Question Describe clearly your approach to estimating the parameters for a single equation model based on the data presented in the graph. Describe clearly your approach to estimating the parameters for a single equation model based on the data presented in the graph. Canadian Exports by Year by Country 101000 100800 100 600 100400 100 200 Exports ($ thousands) 100 000 99800 99600 99400 99200 1995 2000 2005 2010 2015 2020 Year • USA . China Maximum number of characters (including HTML tags added by text editor): 32,000
Describe clearly your approach to estimating the parameters for a single equation model based on the data presented in the graph.
From the data given in the graph it is clear that a simple linear regression model for the exports (in thousand dollars) for the countries of USA and China is appropriate, where the time (in years or other appropriate units) is the independent variable However, the task is to fuse both models into one equation and that will be done using a dummy variable for the countries Let the model be given as: Yi = u03b20 + u03b21*Ti + u03b22*Ci + ei where u03b20, u03b21 and u03b22 are the parameters of the model and, Yi is the export value (in thousand dollars) for the ith data point in the dataset Ti is the the time (in year or any other appropriate unit) Ci is the dummy variable which is 1 if the ith data point is for USA and 0 if it is for China ei is the error term for ith data point Assuming the standard Gauss-Markov assumptions for performing least squares estimation, the parameters of the model are obtained by performing Least Squares Regression. let L denate the error sum of squares then,L=sum_(i=1)^(n)e_(i)^(2)=sum_(i=1)^(n)(y_(i)-beta_(0)-beta_(1)T_(i)-beta_(2)C_(i))^(2)We will minimize error sum of squares and use the values which minimize as the estimates{:[(de ... See the full answer