Question:
Students in a science class have just received their grades on the first test. The instructor has provided information about the first test 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
|
|
1st Test Grade
|
98
|
77
|
88
|
80
|
96
|
61
|
66
|
95
|
69
|
|
Final Average
|
93
|
78
|
84
|
73
|
84
|
64
|
64
|
95
|
76
|
a) Develop a linear regression model that can be used to predict the final course average based on the first test grade for these nine students. Provide the correct independent and dependent variables and provide the linear regression relationship in terms of these independent and dependent variables.
b) Predict the final average of a student who made an 83 on the first test.
c) Would you recommend using this relationship for forecasting the final averages? Why? Base your recommendation on analytical reasons.
d) Suppose a student scored a 41 on the first test. Predict the final average of a student who had this score? What cautions would you recommend about using this linear regression relationship for predicting a final average?