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Linear discriminant Analysis Statistics assignment  STATS 767/302 Assignment 2 This assignment concerns chemical levels found in tissue samples from stranded cetaceans (whales)

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Linear discriminant Analysis Statistics assignment  STATS 767/302 Assignment 2

This assignment concerns chemical levels found in tissue samples from stranded cetaceans (whales). You can read the data in from pollution.csv. The first variable is categorical, indicating whether the animal was stranded on its own, or as part of a mass stranding. If the latter, which of two mass strandings is specified.

 

Perform linear discriminant analysis and make a plot of the first two component scores, coloring the points based on their group. Describe which groups are well separated, and which components separate them.

 

Compute the correlations between the original variables and each discriminant analysis score. Display these in a matrix with row and column labels, and rounded to two decimal places. What are the most important original variables for distinguishing single vs mass strandings? and for distinguishing between the two mass strandings?

 

Use the three group model, but consider prediction of whether a dolphin is from a single or mass stranding. What is your estimate of the error rate based on cross validation? Why do we prefer this error rate to the one based on all the data?

 

Compute the correlation matrix for the original variables, and make a coloured tile plot of the matrix, with rows and columns labeled with the variable names. Based on this and your observations in (2), pick two variables to use in a QDA to distinguish mass and single strandings. Explain why you have chosen these two variables.

Explain why we could not use all the variables in a QDA. What would be a reason to consider QDA rather than LDA? How strong is that reason here? Compute the cross validation error rate for QDA. Does it improve on the prediction?

 

Group   Sum_6Indicator.PCBs     PBDE_Sum          SumDDT               Dieldrin HCB        Mirex    Oxychlordane

Single    9600       345         3.735     0.033     0.028     0.12        0.005

Single    8400       325.6     7.729     0.14        0.11        0.77        0.029

Live Mass 1         10000    332.5     60.96     0.059     0.11        3.9          0.093

Live Mass 1         3600       131.5     15.807   0.023     0.043     1.6          0.023

Live Mass 1         1600       84.2        3.815     0.027     0.052     0.65        0.005

Live Mass 1         2700       137.9     2.434     0.005     0.013     0.44        0.005

Live Mass 1         3600       125.2     12.013   0.025     0.057     1.1          0.024

Live Mass 1         970         55.6        3.181     0.022     0.04        0.46        0.005

Live Mass 1         3200       107.3     18.399   0.029     0.055     1              0.023

Live Mass 1         5200       248.7     28.486   0.025     0.05        1.7          0.044

Live Mass 1         5700       355.9     34.373   0.13        0.28        1.5          0.076

Single    7800       423.8     8.08        0.054     0.085     0.56        0.037

Live Mass 2         4500       181         9.458     0.018     0.035     1.3          0.014

Live Mass 2         400         28.3        0.476     0.005     0.013     0.36        0.005

Live Mass 2         5600       275.6     21.181   0.059     0.39        3.7          0.054

Live Mass 2         4700       94.9        4.084     0.005     0.018     0.5          0.005

Live Mass 2         3500       39.7        1.149     0.005     0.022     0.4          0.005

Single    10734    556.4     23.253   0.052     0.079     0.45        0.035