+1 862 207 3288 1) Salary
The file below contains the following 3 variables collected from a sample of 25 professionals in their 40s:
Salary40: Monthly income at age 40 (in $)
Salary20: Monthly income at age 20 (in $)
Edu: Years of education after high school
a) Use gretl to estimate a simple linear regression model to explain a person’s salary at 40 using his/her salary at 20.
b) Write your estimated regression model.
c) Diagnose this simple regression model for heteroscedasticity: plot the residual against the independent variable. Is there heteroscedasticity?
d) Transform your variables to get rid of heteroscedasticity. Write your new regression model
e) Add education to your new model. Did it improve your model? Explain
2) Petrol Consumption
The file below contains data on petrol consumption and number of cars in the 50 states of the USA in 1985.
PCON: Petrol consumption (in trillions of BTUs)
REG: number of registered vehicles (in thousands)
POP: population of the state (in thousands)
TAX: tax on gasoline (cents per gallon)
a) Use gretl to estimate a multiple linear regression model to explain Petrol Consumption in a state using its population, number of registered cars and tax on gasoline.
b) Why aren’t all the coefficients significant? In other words, which problem does the model have?
c) Solve the problem and re-estimate your new model using gretl.
d) Diagnose this model for heteroscedasticity: plot the residual against each of the independent variables.
3) Coal
Coal is an important source of energy to generate electricity in thermal power stations. The international price of coal seems to depend a lot on the price of oil. The file below contains data on the prices of coal and oil since December 1994.
a) Use the data to estimate a regression model to explain the price of coal as a function of the price of oil.
b) Test your model for serial correlation graphically.
c) Which transform would get rid of serial correlation?
d) Estimate your new regression model and make sure it does not contain serial correlation.
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