Stat 301 – Fall 2015 - HW 10 answers
1. Predicting MTBE in drinking water wells
a. 2 pts. Using AICc, the model should include IndPct and Depth
b. 1 pt. The second best model is only 0.18 units different from the best model. You should not
ignore the second best model.
Note: AICc values are 1155.59 for the best model and 1155.77 for the second best with only IndPct.
c. 1 pt. Using BIC, the best model has only IndPct.
d. 2 pts. 1158.28. That’s more than 2 from the best but less than 10 from the best. It’s in a grey zone.
Can probably ignore, unless there is a strong subject-matter reason to consider.
Note: Also acceptable to say, yes can ignore because AICc is more than 2 from the best.
e. 2 pts. 1193.97. Yes, can ignore this model. AICc is more than 10 from the best.
f. 1 pt. All 8 variables are included in the model.
g. 2 pts. IndPct & Depth: 5386.0,
IndPct: 5348.06,
DissOxy, IndPct, Depth, and Distance: 5559.34
Depth: 5736.59
all 8: 5698.09
The model with IndPct only makes the best out-of-sample predictions.
h. 1 pt. Various answers are possible and were accepted if accompanied by a valid reason.
I would use IndPct and Depth or just IndPct because they have the lowest AICc or BIC statistics.
Note: Actually, because of part i and what I know about MTBE, I would fix those issues, then reconsider
the variable selection.
i. 2 pts. Our answers are based on the model with IndPct and Depth. Different models have similar
issues. We see: residual vs predicted value plot is not flat. There are some huge standardized residuals,
exceeding 8. No concerns in the Cook’s D plot (largest D is about 0.5).
2. Was MTBE detected?
a. 1 pt. 21.8% of private wells are “Detect” samples.
Note: If you answered 33.0% or something close to that, you looked at all wells, not just the private
wells.
b. 1 pt. (14.1%, 32.2%) Or: (14%, 32%).
c. 3 pts. Chi-square statistic: 7.468, p: 0.0063.
Strong evidence that the proportion of “Detect” samples is different in public and private wells.
Note: If you answered with Chi-square: 7.697, p: 0.0055, you reported the Likelihood Ratio statistic
(what some call the g-statistic) not the Chi-square statistic.
d. 1 pt. No issues using the Chi-square statistic. All expected counts are larger than 5.