3. An educator is interested in studying the difference between public and private four-year institutions that award a chemical engineering degree. The educator selected eight public institutions and eight private institutions. The following data give the number of graduates (Y) hired during campus interviews, the number of students X1 in the graduating class with a chemical engineering degree, and the type of institution X2. Note that we have set X2 = 1 for each public institution and X2 = 0 for each private institution. Fit an appropriate linear regression model to these data.

Y 25 32 34 30 35 26 26 33 21 23 26 28 23 28 25 21 X1 57 56 42 59 51 42 43 59 73 53 79 59 61 69 68 69 X2 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0