One way to think about writing this up, is to imagine you have to write an explanation of your analysis for "Ranger Rick" (some of you may remember this - but otherwise it was (is?) a childern's nature magazine.) While this might be a bit extreme in the degree of simplification, you should focus more on what your results say about pollution. Remember R^2 tells how much of the variation in 1985 PCB levels can be explained by using 1984 levels, but does not tell us anything about whether pollution is increasing, decreasing or staying the same, or anything about the rate of change! Most of you discussed R^2, but stopped short when it came time to explain the rest of the model.
Also, "Ranger Rick Readers" probably have a hard time understanding logarithms (base 10 or natural), so you need to explain the model in the original units -- or explain logarithms....). What does a 1 unit increase in log base 10 of the PCB concentration mean? i.e. if the log(PCB84) = 2, PCB84 = 100 = 10^2; an increase of 1 unit means log(PCB84) = 3 or PCB84 = 1000, an increase of PCBlevels of 10 times. Note the effect is multiplicative in the original units (remember the adder joke? :-)
SO remember to get back the original units you take 10^yhat or 10^log10(PCB85). Then we have,
PCB85(with a 10 fold increase in PCB84) = 10^[b0 + b1 (log10(PCB84) + 1)]
= 10^[b0 + b1 log10(PCB84)]* 10^b1
= PCB85(X=logPCB84) *10^b1
Every 10 fold increase in PCB84 (a 1 unit increase in log PCB levels)
then corresponds to an increase in PCB85 of 10^b1 times. Something to think about in your write up, what are the implications of a model with slope = 1? Is there any evidence in favour of this? What are the implications of a model with intercept = 0? (is this an easier model to explain?!)
For the really energetic student/group. Many of you decided that Deleware was an outlier. If we do leave it out, how well does the model predict it? Find the predicted value for Deleware and a prediction interval -- Is the observed 1985 level in the prediction interval? Make sure, you eventually get back to the original units. If you missed problem 3 on the inclass exam, here is your chance to make it up!