Comparing two fitted models, residuals relative to scatter, classification, extrapolation
freshwater monitoring
A regional council monitors streams in two catchments, Awa A (bush-covered) and Awa B (mostly pasture). For 30 samples from each, water temperature (°C) and dissolved oxygen (DO, mg/L) were recorded. Temperatures ranged from 8 to 22 °C. Figure 1 shows the data with the fitted lines, and Figure 2 shows the residuals from each line. Linear models:
Awa A: DO=13.814−0.2957T, r=−0.981, residual SD =0.270 mg/L
Awa B: DO=10.993−0.2154T, r=−0.950, residual SD =0.329 mg/L
A sample bottle lost its label (S1 in Figure 1). It recorded T=15.0 °C and DO =9.5 mg/L. A second unlabelled reading (S2) was T=24.5 °C, DO =7.0 mg/L.
Scatterplot of dissolved oxygen (mg/L) against water temperature (8 to 22 °C) for 30 samples from each of Awa A and Awa B, with the two fitted lines; both relationships are negative and linear, Awa A is higher and steeper, and the lines converge as temperature rises. The two unlabelled readings S1 and S2 are marked.Residual plot: residuals (mg/L) from each catchment's fitted line against water temperature (8 to 22 °C), Awa A as filled blue dots and Awa B as open red circles. Both sets are scattered evenly about 0 with no curve or fan shape. Awa A residuals lie between about −0.43 and +0.61 mg/L, Awa B between about −0.59 and +0.56 mg/L. No samples lie above 22 °C.Facts you may need
(a)
Use Figures 1 and 2 and the models to compare the relationships between temperature and DO in the two catchments.
(b)
Use both models to decide which catchment the 15.0 °C sample most likely came from. Justify with calculations.
(c)
Repeat for the 24.5 °C reading (S2) and discuss how confident you can be.
(d)
Explain ONE other reason DO readings could mislead the classification.
