HSC Commerce: Marketing and Salesmanship इयत्ता १२ वी - Maharashtra State Board Question Bank Solutions

The following data about the sales and advertisement expenditure of a firms is given below (in ₹ Crores)

Coefficient of correlation between sales and advertisement expenditure is 0.9.

Estimate the likely sales for a proposed advertisement expenditure of ₹ 10 crores.

The following data about the sales and advertisement expenditure of a firms is given below (in ₹ Crores)

Coefficient of correlation between sales and advertisement expenditure is 0.9.

What should be the advertisement expenditure if the firm proposes a sales target ₹ 60 crores?

For certain bivariate data the following information is available.

Correlation coefficient between x and y is 0.6. estimate x when y = 15 and estimate y when x = 10.

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

1. The mean values of X and Y.
2. Correlation coefficient between X and Y.
3. 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 `(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.

The equations of two regression lines are
2x + 3y − 6 = 0
and 3x + 2y − 12 = 0 Find 

1. Correlation coefficient
2. `sigma_"X"/sigma_"Y"`

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 equations of two regression lines are x − 4y = 5 and 16y − x = 64. Find means of X and Y. Also, find correlation coefficient between X and Y.

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

1. Mean values of X and Y
2. Standard deviation of Y
3. 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

1. `bar x`,
2. `bar y`,
3. b_YX
4. b_XY
5. r [Given `sqrt0.375` = 0.61]

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

Two lines of regression are 10x + 3y − 62 = 0 and 6x + 5y − 50 = 0. Identify the regression of x on y. Hence find `bar x, bar y` and r.

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.

Regression equations of two series are 2x − y − 15 = 0 and 3x − 4y + 25 = 0. Find `bar x, bar y` and regression coefficients. Also find coefficients of correlation. [Given `sqrt0.375` = 0.61]

The two regression lines between height (X) in inches and weight (Y) in kgs of girls are,
4y − 15x + 500 = 0
and 20x − 3y − 900 = 0
Find the mean height and weight of the group. Also, estimate the weight of a girl whose height is 70 inches.

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

n = 8, `sum(x_i - bar x)^2 = 36, sum(y_i - bar y)^2 = 44, sum(x_i - bar x)(y_i - bar y) = 24`

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