Data
The raw data of tree ring measurement is shown in Table 3. Based on the provenance, region and year, final summarized data set is in Table 4.
Each sample tree is one sampling unit. The predictor variable is the climatic factors(monthly temperature and precipitation) of the common garden.The response variable is the annual tree ring widths. Since we cannot manipulate climatic conditions in the common garden, in this project we just simply observed the predictor variables (climatic factors) changing. In total, we have 2992 (with 404 missing) tree ring measurements of 50 sample trees from 10 provenances. The range of ring widths is from 0.15 to 7.38 mm; the mean of ring widths is 2.34 and the median is 2.20, standard deviation is 1.10 . The distribution of tree ring width is shown in Graph 1. As the histogram(Graph 1) and QQplot(Graph 2) shows, the distribution of ring width is not perfectly normal for the long right tail.
Tree ring width distributions among regions and years can be found in Graph 3 and Graph 4. Each region has different sample sizes from 272(Alberta) to 1122(Northwestern). The average width among provenances are similar, and there are overlap of the width range. Samples from ON have wide range of tree ring width. The outliers of regions are from year 1996. Annual distribution of ring width(Graph 4) suggest high variation in year 1990-1996 and 2003-2008; the drop in year 1999 and 2002 is very obvious. In general, pattern of tree ring width is increasing before year 2000 and decreasing afterwards.
The average ring width for each provenance and region(Graph 5) indicates that trees origin from AB, ON, and SK have high annual ring widths, but individuals from NS and NW have relative lower widths.
Transformation? Not really. Since we apply non-linear regression to fit the data, there is no very solid assumptions to follow. Although there is unbalanced design, BLUEs can cope this situation.