In Economic Policy (January 2011), researchers from the London School of Economics conducted a cross-country analysis of the relationship between teacher's pay and pupils' performance. Data collected for 39 countries were used to model y = the country's average standardized score of its pupils. The independent variables under consideration were: x1 = country's total teaching staff as a percentage of the country's labor force, x2 = percentage of women on country's total teaching staff, x3 = country's pupil-teacher ratio, x4 = average teacher's salary after 15 years on staff, x5 = average teaching hours per year, x6, = GDP growth of country (%), x7 = country's educational spending per year, and x8 = percentile position of country's teachers' salaries after 15 years on staff. Consider a stepwise regression run on the data.
a. What is the form of the model fit in step 1? How many models are fit? How is the "best" independent variable selected in this step?
b. What is the form of the model fit in step 2? How many models are fit? How is the "best" independent variable selected in this step?
c. What is the form of the model fit in step 3? How many models are fit? How is the "best" independent variable selected in this step?
d. The variables x3, x4, and x6, were deemed the best variables for predicting y. How do you recommend the researchers proceed from here? Why?