MEI Econometrics practical work

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Task 1. District enterprises (enterprise number X) are ordered by the volume of output. The indicator Y characterizes the number of managerial personnel. The data are tabulated. According to the table, calculate the linear regression coefficients using the least squares method.
Task 2. Calculate what is the sum of squares, explained by the ESS model, if the total sum of squares, and the residual sum of squares?
Task 4. We obtained an estimate of the change in the dependent variable (suppose expenses) from independent variables (DPI income and prices P) in the form:. How can the coefficients with independent variables be interpreted?

Task 5. The Gaussian distribution is symmetrical about zero, and this assumes that positive errors are just as likely as negative ones; at the same time, small errors are more common than large ones. If the random error has a Gaussian distribution with a parameter, then with a probability of 0.95 its value will be in the range from to. What intervals will the random error be for the same probability value, if?
Task 6. When and on the basis of what can we say (assert) about the preference of a one-sided criterion in comparison with a two-sided one about using it as an alternative hypothesis?
Task 7. For data on the size of total disposable income and total expenditure on personal consumption in the United States from 1970 to 1979 (in billions of dollars, in 1972 prices), the estimated linear relationship model has the form.
Let us imagine that we are in 1979 and we expect an increase in 1980 in total disposable income (at the same prices) to DPI * = 1030 billion dollars. Then the projected model for total consumption for personal consumption in 1980 is equal to
so if you choose a confidence level of 0.95, then
What will be the confidence interval for the corresponding DPI * = 1030 value?

Additional information

Task 8. Consider three options for forecasting the consumption (s) of household appliances from income (x). We have:
• observed values;
• values ​​obtained from the model constructed without taking into account the autocorrelation of errors;
• values ​​obtained from the model, the parameters of which are corrected for autocorrelation of errors;
• values, which version of the model for the forecast should be preferred if the mean squares of the differences when using these three methods for calculating values. Are these mean squares equal, respectively?

Task 9. The administration of the insurance company decided to introduce a new type of service - fire insurance. In order to determine the tariffs for a sample of 10 fire cases, the dependence of the cost of damage caused by a fire on the distance to the nearest fire station is analyzed:

Task 10. There are the following data on prices and dividends on ordinary shares, as well as the company´s profitability

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