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 123456789 Midterm 98 77 88 78 96 61 66 95 69 Finalaverage 93 78 84 72 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 r2for 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.)

Problem 2 (Exams) 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: manna III-WEE mun-mam (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.)