Statistics 3N03 - Test #1 Solutions

1999-10-09


I have done the analyses in Splus rather than MINITAB because the Splus graphs look nice on the screen and because the BSB lab closes early on Friday so I couldn't get in to use MINITAB.

The discussion of a graph should point out any particularly interesting features that say something about the process being studied. A general description of the graph isn't necessary, it would be redundant when you can look at the graph.

[Marks are indicated in red. Full marks = 30]

Q1 [5 for two plots, 5 for discussion]

Protopectin is definitely less at 21 days than at 0 days; at intermediate storage times (7 and 14 days) it is very variable.

The difference between lots is worrisome, especially as the median and hinge spread of protopectin level seem to be decreasing with lot number. This needs further study because it it turns out that there are significant differences between lots, a more elaborate experimental design will be required.

Q2 [6 for at least two plots, 6 for discussion]

The time series shows either an increasing trend, or a change in the mean level around the 60th observation. It is hard to say which has happened. The change in the mean level is shown by the second plot, which has a line through the overall mean level and separate lines through the means of observations 1-60 and observations 61-80.

The lag-1 plot shows very little evidence of autocorrelation, suggesting that the observed fluctuations are random noise.

A box plot to compare observations 1 to 60 with observations 61 to 80 suggests that, if the median level rose around the 60th observation in the sequence, then it rose by about 2 units. This is consistent with the stem-and-leaf plot of the whole series, which shows a long right tail due to the high observations at the end of the series.

N = 80   Median = 15.31
Quartiles = 14.455, 16.385
 
Decimal point is at the colon
 
   12 : 34
   12 :
   13 :
   13 : 5677889999
   14 : 01113334
   14 : 555566777999
   15 : 11111233344
   15 : 556777788
   16 : 011112334
   16 : 57889
   17 : 12334
   17 : 55688
   18 : 0123

Q3 [4 for a plot, 4 for discussion]

There is not a lot to say here. The scatterplot matrix does not show any strong relationships. It doesn't help that some variables are measured rather coarsely; e.g. HC has only 4 distinct values in this sample.

There is a weak negative relation between wind and solar radiation, and very weak positive relations between CO and NO, NO2 and O3. The scale used makes it difficult to say anything about HC.


Statistics 3N03