4 (15 marks) A naturalist for the Alaska Fish and Game Department studies grizzly bears with the goal of maintaining a h

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4 15 Marks A Naturalist For The Alaska Fish And Game Department Studies Grizzly Bears With The Goal Of Maintaining A H 1 (189.79 KiB) Viewed 29 times

4 (15 marks) A naturalist for the Alaska Fish and Game Department studies grizzly bears with the goal of maintaining a healthy population. Measurements on n = 61 bears provided the following summary statistics Variable Weight Body length Neck Girth (kg) (cm) (cm) (cm) Head length Head Width (cm) (cm) Sample mean C 95.52 164.38 55.69 93.39 17.98 31.13 Covariance matrix S 3266.46 1343.97 731.54 1175.50 162.68 238.37 1343.97 721.91 324.25 537.35 80.17 117.73 731.54 324.25 179.28 281.17 39.15 56.80 1175.50 537.35 281.17 474.98 63.73 94.85 162.68 80.17 39.15 63.73 9.95 13.88 238.37 117.73 56.80 94.85 13.88 21.26 (a) Perform a principal component analysis using the covariance matrix. Can the data be effectively summarized in fewer than six dimensions? (5 marks) (b) Perform a principal component analysis using the correlation matrix. (5 marks) (c) Comment on the similarities and differences between the two analyses. (5 marks)