We Helped With This Statistics Homework: Have A Similar One?

GLY 429/529 _– Assignment #5

Report due in class or in my mailbox by 5:00 pm: April 11

You now want to investigate whether there are spatial patterns to the overall concentration data at the Jura site.  This analysis is difficult to do directly using the concentration data since there are seven different metals (i.e., seven different maps) that you would need to compare and analyze to try and find trends.  To simplify the analysis and help you identify trends you will try to reduce the number of variables by using principal component analysis (PCA).  You also want to determine whether land use or rock type could be a useful indicator for different contaminant zones.

In your report, make sure to complete the following tasks:

(1)               Perform PCA using the data covariance matrix and determine which principal

(2)               Map the variation of the principal component scores for your data.  Do you components are most important for representing your data.  Evaluate which of the concentration variables contribute to the dominant principal components. [10 pts]        

see any trends?  (Hint: use the function “scatter” with ‘filled’ option.) [10 pts]

Graduate Students Only

(3)               Determine if there is a relationship between the principal components and

b. Qualitatively determine if your data fall into distinct groups that are land use or rock type:  

a.     Make a qualitative assessment by comparing maps of the principal   against each other and make the color of each point in the scatter plot scores versus maps of rock type and land use. [10 pts]   related to land use or rock type by plotting the principal components

represent land use or rock type.  (Hint: use the function scatter or scatter3.) [10 pts]

c.  Make a quantitative assessment of whether the concentration data fall

into groups related to land use or rock type by comparing the conditional cdfs for the PCA scores.  (Do this for at minimum 2 principal components, that with the highest and that with the lowest

 weight.) [10 pts]