Statistics For Engineers And Scientists - 4 Edition - Chapter 7.2 - Problem 16e
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# A mixture of sucrose and water was heated on a hot plate,

Statistics for Engineers and Scientists | 4th Edition

Problem 16E

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}

Accepted Solution
Step-by-Step Solution:

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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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