One of your peers wants to analyze whether or not participating in varsity sports lowers or increases the GPA of students

She decides to collect data from 110 male and female students on their GPA and the number of hours they spend participating in varsity sports. The coefficient in the simple regression function turns out to be significantly negative, using the t-statistic and carrying out the appropriate hypothesis test. Upon reflection, she is concerned that she did not ask the students in her sample whether or not they were female or male. You point out to her that you are more concerned about the effect of omitted variables in her regression, such as the incoming SAT score of the students, and whether or not they are in a major from a high/low grading department. Elaborate on your argument.
What will be an ideal response?

Answer: The presence of omitted variables will result in an inconsistent estimator for the included variable (number of hours spent in varsity sports) if at least one of the following two conditions holds: the omitted variable is relevant in affecting the GPA and/or the omitted variable is correlated with the included variable. Incoming SAT scores are clearly relevant in predicting GPAs, at least in the earlier years. Hence it is relevant. Departmental differences in the general level of grading will even more obviously have an effect on the GPA. The relationship therefore suffers from omitted variable bias.