QUESTION 1 [25 MARKS] 1 1 Explain why most regression models have a constant term. (4) 12 Write out a population regression model based on cross-sectional data from population of size N and involving two explanatory/independent variables. Now explain or identify each and every term in the model. (7) 1.3 Suppose that one of your three explanatory variables in Question 1.2 is a dummy variable. Explain what a dummy variable is, what values it may take, and why you would use one in a regression model. (4) 1 4 The following table gives pairs of dependent and explanatory variables. In each case state whether you would expect the relationship between the two variables to be positive, negative, uncertain, or non-existent (.e. no relationship). Give a brief justification in each case. (10) Dependent Variable Explanatory Variable Personal savings Rate of interest Price of maize meal Demand for rice Student's mark on Test 2 Student's mark on Test 1 Demand for cigarettes Tax rate on cigarettes Wages Age