Suppose we conducted a survey of college students, and performed least squares linear regression to obtain the following relationship:

W = 0.05H + 0.001S where W is the net worth (in millions) of student after 10 years of graduating, H is the hours of study per week, and S is the SAT score from high school.

The average squared residual on both training and held-out test data points was 0.2.

For each of the following phenomena, explain in about 1-2 sentences why they dont contradict this finding.

(a) 25% of the students in the held-out test set showed squared residual exceeding 0.4.

(b) After reading this equation, all undergrads decide to increase their study hours by 10 hours/week. But 10 years later, their net worth is lower than their projected net worth. \

(c) Many undergrads in the training dataset reported studying more than 60 hours per week and scoring 1600 on the SAT. However, contrary to the model, these students net worth after 10 years is less than 4.0 million dollars.