Recommend a transformed regression model
The explanatory variable is input setting (units), symbol i; the response variable is signal power (mW), symbol P. Fit each candidate to the displayed raw observations, using exact square and reciprocal values. Round each base-10 logarithmic coordinate to three decimal places before fitting; retain full coefficients of that fit. Report explained variation to the nearest whole percentage point on that candidate's fitted response scale
The displayed data contain 6 cases and are used to assess several one-axis transformed regression models
| signal power (mW) | input setting (units) |
|---|---|
| \(\frac{1}{50}\) | 2 |
| \(\frac{1}{5}\) | 3 |
| 20 | 4 |
| 2,000 | 5 |
| 20,000 | 6 |
| 200,000 | 7 |
Each residual plot has a horizontal zero reference line. Use the original explanatory-variable and response-variable roles shown by the axis labels
Use this exercise rule: first reject clear residual structure, then prefer the larger reported percentage among the remaining candidates. If reported percentages tie, use the following reporting preference, from first to last: input square; input reciprocal or response square; input logarithm or response reciprocal; response logarithm. This is a stated task preference, not a universal ranking of transformations. Percentages for different response scales do not describe the same original-response variation