Question

Tuition at your school has gone up, and administrators argue that the reason for the increase is that the reputation of the school has increased. You decide to investigate this hypothesis by collecting data randomly for 100 national universities and liberal arts colleges from the 2017-2018 U.S News and World Report annual rankings. You run the following regression:

Cost = 7311.17 +3985.20 . Rep -0.20 Size + 8406.79 Dpriv-416.38 Dlibart - 2376.51. Drel R2 = 0.72, SER = 3773.35

where Cost is the tuition in dollars, Rep is the index in the U.S. News and World Report that ranges from 1 to 5 with 5 being the bets reputation, Size is the number of undergraduate students, Dpriv is a binary variable equal to 1 if the school is private, Dlibart is a binary variable equal to 1 if the school is a liberal arts school, and Drel is a binary variable equal to 1 if the school has a religious affiliation.

a) What is the forecasted cost for a private liberal arts college, which has no religious affiliation, a size of 1500 students, and a reputation level of 4.5?

Answer 1

The forecasted cost of tuition for a private liberal arts college with no religious affiliation, a size of 1500 students, and a reputation level of 4.5 is $34,934.98.

Step-by-step explanation:

The forecasted cost of tuition for a private liberal arts college with no religious affiliation, a size of 1500 students, and a reputation level of 4.5 can be calculated using the regression equation provided:

Cost = 7311.17 + (3985.20 × Rep) - (0.20 × Size) + (8406.79 × Dpriv) - (416.38 × Dlibart) - (2376.51 × Drel)

• Size: 1500 students
• Reputation (Rep): 4.5
• Dpriv (private school): 1
• Dlibart (liberal arts school): 1
• Drel (religious affiliation): 0

Substituting these values into the equation:

Cost = 7311.17 + (3985.20 × 4.5) - (0.20 × 1500) + (8406.79 × 1) - (416.38 × 1) - (2376.51 × 0)

Cost = 7311.17 + 17933.40 - 300 + 8406.79 - 416.38

Cost = $34,934.98

The predicted tuition cost for such a college would be $34,934.98.