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bachelor in business administration
Polytechnic State University Sanluis
Jan-2006 - Nov-2010
CPA
Polytechnic State University
Jan-2012 - Nov-2016
Professor
Harvard Square Academy (HS2)
Mar-2012 - Present
A mixture of sucrose and water was heated on a hot plate, and the temperature (in °C) was recorded each minute for 20 minutes by three thermocouples. The results are shown in the following table.
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|
Time |
T1 |
T2 |
T3 |
|
0 |
20 |
18 |
21 |
|
1 |
18 |
22 |
11 |
|
2 |
29 |
22 |
26 |
|
3 |
32 |
25 |
35 |
|
4 |
37 |
37 |
33 |
|
5 |
36 |
46 |
35 |
|
6 |
46 |
45 |
44 |
|
7 |
46 |
44 |
43 |
|
8 |
56 |
54 |
63 |
|
9 |
58 |
64 |
68 |
|
10 |
64 |
69 |
62 |
|
11 |
72 |
65 |
65 |
|
12 |
79 |
80 |
80 |
|
13 |
84 |
74 |
75 |
|
14 |
82 |
87 |
78 |
|
15 |
87 |
93 |
88 |
|
16 |
98 |
90 |
91 |
|
17 |
103 |
100 |
103 |
|
18 |
101 |
98 |
109 |
|
19 |
103 |
103 |
107 |
|
20 |
102 |
103 |
104 |
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a. Compute the least-squares line for estimating the temperature as a function of time, using T1 as the value for temperature.
b. Compute the least-squares line for estimating the temperature as a function of time, using T2 as the value for temperature.
c. Compute the least-squares line for estimating the temperature as a function of time, using T3 as the value for temperature.
d. It is desired to compute a single line to estimate temperature as a function of time. One person suggests averaging the three slope estimates to obtain a single slope estimate, and averaging the three intercept estimates to obtain a single intercept estimate. Find the equation of the line that results from this method.
e. Someone else suggests averaging the three temperature measurements at each time to obtain T =
(T1 + T2 + T3)/3. Compute the least-squares line using T as the value for temperature. f. Are the results of parts (d) and (e) different?
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