Solution for problem 16E Chapter 7.2
A mixture of sucrose and water was heated on a hot plate,
Statistics for Engineers and Scientists | 4th Edition
A mixture of sucrose and water was heated on a hot plate, and the temperature (in \({ }^{\circ} \mathrm{C}\)) was recorded each minute for 20 minutes by three thermocouples. The results are shown in the following table.
a. Compute the least-squares line for estimating the temperature as a function of time, using \(T_{1}\) as the value for temperature.
b. Compute the least-squares line for estimating the temperature as a function of time, using \(T_{2}\) as the value for temperature.
c. Compute the least-squares line for estimating the temperature as a function of time, using \(T_{3}\) 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 \(\overline{T}=\left(T_{1}+T_{2}+T_{3}\right) / 3\). Compute the least-squares line using \(\overline{T}\) as the value for temperature.
f. Are the results of parts (d) and (e) different?
Equation Transcription:
Text Transcription:
^oC
T_1
T_2
T_3
T_1
T_2
T_3
overline{T}=(T_1+T_2+T_3)/3
overline{T}
Step 1 of 7
Given:
The temperatures of a heated mixture of sucrose and water are recorded in degrees Celsius at different times.
Chapter 7.2, Problem 16E is Solved
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A mixture of sucrose and water was heated on a hot plate,