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

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`

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 = ______.

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.

Which of the following can’t be a component of a time series?

Choose the correct alternative:

The following trend line equation was developed for annual sales from 1984 to 1990 with 1984 as base or zero year.

Y = 500 + 60X (in 1000 ₹). The estimated sales for 1984 (in 1000 ₹) is

The complicated but efficient method of measuring trend of time series is ______

State whether the following statement is True or False: 

Moving average method of finding trend is very complicated and involves several calculations

Following table shows the amount of sugar production (in lac tons) for the years 1971 to 1982

Fit a trend line by the method of least squares

Obtain the trend values for the data, using 3-yearly moving averages

Use the method of least squares to fit a trend line to the data given below. Also, obtain the trend value for the year 1975.

Complete the table using 4 yearly moving average method.