Recommend a transformed regression model
The explanatory variable is rainfall (mm), symbol r; the response variable is reservoir inflow (ML), symbol v. 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
| rainfall (mm) | reservoir inflow (ML) |
|---|---|
| 2 | 53 |
| 3 | \(\frac{329}{5}\) |
| 4 | \(\frac{313}{5}\) |
| 5 | \(\frac{417}{5}\) |
| 6 | \(\frac{361}{5}\) |
| 7 | 101 |
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