HSC Commerce: Marketing and Salesmanship 12th Standard Board Exam - Maharashtra State Board Important Questions for Mathematics and Statistics

For the following bivariate data obtain the equations of two regression lines:

For the following data, find the regression line of Y on X

Hence find the most likely value of y when x = 4.

For bivariate data. `bar x = 53`, `bar y = 28`, b_yx = −1.2, b_xy = −0.3. Find the correlation coefficient between x and y.

From the data of 20 pairs of observations on X and Y, following results are obtained.

`barx` = 199, `bary` = 94,

`sum(x_i - barx)^2` = 1200, `sum(y_i - bary)^2` = 300,

`sum(x_i - bar x)(y_i - bar y)` = –250

Find:

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

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

Correlation coefficient between X and Y is 0.8

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

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.

For a bivariate data, `bar x = 53`, `bar y = 28`, b_yx = −1.5 and b_xy = −0.2. Estimate y when x = 50.

The two regression equations are 5x − 6y + 90 = 0 and 15x − 8y − 130 = 0. Find `bar x, bar y`, r.

b_YX is ______.

|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:

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

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?