Assume a professor is interested in analyzing the factors that contribute to students failure to pass a masters program at a university. The professor collects a sample of the actual records of students pass and failure in this program. The sample includes 100 students each year for 5 years (2018-2022). The dependent variable (fail ) takes the value 1 if a particular student failed, and 0 elsewhere. The explanatory variables used in this professors analysis include: (i) Age, i.e., the age of the student; (ii) work experience, which equals 1 if the student has work experience, and 0 otherwise; (iii) pg degree, which equals 1 if the student has a postgraduate degree, and 0 otherwise; (iv) agrade, which equals 1 if the student achieved an A-grade at the undergrad level, and 0 otherwise; (v) belowbgrade, which equals 1 if the students undergraduate degree is below B, and 0 otherwise; Please answer the following questions based on the information above. (a) If the professor wants to use a linear probability model (LPM) for empirical analysis, please write out the specification of the econometric model that this professor should use. Please note that the error term should be denoted as ut , and you must include this error term in your econometric model. (b) Please demonstrate mathematically that the LPM above can also describe a students probability of failing the program. (c) Please provide an explanation within the context of this specific empirical analysis as to why the LPM is not the most suitable model. (d) If this professor eventually decides to use logit model for the analysis, please write out the specification of the logit model that this professor should use. (e) Assume the estimated coefficient of work experience equals -0.45 which is statistically significant at 5% level. Please explain the economic meaning of the sign of this estimate.