Students in a management science class have just received their grades on the midterm test. The instructor has provided information about the midterm grades in some previous classes as well as the final average for the same students. Some of these grades have been sampled and are as follows:

Student	1	2	3	4	5	6	7	8	9
Midterm	98	77	88	78	96	61	66	95	69
Final average	93	78	84	82	84	64	64	95	76

(a) Develop a linear regression model that could be used to predict the final average in the course based on the midterm grade.

(b) Give the value of r2 for this model. Interpret its meaning in the context of this problem.

(c) A student got 85 in the midterm. If the teacher mistakenly gave him 80, how much would his final exam score be affected?

(d) If a student had worked harder and improved his midterm score from 80 to 85, how much improvement of final score can the student expect if he would continue with the effort level? (Assume that the historical scores in the data are from the same year.)