Logistic regression in a famous research paper, econometrics researchers investigated the effectiveness of a teaching method known as the personalized system of instruction (psi) for the teaching of economics. they randomly selected 32 students from two intermediate econ classes. students from one of the classes were being taught using psi; in the other class, the traditional lecture method was used. the researchers then recorded 1) whether or not the students' grades had improved (yes or no) from their introductory econ class, 2) their performance in the introductory class assessed using the test for the understanding of college economics (tuce), and 3) their overall gpa upon entering the intermediate course. using minitab, a binary logistic regression was done to assess the probability of grade improvement from the other variables. the output is below. use it to answer the questions that follow. binary logistic regression: improve versus psi, tuce, gpa model summary deviance deviance r-sqr-soad) 37.409 30.125 aic 33.78 coefficients term coef se coet vif constant 13.02 493 psi 2.38 1.06 1.15 tuce 0.095 0.142 1.08 gpa 2.831.26 1.19 odds ratios for continuous predictors odds ratio 95% ci psi 10.7907 (1.3394 86.9367) tuce 1.0998 (0.8334, 14515) gpa 16.8797 (1.4202, 200.6205) regression equation p(1) - expl/1 exply) y -13.02 2.38 psi+0.095 tuce + 2.83 gpa a. using this model, what is the predicted probability of grade improvement for a student in the psi class who had a 22 score on the tuce and a gpa of 3.0? b. using this model, what is the predicted probability of grade improvement for a student not in the psi class who had a 22 score on the tuce and a gpa of 3.0? c. interpret the slope of the psi predictor. (psi was recorded as 0 (no) or 1 ( d. which of the factors recorded appears to have little effect on the probability of grade improvement? upon what in the output is your answer based? (food for thought: what implications might this have for these researchers? )