A weighted straight-line fit to twelve points gives slope with

PHYSICS · Subjective · Fermi University Physics · Scientific Practice & Experimental Methods · Data analysis and model fitting in the laboratory · Data analysis and model fitting in the laboratory

Measurement and Method, Ch Graphs, straight lines and least squares

Problem

A weighted straight-line fit to twelve points gives slope m=(2.50±0.04) mV K−1m=(2.50\pm0.04)\,\mathrm{mV\,K^{-1}} with χ2=30.0\chi^2=30.0. The residual plot shows no arch, no trend and no single point far from the rest, and a search of the apparatus and the notebook finds no cause. Find ν\nu and χν2\chi^2_\nu. Decide whether to apply the inflation factor; if so, find it and the inflated u(m)u(m). State in one sentence what the inflated uncertainty concedes. Had the residuals instead formed an arch, with the same χ2\chi^2, would inflation be the right response? Say why.

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