Question

In: Statistics and Probability

solve using r and Consider the data birds.txt. A wildlife ecologist measured X1 = Tail length...

solve using r and

Consider the data birds.txt. A wildlife ecologist measured X1 = Tail length (in millimeters)

and X2 = Wing length (in millimeters) for a sample of n = 45 female hook-billed kites.

(a) Evaluate the sample mean vector x.

(b) Evaluate the sample variance-covariance matrix, S.

(c) Determine the eigenvalue and eigenvector pairs for S.

(d) Evaluate the sample correlation matrix R. Interpret the sample correlation, r12.

the data is

Tail  Wing 
  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

Solutions

Expert Solution

> Tail<-c(191,197,208,180,180,188,210,196,191,179,208,202,200,192,199,186,197,201,190,209,187,207,178,202,205,190,189,211,216,189,173,194,198,180,190,191,196,207,209,179,186,174,181,189,188)
> Wing<-c(284,285,288,273,275,280,283,288,271,257,289,285,272,282,280,266,285,295,282,305,285,297,268,271,285,280,277,310,305,274,271,280,300,272,292,286,285,286,303,261,262,245,250,262,258)
> A<-data.frame(Tail,Wing)

a.

> mean(Tail)
[1] 193.6222
> mean(Wing)
[1] 279.7778
b.

> var(Tail)
[1] 120.6949
> var(Wing)
[1] 208.5404
> cov(A)
Tail Wing
Tail 120.6949 122.3460
Wing 122.3460 208.5404
c.

> eigen(B)
eigen() decomposition
$values
[1] 294.60898 34.62637

$vectors
[,1]    [,2]
[1,] 0.5753739 -0.8178905
[2,] 0.8178905 0.5753739
d.

> cor(A)
Tail Wing
Tail 1.0000000 0.7711697
Wing 0.7711697 1.0000000
The correlation between Tail Length and Wing Length for the female Hook-billed Kites is 77.11697%, a Fairly Strong relation between the two variables

orchestra answered 1 year ago
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