HSC Commerce (English Medium) १२ वीं कक्षा - Maharashtra State Board Important Questions for Mathematics and Statistics

|b_xy + b_yx | ≥ ______.

b_xy and b_yx are _______.

Find the equation of the line of regression of Y on X for the following data:

n = 8, `sum(x_i - barx).(y_i - bary) = 120, barx = 20, bary = 36, sigma_x = 2, sigma_y = 3`

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

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. b_YX and b_XY
3. If var (Y) = 36, obtain var (X)
4. r

Choose the correct alternative:

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

Choose the correct alternative:

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

State whether the following statement is True or False:

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

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

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

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?

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 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`

For certain bivariate data on 5 pairs of observations given:

∑x = 20, ∑y = 20, ∑x² = 90, ∑y² = 90, ∑xy = 76 then b_xy = ______.

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

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

For a bivariate data:

`sum(x - overlinex)^2` = 1200, `sum(y - overliney)^2` = 300, `sum(x - overlinex)(y - overliney)` = – 250

Find: 

1. b_yx
2. b_xy
3. Correlation coefficient between x and y.

Following table shows the all India infant mortality rates (per '000) for years 1980 to 2010:

Fit the trend line to the above data by the method of least squares.

For a bivariate data `barx = 10`, `bary = 12`, V(X) = 9, σ_y = 4 and r = 0.6
Estimate y when x = 5

Solution: Line of regression of Y on X is

`"Y" - bary = square ("X" - barx)`

∴ Y − 12 = `r.(σ_y)/(σ_x)("X" - 10)`

∴ Y − 12 = `0.6 xx 4/square ("X" - 10)`

∴ When x = 5

Y − 12 = `square(5 - 10)`

∴ Y − 12 = −4

∴ Y = `square`

Obtain the trend values for the data in using 4-yearly centered moving averages.