STATISTICS 3N03/3J04
This test is to be written in the BSB Student Technology Centre. The duration of the test is 2 hours.
Any calculators and one sheet of notes (8.5" x 11", one side only) are permitted.
You may consult any of the web pages for this course, but you may not look at any other web pages, use e-mail or communicate with anyone else.
Use R to do your analyses and draw graphs. Your response to each question should be in the form of a report. Prepare the report in a word processor, integrating graphics and discussion. Include your R code as an appendix at the end of each question. Print out and submit your report at the end of the test period.
Only printed reports will be accepted. Electronic submissions will not be accepted.
Mr Derek Whiteside of the UK Building Research Station recorded the weekly gas consumption (1000s of cubic feet) and average external temperature (degrees Celsius) at his own house in south-east England for two heating seasons, one of 26 weeks before, and one of 30 weeks after cavity-wall insulation was installed. The object of the exercise was to assess the effect of the insulation on gas consumption.
In R, attach the MASS library with the command library(MASS) and you will be then able to use the whiteside data frame. Do an exploratory graphical analysis of the Whiteside dataset, including a graph to compare the temperature-gas consumption relationship before and after insulating.
It might also be interesting to analyse these data as time series; why can't we do that?
Question 2
A study was done to study the sorption of the herbicide trifluralin. The factors were the initial trifluralin concentration (15, 40 100 M) and the Fe2+:H2O2 delivery ratio (1:0, 1:1, 1:5, 1:10). The outcome measured was the % sorption with 3 replications for each treatment. Analyse the data graphically.
| Delivery ratio | |||||
| 1:0 | 1:1 | 1:5 | 1:10 | ||
| Initial Concentration | 15M | 10.90, 8.47, 12.43 | 3.33, 2.40, 2.67 | 0.79, 0.76, 0.84 | 0.54, 0.69, 0.57 |
| 40M | 6.84, 7.68, 6.79 | 1.72, 1.55, 1.82 | 0.68, 0.83, 0.89 | 0.58, 1.13, 1.28 | |
| 100M | 6.61, 6.66, 7.43 | 1.25, 1.46, 1.49 | 1.17, 1.27, 1.16 | 0.93, 0.67, 0.80 |
The file series_b.txt includes three artificially generated time series. The series are unrelated to each other so you should study each one separately. Plot each series with and without smoothing and, using graphical methods, determine if it the observations are independent, autocorrelated with lag 1, or autocorrelated with lag > 1. Does a log transformation help you interpret any of the series? Was smoothing useful in these examples?