HSC Commerce (English Medium) 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

`(x + 2y^3 ) dy/dx = y`

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.

For bivariate data. `bar x = 53, bar y = 28, "b"_"YX" = - 1.2, "b"_"XY" = - 0.3` Find estimate of Y for X = 50.

For bivariate data. `bar x = 53, bar y = 28, "b"_"YX" = - 1.2, "b"_"XY" = - 0.3` Find estimate of X for Y = 25.

From the data of 7 pairs of observations on X and Y, following results are obtained.

∑(x_i - 70) = - 35,  ∑(y_i - 60) = - 7,

∑(x_i - 70)² = 2989,    ∑(y_i - 60)² = 476, 

∑(x_i - 70)(y_i - 60) = 1064

[Given: `sqrt0.7884` = 0.8879]

Obtain

1. The line of regression of Y on X.
2. The line regression of X on Y.
3. The 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?

Bring out the inconsistency in the following:

b_YX + b_XY = 1.30 and r = 0.75 

Bring out the inconsistency in the following:

b_YX = b_XY = 1.50 and r = - 0.9 

Bring out the inconsistency in the following:

b_YX = 1.9 and b_XY = - 0.25

Bring out the inconsistency in the following:

b_YX = 2.6 and b_XY = `1/2.6`

For a certain bivariate data

And r = 0.5. Estimate y when x = 10 and estimate x when y = 16

Given the following information about the production and demand of a commodity obtain the two regression lines:

The coefficient of correlation between X and Y is 0.6. Also estimate the production when demand is 100.

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 respective means is 136 and 150. The sum of the product of deviations from respective means is 123. Obtain the equation of the line of regression of X on Y.

An inquiry of 50 families to study the relationship between expenditure on accommodation (₹ x) and expenditure on food and entertainment (₹ y) gave the following results: 

∑ x = 8500, ∑ y = 9600, σ_X = 60, σ_Y = 20, r = 0.6

Estimate the expenditure on food and entertainment when expenditure on accommodation is Rs 200.

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.