Using Rstudio and data from dataset shown below for a sample of birds taken last year, if the average tail and wing length are given for the past have centuries:

Years [1900-1950] : ' = [170, 240]

Years [1950-2000]: ' = [190, 280]

a) provide the S and S -1 matrices, is there a correlation between the X1 ,and X2 variables, how can you tell?

b) Which part of the century is the sample most like, if any? What tests would you conduct as a researcher based on the information above, and how do you interpret your findings?

c) Determine the length and directions of the 95% confidence region

d) Sketch the confidence interval for tail and wing length on a graph.

e) Sketch (using Powerpoint,Word or R), the two dimensional confidence ellipsoid based on the axis. You do not need to use R, although you can if you want. This is a test of your understanding of what the confidence ellipsoid looks like.

#Data was collected from birds regarding their tail and wing length.

# Col. 1: x1 = tail length # Col. 2: x2 = wing length

Col. 1	Col.2
191	284
197	285
208	288
180	273
180	275
188	280
210	283
196	288
191	271
179	257
208	289
202	285
200	272
192	282
199	280
186	266
197	285
201	295
190	282
209	305
187	285
207	297
178	268
202	271
205	285
190	280
189	277
211	310
216	305
189	274
173	271
194	280
198	300
180	272
190	292
191	286
196	285
207	286
209	303
179	261
186	262
174	245
181	250
189	262
188	258