Several studies have reported lower participation in the science, technology, engineering, and mathematics (STEM) careers by female and minority students. A high school counselor surveys 240 college-bound students, collecting information on whether the student has applied to a STEM field (1 if STEM, 0 otherwise), whether or not the student is female (1 if female, 0 otherwise), white (1 if white, 0 otherwise), and Asian (1 if Asian, 0 otherwise). Also included in the survey is the information on the student’s high school GPA and the SAT scores. A portion of the data is shown in the accompanying table.

a. Estimate and interpret the logistic regression model using STEM as the response variable, and GPA, SAT, White, Female, and Asian as the predictor variables. 

b. Find the predicted probability that a white male student will apply to a STEM field with GPA = 3.4 and SAT = 1400. Find the corresponding probabilities for an Asian male and a male who is neither white nor Asian. 

c. Find the predicted probability that a white female student will apply to a STEM field with GPA = 3.4 and SAT = 1400. Find the corresponding probabilities for an Asian female and a female who is neither white nor Asian.

Transcribed Image Text:

STEM GPA SAT White Female 0 3.70 1420 0 0 4.40 1240 1 ⠀ 1 I 3.80 1390 1 0 I 0 0 E 0 Asian 1 1 # 0