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.

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 TÌ… = (T₁ + T₂ + T₃)/3. Compute the least-squares line using TÌ… as the value for temperature.

f. Are the results of parts (d) and (e) different?

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Time T, T2 T3 20 18 21 18 22 11 29 22 26 3 32 25 35 37 37 33 5 36 46 35 46 45 44 46 44 43 56 54 63 9. 58 64 68 64 10 69 62 72 11 65 65 12 79 80 80 13 84 74 75 14 82 87 78 15 87 93 88 16 98 90 91 17 103 100 103 101 98 109 107 18 19 103 103 103 20 102 104