Suppose that a square-law circuit has the input–output relationship

where x is the input voltage and y is the output voltage.

(a) Derive a least-squares procedure for calculating k.

(b) Experimentation with the circuit yields the following data pairs:

Find the least-squares value for k for these data.

(c) To illustrate the effects of erroneous data, suppose that an additional data point, x = 1.5 and y = 3.30, is taken. From part (b) We know that for x = 1.5, y should be approximately 2.25. Hence the additional data point is erroneous, assuming that the data in part (b) Are accurate. Find the percent error in k n using the four data pairs, as compared to the value calculated in part (b).

Transcribed Image Text:

y = kx