## Estimate the values of the dependent variable, Applied Statistics

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1. Suppose you are estimating the imports (from both the U.S. mainland and foreign countries) of fuels and petroleum products in Hawaii (the dependent variable). The values of the dependent variable from 1958 to 2008 are provided in the attached EXCEL file. According to economic theory, imports are affected by total personal income or disposable personal income. In addition, since Hawaii's energy consumption is mainly rely on imported crude oil, the prices of crude oil should also affect the values of imported fuels and petroleum products. The historical data of some potential independent variables (some are relevant, some are irrelevant) from 1958 to 2008 are also provided in the EXCEL file. Based on these data, please do the following:

a. Develop a linear or log-linear (double-log or convert both the DV and the IVs into LN(Y) and LN(X1), LN(X2)...) regression model to estimate the dependent variable based on the data provided in the EXCEL file. Select the independent variables (only include the relevant variables) and the forms (linear or log-linear). [Hint: you should try alternative combinations of independent variables and the regression model with highest Adjusted R Squared Value and all significant independent variables (the P-values of the independent variables should be less than 0.1) should be selected as the best model.] Run the regression models using data from 1958 to 2008.

b. Estimate the values of the dependent variable from 2006 to 2008 using your regression models (both linear and log-linear) and the values of the independent variables provided in the EXCEL file.

c. Calculate the forecasting errors from 2006-2008 based on the mean of absolute errors (MAE) [also called mean absolute deviation or MAD]. The MAE is calculated as follows: first calculate the forecast errors (the actual value of the dependent variable minus the forecasted values of the dependent variable) in each year (2006-2008), and then calculated the average values of the absolute values of the errors. Based on the MAE, which model do you recommend?

d. Run a regression using crude oil price as the only independent variable. Assuming crude oil price in 2009 and 2010 will be \$70/BBL and \$80/BBL, respectively, forecast the imports of fuels and petroleum products in Hawaii in 2009 and 2010.

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