With college costs and student debt on the rise, the choices that families make when searching for and selecting a college have never been more important. Consider the information from 116 colleges on annual post-college earnings of graduates (Earnings in $), the average annual cost (Cost in $), the graduation rate (Grad in %), the percentage of students paying down debt (Debt in %), and whether or not a college is located in a city (City equals 1 if a city location, 0 otherwise). A portion of the data is shown in the accompanying table.

a. Estimate a regression model for the annual post-college earnings on the basis of Cost, Grad, Debt, City, and the interaction between Cost and Grad. Interpret the estimated coefficient of the interaction variable. 

b. Predict the annual post-college earnings of graduates of a college in a city with a graduation rate of 60%, Debt of 80% and the average annual cost of $20,000, $30,000, and $40,000. 

c. Repeat the above analysis with a graduation rate of 80%.  

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Earnings 44800 45100 1 42700 Cost 22920 23429 ⠀ 6616 Grad Debt 62 88 73 92 ⠀ 90 ⠀ 64 City 1 0 ⠀ 1