HSC Commerce (Marathi Medium) 12th Standard Board Exam [इयत्ता १२ वी] - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

State whether the following statement is True or False:

b_xy is the slope of regression line of y on x

Among the given regression lines 6x + y – 31 = 0 and 3x + 2y – 26 = 0, the regression line of x on y is ______

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

The equations of the two lines of regression are 2x + 3y − 6 = 0 and 5x + 7y − 12 = 0. Identify the regression lines

The age in years of 7 young couples is given below. Calculate husband’s age when wife’s age is 38 years.

The equations of the two lines of regression are 6x + y − 31 = 0 and 3x + 2y – 26 = 0. Identify the regression lines

The equations of the two lines of regression are 6x + y − 31 = 0 and 3x + 2y – 26 = 0. Calculate the mean values of x and y

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

If n = 5, Σx = Σy = 20, Σx² = Σy² = 90, Σxy = 76 Find the regression equation of x on y

If n = 6, Σx = 36, Σy = 60, Σxy = –67, Σx² = 50, Σy² =106, Estimate y when x is 13

The regression equation of x on y is 40x – 18y = 214  ......(i)

The regression equation of y on x is 8x – 10y + 66 = 0  ......(ii)

Solving equations (i) and (ii),

`barx = square`

`bary = square`

∴ b_yx = `square/square`

∴ b_xy = `square/square`

∴ r = `square`

Given variance of x = 9

∴ b_yx = `square/square`

∴ `sigma_y = square`

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

The simplest method of measuring trend of time series is ______

The method of measuring trend of time series using only averages is ______

State whether the following statement is True or False:

The secular trend component of time series represents irregular variations

State whether the following statement is True or False: 

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

State whether the following statement is True or False:

Least squares method of finding trend is very simple and does not involve any 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 trend values for data, using 4-yearly centred moving averages

The following table gives the production of steel (in millions of tons) for years 1976 to 1986.

Obtain the trend value for the year 1990