HSC Commerce: Marketing and Salesmanship 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Obtain the trend values for the data in using 4-yearly centered moving averages.

If for a bivariate data b_yx = – 1.2 and b_xy = – 0.3 then find r.

From the two regression equations y = 4x – 5 and 3x = 2y + 5, find `bar x and bar y`.

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

1. Means of X and Y
2. Correlation coefficient between X and Y
3. Estimate of Y for X = 2
4. var (X) if var (Y) = 36

Fit a trend line to the data in Problem 7 by the method of least squares. Also, obtain the trend value for the year 1990.

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

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 table shows the production of gasoline in U.S.A. for the years 1962 to 1976.

i. Obtain trend values for the above data using 5-yearly moving averages.
ii. Plot the original time series and trend values obtained above on the same graph.

Choose the correct alternative :

We can use regression line for past data to forecast future data. We then use the line which_______.

Choose the correct alternative :

Which of the following is a major problem for forecasting, especially when using the method of least squares?

Regression equation of X on Y is ______

Choose the correct alternative :

What is a disadvantage of the graphical method of determining a trend line?

Regression equation of X on Y is_________

The simplest method of measuring trend of time series is ______.

Fill in the blank :

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

Fill in the blank :

The complicated but efficient method of measuring trend of time series is _______.

State whether the following is True or False :

Graphical method of finding trend is very complicated and involves several calculations.

State whether the following is True or False :

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

State whether the following is True or False :

Least squares method of finding trend is very simple and does not involve any calculations.

State whether the following is True or False :

All the three methods of measuring trend will always give the same results.