### Find the least squares regression line

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10. The operation manager of a musical instrument distributor wishes that demand for bass drums may be related to the number of television appearance through 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?
11. 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.
12) 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 Admissions 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?

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