HSC Commerce (English Medium) १२ वीं कक्षा - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Obtain the trend line for the above data using 5 yearly moving averages.

The data obtained on X, the length of time in weeks that a promotional project has been in progress at a small business, and Y, the percentage increase in weekly sales over the period just prior to the beginning of the campaign.

Find the equation of the regression line to predict the percentage increase in sales if the campaign has been in progress for 1.5 weeks.

If for bivariate data `bar x = 10, bar y = 12,` v(x) = 9, σ_y = 4 and r = 0.6 estimate y, when x = 5.

Fit a trend line to the data in Problem 4 above by the method of least squares. Also, obtain the trend value for the index of industrial production for the year 1987.

The equation of the line of regression of y on x is y = `2/9` x and x on y is x = `"y"/2 + 7/6`.
Find (i) r,  (ii) `sigma_"y"^2 if sigma_"x"^2 = 4`

Identify the regression equations of x on y and y on x from the following equations, 2x + 3y = 6 and 5x + 7y − 12 = 0

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 ______.