Practical econometrics MPEI
Replenishment date: 03.02.2011
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Description
Task 1. Enterprises of the district (number of the enterprise X) are ordered by the volume of products. Indicator Y characterizes the number of management personnel. The data are summarized in the Table. From the table, calculate the linear regression coefficients using the least squares method.
TABLE.
Х 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
У 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
Exercise 2. Calculate what is the sum of squares explained by the ESS model if the total sum of squares is TSS = 0.204705 and the residual sum of squares is RSS = 0.161231?
Task 3. For the data of Task 1, calculate the correlation coefficient.
Task 4. We have obtained an estimate of the change in the dependent variable (assume costs) from independent variables (income and prices) in the form:
how can the coefficients of the independent variables be interpreted?
Exercise 5. The Gaussian distribution is symmetric about zero, which suggests that positive errors are as likely as negative ones; however, small errors are more common than large ones. If the random error has a Gaussian distribution with a parameter, then with probability its value will be in the range from to. In what intervals will the random error be located at the same probability value, if,,?
Task 6. When and on what basis can one speak (assert) about the preference of a one-sided criterion over a two-sided one when used as an alternative hypothesis?
Task 7. For data on the size of the total disposable income and the total expenditure on personal consumption in the United States in the period from 1970 to 1979 (in billions of dollars, in 1972 prices), the estimated linear relationship model has the form.
Let's imagine that we are in 1979 and expect the total disposable income (at the same prices) to increase in 1980 to a billion dollars. Then, according to the fitted model, the volume of total expenditures on personal consumption in 1980 is equal to
so if you choose the level of trust, then
What will be the confidence interval for the corresponding value?
TABLE.
Х 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
У 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
Exercise 2. Calculate what is the sum of squares explained by the ESS model if the total sum of squares is TSS = 0.204705 and the residual sum of squares is RSS = 0.161231?
Task 3. For the data of Task 1, calculate the correlation coefficient.
Task 4. We have obtained an estimate of the change in the dependent variable (assume costs) from independent variables (income and prices) in the form:
how can the coefficients of the independent variables be interpreted?
Exercise 5. The Gaussian distribution is symmetric about zero, which suggests that positive errors are as likely as negative ones; however, small errors are more common than large ones. If the random error has a Gaussian distribution with a parameter, then with probability its value will be in the range from to. In what intervals will the random error be located at the same probability value, if,,?
Task 6. When and on what basis can one speak (assert) about the preference of a one-sided criterion over a two-sided one when used as an alternative hypothesis?
Task 7. For data on the size of the total disposable income and the total expenditure on personal consumption in the United States in the period from 1970 to 1979 (in billions of dollars, in 1972 prices), the estimated linear relationship model has the form.
Let's imagine that we are in 1979 and expect the total disposable income (at the same prices) to increase in 1980 to a billion dollars. Then, according to the fitted model, the volume of total expenditures on personal consumption in 1980 is equal to
so if you choose the level of trust, then
What will be the confidence interval for the corresponding value?
Additional Information
Task 1. Enterprises of the district (number of the enterprise X) are ordered by the volume of products. Indicator Y characterizes the number of management personnel. The data are summarized in the Table. From the table, calculate the linear regression coefficients using the least squares method.TABLE.
Х 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
У 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
Exercise 2. Calculate what is the sum of squares explained by the ESS model if the total sum of squares is TSS = 0.204705 and the residual sum of squares is RSS = 0.161231?
Task 3. For the data of Task 1, calculate the correlation coefficient.
Task 4. We have obtained an estimate of the change in the dependent variable (assume costs) from independent variables (income and prices) in the form:
how can the coefficients of the independent variables be interpreted?
Exercise 5. The Gaussian distribution is symmetric about zero, which suggests that positive errors are as likely as negative ones; however, small errors are more common than large ones. If the random error has a Gaussian distribution with a parameter, then with probability its value will be in the range from to. In what intervals will the random error be located at the same probability value, if,,?
Task 6. When and on what basis can one speak (assert) about the preference of a one-sided criterion over a two-sided one when used as an alternative hypothesis?
Task 7. For data on the size of the total disposable income and the total expenditure on personal consumption in the United States in the period from 1970 to 1979 (in billions of dollars, in 1972 prices), the estimated linear relationship model has the form.
Let's imagine that we are in 1979 and expect the total disposable income (at the same prices) to increase in 1980 to a billion dollars. Then, according to the fitted model, the volume of total expenditures on personal consumption in 1980 is equal to
so if you choose the level of trust, then
What will be the confidence interval for the corresponding value?
