A researcher is analyzing data on the english test scores for students from 29 countries from the years 2003 to 2006. The researcher is interested in the relationship between the student's PISA test score and their parent's income in USD. Assume that students can only take the test once. She uses the following model with a full set of country and year fixed effects: scoresct=a+lincomesct+t+yc+esctscoresct-a+lincomesct+t+yc+Esct The subscripts sct denote that the observation is for student s from country c in the year t. (a) [2 points] Wwhat is the number of independent variables in the model? Answer with a quantitative analysis. (b) [4 points] Give an example of a potential lurking variable (in a simple regression model) that the country fixed effects allow the researcher to control for in her model. Clearly explain why the variable you identified is a lurking variable. Answer with 2-3 sentences. (C) [2 points] The researcher is also considering including a full set of fixed effects for the students. How wll this help the researcher? Briefly discuss. Answer with 1-2 sentences. (d) [2 points] Suppose that the researcher estimates a positive and statistically significant coefficient on the income variable. Next, the researcher decides to control for the grade that the students are enrolled in by adding a full set of fixed effects for grades. Would you be surprised to find out that the new point estimate of 11 is approximately 50% lower than the earlier estimate? Answer with 1-2 sentences.