y) 

If n = 5, Σx = Σy = 20, Σx² = Σy² = 90, Σxy = 76 Find the regression equation of x on y

If n = 6, Σx = 36, Σy = 60, Σxy = –67, Σx² = 50, Σy² =106, Estimate y when x is 13

Compute the appropriate regression equation for the following data:

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):

If r = 0.6, Estimate x when y = 16 and y when x = 10

Mean of x = `barx = square`

Mean of y = `bary = square`

b_xy = `square/square`

b_yx = `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

b_yx = `square`

b_xy = `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

∴ b_yx = `square/square`

∴ b_yx = `square/square`

∴ r = `square`

The regression equation of x on y is 40x – 18y = 214  ......(i)

The regression equation of y on x is 8x – 10y + 66 = 0  ......(ii)

Solving equations (i) and (ii),

`barx = square`

`bary = square`

∴ b_yx = `square/square`

∴ b_xy = `square/square`

∴ r = `square`

Given variance of x = 9

∴ b_yx = `square/square`

∴ `sigma_y = square`

b_xy = `square/square`

b_yx = `square/square`

∴ Regression equation of x on y is `square`

∴ Regression equation of y on x is `square`