HSC Commerce (English Medium) १२ वीं कक्षा - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

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 coefficient of x on y is the slope of regression line of x on y

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

|b_xy + b_yx| ≥ ______

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

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 ______

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. Find the value of the correlation coefficient `("Given"  sqrt(0.933) = 0.9667)`

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. Find the value of the correlation coefficient

If n = 5, Σx = Σy = 20, Σx² = Σy² = 90 , Σxy = 76 Find Covariance (x,y) 

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`