# [R] Linear models and a simple time series

gheine at mathnmaps.com gheine at mathnmaps.com
Thu Aug 16 16:49:50 CEST 2007

```Working on modeling a wild animal population.  Two data vectors:  the herd
count from year to year (estimated by a
sampling procedure), and the number of animals killed by hunters.  Task is
to find the natural growth rate of the herd
(A simplification, but preserves the essentials.)

My question is whether the R procedure lm() is an appropriate tool to
estimate the growth rate.

year       <-1991:2007
killed
<-c(7008,6663,8545,7868,9286,9365,10443,6389,6004,8631,13277,12029,10081,989
9,11023,9926,7000)
herdsize
<-c(50697,54804,46462,42410,43593,42138,43037,44495,45968,47376,45469,38815,
37186,37135,31760,31206,28563)
year.0     <-which(year==1991)
year.1     <-year.0+1
year.ult   <-length(year)
year.penult<-length(year)-1

y<-heardsize[year.1:year.ult]
x<-herdsize[year.0:year.penult]-killed[year.0:year.penult]
LM<-lm(y~bb-1)

summary(LM)

#Call:
#lm(formula = y ~ x - 1)
#
#Residuals:
#   Min     1Q Median     3Q    Max
#-11893  -1114   1137   3553   6069
#
#Coefficients:
#   Estimate Std. Error t value Pr(>|t|)
#bb  1.21217    0.03185   38.05 2.45e-16 ***
#---
#Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#
#Residual standard error: 4372 on 15 degrees of freedom
#Multiple R-Squared: 0.9897,     Adjusted R-squared: 0.9891
#F-statistic:  1448 on 1 and 15 DF,  p-value: 2.453e-16

The model seems to fit the data very well, and I am willing to believe that
a growth rate of 1.21217 gives the best fit
in a least-squares sense.  However, because the dependent and independent
variables are highly correlated, I question whether
the variance calculations are accurate in this case.  Is lm() really the
appropriate tool to be using here?

Any insights would be welcome.

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