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# Accurate estimate for the intercept? For the slope?

Two scientists want to measure the resistivity, R(T), of a material as a function of temperature. They assume that R(T) = a1+a2T, where a1 and a2 are the constants to be determined. The first scientist measures R for temperatures T = 0°, 10°, 20°, ..., 100°. The second performs the measurement at T = 0°, 100°, ..., 400°. Assuming that they use the same instruments and that the measurement error is constant, which scientist will obtain the more accurate estimate for the intercept? For the slope?

#### Solution Preview

Dear Student,

Please try to understand in the following two cases. I have described a bit elaborately for the sake of simplicity. Let us consider that measured resistances for the two cases may be written as 1RT and 2RT at temperature T, constants 1a2 and 2a2 are constants for the two temperature ranges.

(a) T Range = 0 to 100 in steps of 10
Measured values will be:
1R0 = 0. 1a2 + 1a1
1R10 = 10. 1a2 + 1a1 (Here, 1a2 and 1a1 are constant for this set.)
1R20 = ...

#### Solution Summary

This solution explains how to measure the resistivity.

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