Regression with dummy variables, and Univariate time series analysis 

 1. Define a dummy variable which takes the value of 1 if a country’s population is increasing, and 0 otherwise. Calculate the value of this new variable for all countries in the dataset. 2. Run a bivariate regression using the dummy calculated for the previous question (as dependent variable) and the population of the country. Interpret the results, including the significance of the parameters, the R2 and the F statistic. Please use the file “schools.xls”, which includes data on schools from a US state. 3. Define two new dummy variables. D1 = 1 if the percentage of students receiving free meals is greater than 50%, and 0 otherwise. D2 = 1 if the percentage of students for whom English is not the first language is greater than 50%, and 0 otherwise. Calculate the values of these new variables for all schools. What do these two variables measure? 4. Explain the academic performance of schools using the two dummies calculated for the previous question, average class size and the share of students whose parents have a college or university degree. Interpret the results. 5. Would the academic performance of schools improve, if schools with higher percentages of students for whom English is not the first language had smaller class sizes? Modify the regression in the previous question accordingly and interpret the results. (Tip: you will need to calculate a new interaction variable)