Consider this example

Suppose that you've been hired as an analyst by the health ministry. 1Your rst project is to investigate the safety record of hotdog eating contests [a hotdog eating contest. is a competition in which a contestant. who is able to eat. the largest number of hotdogs wins} 'While fun, such contests sonletirnes lead to hospitalizations due to overeating. Using the historical data, suppose that you estimated the following logit model {using MLE}: 1 east-1x3} = W {3} where Y,- = 1 indicates that contestant i was hospitalized [Y1- = I] if not}, X2,- is the nurnber of hotdogs successfully consumed by contestant i, and X3; is the contestant's body weight [in pounds}. Suppose that you've obtained the following est-imat-m: mm m -E-___ \"1_ Table 1: Model (3] MLE Estimates {a} [ti points} Based on these estimates, what- are the odds that a person who weights X3; = 1TH pounds will become hospitalized after eating Xzi = ll hotpdogs? That is, calculate the appropriate odds ratio. {b} [ll] points} 1What is the probability that a person weighting Xgi = 1711} pounds will beoome hospitalized after eating X2,- = ll hotpdogs? By how much would this probability change is this person eats one additional hotdog? {c} [1 points} Briey explain the key advantages of the Legit model over the linear proba bility model. In this case, in your opinion, what is the key reason for choosing the Logit model over the linear probability model?I