Problem 1: The operation manager of a musical instrument distributor feels that demand for bass drums may be related to the number of television appearance by popular rock group Green Shades during the preceding month. The manager has collected the data shown in the following table:
|
demand for bass drums
|
Green shades Tv appearance
|
|
3
|
3
|
|
6
|
4
|
|
7
|
7
|
|
5
|
6
|
|
10
|
8
|
|
8
|
5
|
a) Graph these data whether to see a linear equation might describe the relationship between the group’s television shows and bass drum sales.
b) Using the equation compute SST, SSE and SSR. Find the least squares regression line for this data.
c) What is your estimate for bass drum sales if the Green Shades performed on TV six times last month?
Problem 2: Student in a management 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 followed.
|
student
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
|
1 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 regression model that could be used to predict the final average in the course based on the first test grade.
b) Predict the final average of a student who made an 83 on the first test.
c) Give the values of r and r2 for this model. Interpret the value of r2 in the context of this problem.
Problem 3: The total expenses of a hospital are related to many factors. Two of these are the number of beds in the hospital, and the number of admissions. Data was collected on 14 hospitals as shown in the table below.
|
Hospital
|
Number
|
Admisions
|
Total expenses
|
|
of beds
|
(100s)
|
Millions
|
|
1
|
215
|
77
|
57
|
|
2
|
336
|
160
|
127
|
|
3
|
520
|
230
|
157
|
|
4
|
135
|
43
|
24
|
|
5
|
35
|
9
|
14
|
|
6
|
210
|
155
|
93
|
|
7
|
140
|
53
|
45
|
|
8
|
90
|
6
|
6
|
|
9
|
410
|
159
|
99
|
|
10
|
50
|
18
|
12
|
|
11
|
65
|
16
|
11
|
|
12
|
42
|
29
|
15
|
|
13
|
110
|
28
|
21
|
|
14
|
305
|
98
|
63
|
Find the best regression model to predict the total expenses of a hospital. Discuss the accuracy of this model. Should both variables be included in the model? Why or Why not?