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# Econometrics. Practical work

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**29.06.2016**

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## Description

Practical tasks on discipline "Econometrics"

Task 1. Enterprises region (number of enterprise A) are ordered in terms of output. Index have characterized the number of managerial staff. The data are summarized in Table. According to the table, calculate a least squares linear regression coefficients.

Table.

X 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

In 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3

X 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Y 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5

Task 2. Calculate What is the sum of the squares, the explanation model the ESS, if the total sum of squares TSS = 0.204705, and the residual sum of squares RSS = 0.161231?

Task 3. Data Targets 1, calculate the correlation coefficient.

Task 4. We received a change of assessment of the dependent variable (assume the costs) of the independent variables (income and prices) in the form of:

It can be interpreted as the coefficients of the independent variables?

Task 5. Gaussian distribution is symmetric with respect to zero, and this suggests that positive errors as likely as negative; in this case, small errors are more common than big ones. If the random error has a Gaussian distribution with a parameter, then the probability of its value will be entered into between and. At what intervals will be located a random error for the same value of probability, if,?

Task 6. When and on what basis we can talk (argue) a preference for one-sided test, compared with two-way when used as an alternative hypothesis?

Task 7. For information about the size of the aggregate disposable income and total expenditure on private consumption in the US from 1970 to 1979 (in billion. Dollars in 1972 prices), the estimated linear relationship model is given.

Let us imagine that we are in 1979 and expect to increase in 1980, the total disposable income (for the same price) to bn. Dollars. Then the model projected on the selected volume of the total private consumption expenditure in 1980 is

so if you choose the level of trust,

What will be equal and the confidence interval for the specified value?

Task 8. Consider three ways of consumption forecast (y) from the household appliances income (x). We have:

• observed values;

• values obtained by model constructed without considering autocorrelation of errors;

• values obtained by the model, the parameters of which are adjusted for autocorrelation of errors;

• values which alternative models for the prediction should be preferred, if the average discrepancy squares using the three methods of calculating the value. These mean squares are equal to?

Task 9. The administration of the insurance company decided to introduce a new type of services - insurance in case of fire. In order to determine tariffs based on a sample of 10 cases of fires analyzed dependence value of the damage caused by fire to the distance to the nearest fire station:

№ p / p 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

The total amount of damage, mln. 26.2 17.8 31.3 23.1 27.5 36.0 14.1 22.3 19.6 31.3

The distance to the nearest station, km 3.4 1.8 4.6 2.3 3.1 5.5 0.7 3.0 2.6 4.3

9.1. Construct a scatterplot of the resulting values (total damage) and the independent variable (the distance to the nearest station)

9.2. Determine the parameters a and b of the equation Simple Linear Regression.

9.3. Calculate the linear correlation coefficient.

9.4. Check the statistical significance of regression coefficient «b» by using Student´s t-test

9.5. To evaluate the statistical significance of the regression model constructed generally using the Fisher F-test

Task 10. The available data on prices and dividends on ordinary shares, and on the company´s profitability.

Number stock price (US dollar)% return on equity level of dividend%

January 25 15.2 2.6

February 20 13.9 2.1

on March 15