A mixture of sucrose and water was heated on a hot plate,

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}