abt181 week4
2025-02-02
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if (!require("rspat")) remotes::install_github('rspatial/rspat')## Loading required package: rspat## Loading required package: terra## terra 1.8.10## Loading required package: rspat
## Loading required package: terra
## terra 1.8.8library(rspat)
d <- spat_data('precipitation')
head(d)## ID NAME LAT LONG ALT JAN FEB MAR APR MAY JUN JUL
## 1 ID741 DEATH VALLEY 36.47 -116.87 -59 7.4 9.5 7.5 3.4 1.7 1.0 3.7
## 2 ID743 THERMAL/FAA AIRPORT 33.63 -116.17 -34 9.2 6.9 7.9 1.8 1.6 0.4 1.9
## 3 ID744 BRAWLEY 2SW 32.96 -115.55 -31 11.3 8.3 7.6 2.0 0.8 0.1 1.9
## 4 ID753 IMPERIAL/FAA AIRPORT 32.83 -115.57 -18 10.6 7.0 6.1 2.5 0.2 0.0 2.4
## 5 ID754 NILAND 33.28 -115.51 -18 9.0 8.0 9.0 3.0 0.0 1.0 8.0
## 6 ID758 EL CENTRO/NAF 32.82 -115.67 -13 9.8 1.6 3.7 3.0 0.4 0.0 3.0
## AUG SEP OCT NOV DEC
## 1 2.8 4.3 2.2 4.7 3.9
## 2 3.4 5.3 2.0 6.3 5.5
## 3 9.2 6.5 5.0 4.8 9.7
## 4 2.6 8.3 5.4 7.7 7.3
## 5 9.0 7.0 8.0 7.0 9.0
## 6 10.8 0.2 0.0 3.3 1.4## ID NAME LAT LONG ALT JAN FEB MAR APR MAY JUN JUL
## 1 ID741 DEATH VALLEY 36.47 -116.87 -59 7.4 9.5 7.5 3.4 1.7 1.0 3.7
## 2 ID743 THERMAL/FAA AIRPORT 33.63 -116.17 -34 9.2 6.9 7.9 1.8 1.6 0.4 1.9
## 3 ID744 BRAWLEY 2SW 32.96 -115.55 -31 11.3 8.3 7.6 2.0 0.8 0.1 1.9
## 4 ID753 IMPERIAL/FAA AIRPORT 32.83 -115.57 -18 10.6 7.0 6.1 2.5 0.2 0.0 2.4
## 5 ID754 NILAND 33.28 -115.51 -18 9.0 8.0 9.0 3.0 0.0 1.0 8.0
## 6 ID758 EL CENTRO/NAF 32.82 -115.67 -13 9.8 1.6 3.7 3.0 0.4 0.0 3.0
## AUG SEP OCT NOV DEC
## 1 2.8 4.3 2.2 4.7 3.9
## 2 3.4 5.3 2.0 6.3 5.5
## 3 9.2 6.5 5.0 4.8 9.7
## 4 2.6 8.3 5.4 7.7 7.3
## 5 9.0 7.0 8.0 7.0 9.0
## 6 10.8 0.2 0.0 3.3 1.4mnts <- toupper(month.abb)
d$prec <- rowSums(d[, mnts])
plot(sort(d$prec), ylab="Annual precipitation (mm)", las=1, xlab="Stations")
dsp <- vect(d, c("LONG", "LAT"), crs="+proj=longlat +datum=NAD83")
CA <- spat_data("counties")
# define groups for mapping
cuts <- c(0,200,300,500,1000,3000)
# set up a palette of interpolated colors
blues <- colorRampPalette(c('yellow', 'orange', 'blue', 'dark blue'))
plot(CA, col="light gray", lwd=4, border="dark gray")
plot(dsp, "prec", type="interval", col=blues(10), legend=TRUE, cex=2,
breaks=cuts, add=TRUE, plg=list(x=-117.27, y=41.54))
lines(CA)
TA <- "+proj=aea +lat_1=34 +lat_2=40.5 +lat_0=0 +lon_0=-120 +x_0=0 +y_0=-4000000 +datum=WGS84 +units=m"
dta <- project(dsp, TA)
cata <- project(CA, TA)RMSE <- function(observed, predicted) {
sqrt(mean((predicted - observed)^2, na.rm=TRUE))
}null <- RMSE(mean(dsp$prec), dsp$prec)
null## [1] 435.3217## [1] 435.3217v <- voronoi(dta)
plot(v)
points(dta)
vca <- crop(v, cata)
plot(vca, "prec")
r <- rast(vca, res=10000)
vr <- rasterize(vca, r, "prec")
plot(vr)
## Set the random number seed so that the numbers generated each time make the experiment repeatable
set.seed(5132015)
## Randomly divide the data set into five subsets to ensure that each data has a chance to be used as a test set
kf <- sample(1:5, nrow(dta), replace=TRUE)
## Create a vector of length 5 to store the mean square error of each cross-validation, with the initial value being NA
rmse <- rep(NA, 5)
## Each cycle represents a different cross-validation
for (k in 1:5) {
## Select the current subset as the test set
test <- dta[kf == k, ]
## Select a training set other than the test set
train <- dta[kf != k, ]
## Generate spatial distribution map using training set
v <- voronoi(train)
## Extract the predicted values of the test set from the spatial segmentation map
p <- extract(v, test)
## Calculate the mean square error between the actual value and the predicted value in the test set, and store it in rmse[k]
rmse[k] <- RMSE(test$prec, p$prec)
}
## Output five values of rmse
rmse## [1] 192.0568 203.1304 183.5556 177.5523 205.6921## [1] 192.0568 203.1304 183.5556 177.5523 205.6921
## Calculate the average of rmse
mean(rmse)## [1] 192.3974## [1] 192.3974
# relative model performance
## Compute the relative performance of a model
perf <- 1 - (mean(rmse) / null)
## Round to three decimal places
round(perf, 3)## [1] 0.558## [1] 0.558Question 1: Describe what each step in the code chunk above does (that is, how does cross-validation work?) Ans: see above
Question 2: How does the proximity-polygon approach compare to the NULL model? Ans: The rmse in NULL model is 435.3217, which assumes that its predicted value is the average of all data. This model does not have any complex features. It can only be used as a benchmark model to evaluate whether other models are effective. But the rmse in the proximity-polygon approach is 192.3947. This model is based on the proximity of spatial data, and it can make more accurate predictions based on spatial data.
Question 3: You would not typically use proximty polygons for rainfall data. For what kind of data might you use them? Ans: Vegetation coverage and species distribution are more sensitive to spatial information. Resource allocation data could also use this method to divide regions for emergency services such as nearest hospital and fire station. Proximity polygons are most useful when the variable being measured is assumed to be constant within the nearest station’s influence zone. Spatial relationships can be used to give more accurate predictions.
library(gstat)
d <- data.frame(geom(dta)[,c("x", "y")], as.data.frame(dta))
head(d)## x y ID NAME ALT JAN FEB MAR APR MAY JUN
## 1 280058.6 -167265.5 ID741 DEATH VALLEY -59 7.4 9.5 7.5 3.4 1.7 1.0
## 2 355394.7 -480020.3 ID743 THERMAL/FAA AIRPORT -34 9.2 6.9 7.9 1.8 1.6 0.4
## 3 416370.9 -551681.2 ID744 BRAWLEY 2SW -31 11.3 8.3 7.6 2.0 0.8 0.1
## 4 415173.4 -566152.9 ID753 IMPERIAL/FAA AIRPORT -18 10.6 7.0 6.1 2.5 0.2 0.0
## 5 418432.1 -516087.7 ID754 NILAND -18 9.0 8.0 9.0 3.0 0.0 1.0
## 6 405858.6 -567692.3 ID758 EL CENTRO/NAF -13 9.8 1.6 3.7 3.0 0.4 0.0
## JUL AUG SEP OCT NOV DEC prec
## 1 3.7 2.8 4.3 2.2 4.7 3.9 52.1
## 2 1.9 3.4 5.3 2.0 6.3 5.5 52.2
## 3 1.9 9.2 6.5 5.0 4.8 9.7 67.2
## 4 2.4 2.6 8.3 5.4 7.7 7.3 60.1
## 5 8.0 9.0 7.0 8.0 7.0 9.0 78.0
## 6 3.0 10.8 0.2 0.0 3.3 1.4 37.2## x y ID NAME ALT JAN FEB MAR APR MAY JUN
## 1 280058.6 -167265.5 ID741 DEATH VALLEY -59 7.4 9.5 7.5 3.4 1.7 1.0
## 2 355394.7 -480020.3 ID743 THERMAL/FAA AIRPORT -34 9.2 6.9 7.9 1.8 1.6 0.4
## 3 416370.9 -551681.2 ID744 BRAWLEY 2SW -31 11.3 8.3 7.6 2.0 0.8 0.1
## 4 415173.4 -566152.9 ID753 IMPERIAL/FAA AIRPORT -18 10.6 7.0 6.1 2.5 0.2 0.0
## 5 418432.1 -516087.7 ID754 NILAND -18 9.0 8.0 9.0 3.0 0.0 1.0
## 6 405858.6 -567692.3 ID758 EL CENTRO/NAF -13 9.8 1.6 3.7 3.0 0.4 0.0
## JUL AUG SEP OCT NOV DEC prec
## 1 3.7 2.8 4.3 2.2 4.7 3.9 52.1
## 2 1.9 3.4 5.3 2.0 6.3 5.5 52.2
## 3 1.9 9.2 6.5 5.0 4.8 9.7 67.2
## 4 2.4 2.6 8.3 5.4 7.7 7.3 60.1
## 5 8.0 9.0 7.0 8.0 7.0 9.0 78.0
## 6 3.0 10.8 0.2 0.0 3.3 1.4 37.2
gs <- gstat(formula=prec~1, locations=~x+y, data=d, nmax=5, set=list(idp = 0))
nn <- interpolate(r, gs, debug.level=0)
nnmsk <- mask(nn, vr)
plot(nnmsk, 1)
rmsenn <- rep(NA, 5)
for (k in 1:5) {
test <- d[kf == k, ]
train <- d[kf != k, ]
gscv <- gstat(formula=prec~1, locations=~x+y, data=train, nmax=5, set=list(idp = 0))
p <- predict(gscv, test, debug.level=0)$var1.pred
rmsenn[k] <- RMSE(test$prec, p)
}
rmsenn## [1] 215.0993 209.5838 197.0604 177.1946 189.8130## [1] 215.0993 209.5838 197.0604 177.1946 189.8130
mean(rmsenn)## [1] 197.7502## [1] 197.7502
1 - (mean(rmsenn) / null)## [1] 0.5457377## [1] 0.5457377library(gstat)
gs <- gstat(formula=prec~1, locations=~x+y, data=d)
idw <- interpolate(r, gs, debug.level=0)
idwr <- mask(idw, vr)
plot(idwr, 1)
Question 4: IDW generated rasters tend to have a noticeable artefact. What is that and what causes that? Ans: The IDW method works by giving more weight to nearby points and less to distant ones when making predictions. Because of this, the closest points can strongly influence the result, even if they are not evenly spread out. In areas with few data points, the interpolation may create unnatural “ripple” patterns, leading to distortions.
rmse <- rep(NA, 5)
for (k in 1:5) {
test <- d[kf == k, ]
train <- d[kf != k, ]
gs <- gstat(formula=prec~1, locations=~x+y, data=train)
p <- predict(gs, test, debug.level=0)
rmse[k] <- RMSE(test$prec, p$var1.pred)
}
rmse## [1] 243.3256 212.6271 206.8982 180.1827 207.5791## [1] 243.3256 212.6271 206.8982 180.1827 207.5791
mean(rmse)## [1] 210.1225## [1] 210.1225
1 - (mean(rmse) / null)## [1] 0.5173166## [1] 0.5173166Question 5: Inspect the arguments used for and make a map of the IDW model below. What other name could you give to this method (IDW with these parameters)? Why? Illustrate with a map Ans: Nearest Neighbor Interpolation. Because nmax=1 means that only the single nearest observation point is used for interpolation.
library(gstat)
## formula=prec~1 is the precipitation
## locations=~x+y: x and y are the coordinate variables, and prec will be interpolated based on these coordinates.
## data=d: Contains the observed values of prec and the corresponding spatial coordinates x and y.
## nmax=1: The IDW interpolation method uses only the nearest point for interpolation.
## set=list(idp=1): Sets the power parameter for IDW. idp=1 means inverse distance weighting.
gs2 <- gstat(formula=prec~1, locations=~x+y, data=d, nmax=1, set=list(idp=1))
idw <- interpolate(r, gs2, debug.level=0)
idwr <- mask(idw, vr)
plot(idwr, 1)
x <- rspat::spat_data("airqual")
x$OZDLYAV <- x$OZDLYAV * 1000
x <- vect(x, c("LONGITUDE", "LATITUDE"), crs="+proj=longlat +datum=WGS84")TAkm <- "+proj=aea +lat_1=34 +lat_2=40.5 +lat_0=0 +lon_0=-120 +x_0=0 +y_0=-4000000 +datum=WGS84 +units=km"
aq <- project(x, TAkm)ca <- project(CA, TAkm)
r <- rast(ca)
res(r) <- 10 # 10 km if your CRS's units are in kmp <- data.frame(geom(aq)[, c("x", "y")], as.data.frame(aq))
gs <- gstat(formula=OZDLYAV~1, locations=~x+y, data=p)
v <- variogram(gs, width=20)
v## np dist gamma dir.hor dir.ver id
## 1 1010 11.35040 34.80579 0 0 var1
## 2 1806 30.63737 47.52591 0 0 var1
## 3 2355 50.58656 67.26548 0 0 var1
## 4 2619 70.10411 80.92707 0 0 var1
## 5 2967 90.13917 88.93653 0 0 var1
## 6 3437 110.42302 84.13589 0 0 var1
## 7 3581 130.07080 80.59402 0 0 var1
## 8 3808 149.75625 97.06451 0 0 var1
## 9 3589 170.13526 102.97593 0 0 var1
## 10 3569 189.70054 108.28135 0 0 var1
## 11 3489 210.01413 107.48915 0 0 var1
## 12 3583 230.17040 101.95520 0 0 var1
## 13 3529 250.22845 103.06846 0 0 var1
## 14 3394 269.58370 103.63122 0 0 var1
## 15 3267 290.04602 108.81122 0 0 var1
## 16 3046 309.73363 107.58961 0 0 var1
## 17 2824 329.92996 109.52365 0 0 var1
## 18 2860 349.91455 104.27218 0 0 var1
## 19 2641 369.71992 94.76248 0 0 var1
## 20 2430 389.97879 107.47451 0 0 var1
## 21 2570 409.87266 102.55504 0 0 var1
## 22 2385 429.90866 101.55894 0 0 var1
## 23 1584 446.54929 105.00524 0 0 var1## np dist gamma dir.hor dir.ver id
## 1 1010 11.35040 34.80579 0 0 var1
## 2 1806 30.63737 47.52591 0 0 var1
## 3 2355 50.58656 67.26548 0 0 var1
## 4 2619 70.10411 80.92707 0 0 var1
## 5 2967 90.13917 88.93653 0 0 var1
## 6 3437 110.42302 84.13589 0 0 var1
## 7 3581 130.07080 80.59402 0 0 var1
## 8 3808 149.75625 97.06451 0 0 var1
## 9 3589 170.13526 102.97593 0 0 var1
## 10 3569 189.70054 108.28135 0 0 var1
## 11 3489 210.01413 107.48915 0 0 var1
## 12 3583 230.17040 101.95520 0 0 var1
## 13 3529 250.22845 103.06846 0 0 var1
## 14 3394 269.58370 103.63122 0 0 var1
## 15 3267 290.04602 108.81122 0 0 var1
## 16 3046 309.73363 107.58961 0 0 var1
## 17 2824 329.92996 109.52365 0 0 var1
## 18 2860 349.91455 104.27218 0 0 var1
## 19 2641 369.71992 94.76248 0 0 var1
## 20 2430 389.97879 107.47451 0 0 var1
## 21 2570 409.87266 102.55504 0 0 var1
## 22 2385 429.90866 101.55894 0 0 var1
## 23 1584 446.54929 105.00524 0 0 var1
plot(v)
fve <- fit.variogram(v, vgm(85, "Exp", 75, 20))
fve## model psill range
## 1 Nug 21.96600 0.00000
## 2 Exp 85.52957 72.31404## model psill range
## 1 Nug 21.96600 0.00000
## 2 Exp 85.52957 72.31404
plot(variogramLine(fve, 400), type='l', ylim=c(0,120))
points(v[,2:3], pch=20, col='red')
fvs <- fit.variogram(v, vgm(85, "Sph", 75, 20))
fvs## model psill range
## 1 Nug 25.57019 0.0000
## 2 Sph 72.65881 135.7744## model psill range
## 1 Nug 25.57019 0.0000
## 2 Sph 72.65881 135.7744
plot(variogramLine(fvs, 400), type='l', ylim=c(0,120) ,col='blue', lwd=2)
points(v[,2:3], pch=20, col='red')
plot(v, fve)
k <- gstat(formula=OZDLYAV~1, locations=~x+y, data=p, model=fve)
# predicted values
kp <- interpolate(r, k, debug.level=0)
ok <- mask(kp, ca)
names(ok) <- c('prediction', 'variance')
plot(ok)
idm <- gstat(formula=OZDLYAV~1, locations=~x+y, data=p)
idp <- interpolate(r, idm, debug.level=0)
idp <- mask(idp, ca)
plot(idp, 1)
f1 <- function(x, test, train) {
nmx <- x[1]
idp <- x[2]
if (nmx < 1) return(Inf)
if (idp < .001) return(Inf)
m <- gstat(formula=OZDLYAV~1, locations=~x+y, data=train, nmax=nmx, set=list(idp=idp))
p <- predict(m, newdata=test, debug.level=0)$var1.pred
RMSE(test$OZDLYAV, p)
}
set.seed(20150518)
i <- sample(nrow(aq), 0.2 * nrow(aq))
tst <- p[i,]
trn <- p[-i,]
opt <- optim(c(8, .5), f1, test=tst, train=trn)
str(opt)## List of 5
## $ par : num [1:2] 9.259 0.682
## $ value : num 7.86
## $ counts : Named int [1:2] 35 NA
## ..- attr(*, "names")= chr [1:2] "function" "gradient"
## $ convergence: int 0
## $ message : NULL## List of 5
## $ par : num [1:2] 9.259 0.682
## $ value : num 7.86
## $ counts : Named int [1:2] 35 NA
## ..- attr(*, "names")= chr [1:2] "function" "gradient"
## $ convergence: int 0
## $ message : NULLm <- gstat(formula=OZDLYAV~1, locations=~x+y, data=p, nmax=opt$par[1], set=list(idp=opt$par[2]))
idw <- interpolate(r, m, debug.level=0)
idw <- mask(idw, ca)
plot(idw, 1)
library(fields)## Loading required package: spam## Spam version 2.11-1 (2025-01-20) is loaded.
## Type 'help( Spam)' or 'demo( spam)' for a short introduction
## and overview of this package.
## Help for individual functions is also obtained by adding the
## suffix '.spam' to the function name, e.g. 'help( chol.spam)'.##
## Attaching package: 'spam'## The following objects are masked from 'package:base':
##
## backsolve, forwardsolve## Loading required package: viridisLite##
## Try help(fields) to get started.##
## Attaching package: 'fields'## The following object is masked from 'package:terra':
##
## describem <- fields::Tps(p[,c("x", "y")], p$OZDLYAV)
tps <- interpolate(r, m)
tps <- mask(tps, idw[[1]])
plot(tps)
k <- sample(5, nrow(p), replace=TRUE)
ensrmse <- tpsrmse <- krigrmse <- idwrmse <- rep(NA, 5)
for (i in 1:5) {
test <- p[k!=i,]
train <- p[k==i,]
m <- gstat(formula=OZDLYAV~1, locations=~x+y, data=train, nmax=opt$par[1], set=list(idp=opt$par[2]))
p1 <- predict(m, newdata=test, debug.level=0)$var1.pred
idwrmse[i] <- RMSE(test$OZDLYAV, p1)
m <- gstat(formula=OZDLYAV~1, locations=~x+y, data=train, model=fve)
p2 <- predict(m, newdata=test, debug.level=0)$var1.pred
krigrmse[i] <- RMSE(test$OZDLYAV, p2)
m <- Tps(train[,c("x", "y")], train$OZDLYAV)
p3 <- predict(m, test[,c("x", "y")])
tpsrmse[i] <- RMSE(test$OZDLYAV, p3)
w <- c(idwrmse[i], krigrmse[i], tpsrmse[i])
weights <- w / sum(w)
ensemble <- p1 * weights[1] + p2 * weights[2] + p3 * weights[3]
ensrmse[i] <- RMSE(test$OZDLYAV, ensemble)
}## Warning:
## Grid searches over lambda (nugget and sill variances) with minima at the endpoints:
## (GCV) Generalized Cross-Validation
## minimum at right endpoint lambda = 1.582376e-07 (eff. df= 89.30001 )## Warning:
## Grid searches over lambda (nugget and sill variances) with minima at the endpoints:
## (GCV) Generalized Cross-Validation
## minimum at right endpoint lambda = 1.582376e-07 (eff. df= 89.30001 )
rmi <- mean(idwrmse)
rmk <- mean(krigrmse)
rmt <- mean(tpsrmse)
rms <- c(rmi, rmt, rmk)
rms## [1] 8.011006 9.120307 7.736301## [1] 8.011006 9.120307 7.736301
rme <- mean(ensrmse)
rme## [1] 7.936466## [1] 7.936466Question 6: Which method performed best? Ans: Kriging method. The mean value of krigrmse is the smallest, 7.736301.
nullrmse <- RMSE(test$OZDLYAV, mean(test$OZDLYAV))
w <- nullrmse - rms
# normalize weights to sum to 1
weights <- ( w / sum(w) )
# check
sum(weights)## [1] 1## [1] 1
s <- c(idw[[1]], ok[[1]], tps)
ensemble <- sum(s * weights)s <- c(idw[[1]], ok[[1]], tps, ensemble)
names(s) <- c("IDW", "OK", "TPS", "Ensemble")
plot(s)
Question 7: Show where the largest difference exist between IDW and OK.
k <- sample(5, nrow(p), replace=TRUE)
ensrmse <- tpsrmse <- krigrmse <- idwrmse <- rep(NA, 5)
differences <- 0
for (i in 1:5) {
test <- p[k!=i,]
train <- p[k==i,]
m <- gstat(formula=OZDLYAV~1, locations=~x+y, data=train, nmax=opt$par[1], set=list(idp=opt$par[2]))
p1 <- predict(m, newdata=test, debug.level=0)$var1.pred
#idwrmse[i] <- RMSE(test$OZDLYAV, p1)
m <- gstat(formula=OZDLYAV~1, locations=~x+y, data=train, model=fve)
p2 <- predict(m, newdata=test, debug.level=0)$var1.pred
#krigrmse[i] <- RMSE(test$OZDLYAV, p2)
differences = abs(p1 - p2)
m <- Tps(train[,c("x", "y")], train$OZDLYAV)
p3 <- predict(m, test[,c("x", "y")])
#tpsrmse[i] <- RMSE(test$OZDLYAV, p3)
w <- c(idwrmse[i], krigrmse[i], tpsrmse[i])
weights <- w / sum(w)
ensemble <- p1 * weights[1] + p2 * weights[2] + p3 * weights[3]
ensrmse[i] <- RMSE(test$OZDLYAV, ensemble)
}## Warning:
## Grid searches over lambda (nugget and sill variances) with minima at the endpoints:
## (GCV) Generalized Cross-Validation
## minimum at right endpoint lambda = 1.183545e-06 (eff. df= 84.54992 )max_difference_index = max(differences)
print(max_difference_index)## [1] 10.658Question 8: Show the 95% confidence interval of the OK prediction.
k <- sample(5, nrow(p), replace=TRUE)
ensrmse <- tpsrmse <- krigrmse <- idwrmse <- rep(NA, 5)
differences## [1] 1.411608569 3.937328112 3.034505848 0.729141163 1.459503720
## [6] 0.418545273 0.240505002 3.045110806 1.729669325 3.279963997
## [11] 0.874690332 0.114977136 1.708252310 2.157428859 3.152302891
## [16] 0.277672878 1.354996724 0.114998261 0.169252348 1.283272535
## [21] 0.480993757 3.914818517 2.964948390 1.537499642 3.259149362
## [26] 1.557858311 0.994662964 0.217242232 0.534111887 1.339525721
## [31] 3.120571273 0.075375220 0.027832544 2.151939076 3.037389961
## [36] 1.190463966 0.147416326 3.537403956 0.990309770 3.050968947
## [41] 4.780385631 1.141418930 1.798326869 0.001691297 0.239037547
## [46] 0.614546107 0.169924690 3.679623375 4.317153864 1.184922831
## [51] 2.633313606 0.914260914 1.994949947 1.790529873 1.042779597
## [56] 1.581279556 1.400033941 2.302598551 2.852069959 2.105269420
## [61] 1.022337900 1.075030976 1.368477488 9.453100044 2.024183308
## [66] 0.238482961 1.358050004 2.552634885 0.405759859 0.532829417
## [71] 0.530681743 1.193302456 1.294786814 3.292742680 2.774406382
## [76] 1.372369003 0.239504778 2.965542728 1.037680336 1.182127758
## [81] 1.374952105 0.023869453 0.674821436 0.154626704 3.910614629
## [86] 1.258099350 1.444271423 0.364361065 0.778436779 3.822721062
## [91] 1.098391312 0.372664124 3.084432494 0.152490241 1.687606705
## [96] 0.103020269 1.151806123 1.621366499 2.949008481 0.733487220
## [101] 1.547462930 1.837373177 0.167285569 1.615675199 2.845902913
## [106] 1.694827577 0.297545674 0.940459763 0.311654644 0.298786901
## [111] 1.441117803 6.137965209 0.716332280 0.892878852 0.166220299
## [116] 2.965716163 2.576399673 2.500545607 0.144516664 2.333176330
## [121] 1.791265931 1.752474797 1.804970930 2.009815971 2.137571074
## [126] 1.973030230 2.706703831 0.797302973 3.789529634 2.242955469
## [131] 3.005347180 0.779819805 2.285818221 1.455539868 3.044142885
## [136] 0.106019720 2.945961041 1.428530657 2.901839961 0.113837992
## [141] 0.173084710 0.216782439 0.565834232 3.269913382 0.723490910
## [146] 4.659703793 9.368725900 2.195947223 3.347394158 0.485801348
## [151] 3.116740427 0.242913815 3.839942483 0.800626482 0.221032340
## [156] 3.420900794 2.963815969 3.312715267 3.095482162 0.921494568
## [161] 0.119757649 0.007487289 0.448687595 1.602012497 3.206135262
## [166] 1.049888402 2.670747412 2.807052012 2.316167021 2.954603124
## [171] 0.138707317 0.060435285 0.322312631 2.407303728 1.402381787
## [176] 0.835481530 10.658002221 2.661052764 1.695245437 0.384161185
## [181] 3.064220304 3.554899454 0.410583231 0.967734014 1.436683547
## [186] 0.980066113 4.153169344 1.184812089 2.945854746 0.283577223
## [191] 4.312214696 2.168957539 4.403170391 0.915094410 2.994744320
## [196] 1.402314520 1.383201163 2.002009802 0.104520842 2.912793515
## [201] 1.821434801 4.171582633 3.105374137 3.066475226 2.701243435
## [206] 3.315312580 4.128070426 1.258442268 1.382914891 2.975346067
## [211] 2.858787809 4.176753326 9.725252642 1.846423445 1.301743852
## [216] 6.339317473 0.447401343 4.186454917 1.427111238 1.738305091
## [221] 1.734538557 4.162193905 3.564256728 0.211330648 1.965934127
## [226] 1.501208495 4.447641218 4.767596008 1.398961901 2.526932875
## [231] 7.694601165 0.012581843 1.529303668 3.467706129 6.968235035
## [236] 0.158502851 1.697192617 0.859309174 0.750373466 1.174186886
## [241] 3.020261778 1.331396591 0.849320500 0.469617438 0.176951312
## [246] 1.998230908 2.477222594 0.292003877 0.204481643 0.077242305
## [251] 0.079177749 0.079594286 2.986431651 0.763387940 1.105346480
## [256] 4.188898727 3.618677110 1.696877336 0.450086744 2.653229069
## [261] 2.966010103 3.951870037 2.454043564 2.907625473 1.432503810
## [266] 1.210406204 3.798361339 3.215387769 0.209068586 0.211684891
## [271] 1.503844487 1.274256602 1.199440488 1.797190913 0.166434592
## [276] 8.373614700 1.937190546 1.405660794 2.104346738 0.456850126
## [281] 3.419038612 0.273116376 3.743416185 2.499214070 0.443856436
## [286] 2.551557910 1.699500406 1.705141407 2.376519711 1.669376308
## [291] 1.032899081 3.217954642 3.526964616 5.701462721 2.047888185
## [296] 0.441376309 1.310860716 1.368376029 3.023853132 1.268757433
## [301] 3.077094442 2.558740069 4.765521017 1.735731655 4.771748795
## [306] 3.899515163 9.385208023 8.541412371 1.138709034 0.167579683
## [311] 3.365135213 2.897248174 1.317997989 1.767302167 2.379796038
## [316] 0.207447109 3.939516978 3.050555244 4.029599453 0.918826382
## [321] 2.002169597 1.111991049 9.656511494 3.532718600 0.725137329
## [326] 1.303737765 3.399100370 0.083852191 2.396874529 0.128818398
## [331] 1.418671167 1.026144092 4.828648104 6.721013515 2.003902225
## [336] 2.366789241 0.371414107 3.148803127 0.117411102 3.475707826
## [341] 2.987317269 1.617357090 0.196333594 1.801221190 3.017385054
## [346] 0.445090792 1.134560727 3.101304207 2.494306982 1.762819514
## [351] 0.697923626 1.936920218 2.338807833 1.165486701 1.421526634
## [356] 1.073126314for (i in 1:5) {
test <- p[k!=i,]
train <- p[k==i,]
m <- gstat(formula=OZDLYAV~1, locations=~x+y, data=train, model=fve)
p2 <- predict(m, newdata=test, debug.level=0)$var1.pred
#krigrmse[i] <- RMSE(test$OZDLYAV, p2)
standard_errors = 1.0
lower_bound <- p2 - 1.96 * standard_errors # lower bound
upper_bound <- p2 + 1.96 * standard_errors # upper bound
for (i in 1:length(p2)) {
cat("Predicted value at location", i, ":", p2[i],
"95% confidence interval = (", lower_bound[i], ",", upper_bound[i], ")\n")
}
}## Predicted value at location 1 : 34.66343 95% confidence interval = ( 32.70343 , 36.62343 )
## Predicted value at location 2 : 31.03482 95% confidence interval = ( 29.07482 , 32.99482 )
## Predicted value at location 3 : 29.38859 95% confidence interval = ( 27.42859 , 31.34859 )
## Predicted value at location 4 : 24.87789 95% confidence interval = ( 22.91789 , 26.83789 )
## Predicted value at location 5 : 22.60948 95% confidence interval = ( 20.64948 , 24.56948 )
## Predicted value at location 6 : 48.57229 95% confidence interval = ( 46.61229 , 50.53229 )
## Predicted value at location 7 : 36.31084 95% confidence interval = ( 34.35084 , 38.27084 )
## Predicted value at location 8 : 30.62356 95% confidence interval = ( 28.66356 , 32.58356 )
## Predicted value at location 9 : 31.9412 95% confidence interval = ( 29.9812 , 33.9012 )
## Predicted value at location 10 : 28.80151 95% confidence interval = ( 26.84151 , 30.76151 )
## Predicted value at location 11 : 32.66011 95% confidence interval = ( 30.70011 , 34.62011 )
## Predicted value at location 12 : 27.91611 95% confidence interval = ( 25.95611 , 29.87611 )
## Predicted value at location 13 : 24.82951 95% confidence interval = ( 22.86951 , 26.78951 )
## Predicted value at location 14 : 44.91438 95% confidence interval = ( 42.95438 , 46.87438 )
## Predicted value at location 15 : 44.8057 95% confidence interval = ( 42.8457 , 46.7657 )
## Predicted value at location 16 : 23.04962 95% confidence interval = ( 21.08962 , 25.00962 )
## Predicted value at location 17 : 41.27292 95% confidence interval = ( 39.31292 , 43.23292 )
## Predicted value at location 18 : 32.66038 95% confidence interval = ( 30.70038 , 34.62038 )
## Predicted value at location 19 : 33.07006 95% confidence interval = ( 31.11006 , 35.03006 )
## Predicted value at location 20 : 27.51155 95% confidence interval = ( 25.55155 , 29.47155 )
## Predicted value at location 21 : 29.50669 95% confidence interval = ( 27.54669 , 31.46669 )
## Predicted value at location 22 : 28.25006 95% confidence interval = ( 26.29006 , 30.21006 )
## Predicted value at location 23 : 20.42506 95% confidence interval = ( 18.46506 , 22.38506 )
## Predicted value at location 24 : 24.0805 95% confidence interval = ( 22.1205 , 26.0405 )
## Predicted value at location 25 : 27.10241 95% confidence interval = ( 25.14241 , 29.06241 )
## Predicted value at location 26 : 33.02846 95% confidence interval = ( 31.06846 , 34.98846 )
## Predicted value at location 27 : 29.82494 95% confidence interval = ( 27.86494 , 31.78494 )
## Predicted value at location 28 : 25.2989 95% confidence interval = ( 23.3389 , 27.2589 )
## Predicted value at location 29 : 21.87025 95% confidence interval = ( 19.91025 , 23.83025 )
## Predicted value at location 30 : 25.23676 95% confidence interval = ( 23.27676 , 27.19676 )
## Predicted value at location 31 : 33.04358 95% confidence interval = ( 31.08358 , 35.00358 )
## Predicted value at location 32 : 32.79226 95% confidence interval = ( 30.83226 , 34.75226 )
## Predicted value at location 33 : 22.79741 95% confidence interval = ( 20.83741 , 24.75741 )
## Predicted value at location 34 : 34.68188 95% confidence interval = ( 32.72188 , 36.64188 )
## Predicted value at location 35 : 31.26 95% confidence interval = ( 29.3 , 33.22 )
## Predicted value at location 36 : 34.98937 95% confidence interval = ( 33.02937 , 36.94937 )
## Predicted value at location 37 : 33.87224 95% confidence interval = ( 31.91224 , 35.83224 )
## Predicted value at location 38 : 27.03932 95% confidence interval = ( 25.07932 , 28.99932 )
## Predicted value at location 39 : 28.16637 95% confidence interval = ( 26.20637 , 30.12637 )
## Predicted value at location 40 : 30.55688 95% confidence interval = ( 28.59688 , 32.51688 )
## Predicted value at location 41 : 24.87717 95% confidence interval = ( 22.91717 , 26.83717 )
## Predicted value at location 42 : 40.40002 95% confidence interval = ( 38.44002 , 42.36002 )
## Predicted value at location 43 : 36.20769 95% confidence interval = ( 34.24769 , 38.16769 )
## Predicted value at location 44 : 60.48635 95% confidence interval = ( 58.52635 , 62.44635 )
## Predicted value at location 45 : 35.70077 95% confidence interval = ( 33.74077 , 37.66077 )
## Predicted value at location 46 : 41.86446 95% confidence interval = ( 39.90446 , 43.82446 )
## Predicted value at location 47 : 40.92275 95% confidence interval = ( 38.96275 , 42.88275 )
## Predicted value at location 48 : 28.37947 95% confidence interval = ( 26.41947 , 30.33947 )
## Predicted value at location 49 : 37.02123 95% confidence interval = ( 35.06123 , 38.98123 )
## Predicted value at location 50 : 33.67514 95% confidence interval = ( 31.71514 , 35.63514 )
## Predicted value at location 51 : 35.49889 95% confidence interval = ( 33.53889 , 37.45889 )
## Predicted value at location 52 : 42.26351 95% confidence interval = ( 40.30351 , 44.22351 )
## Predicted value at location 53 : 17.16259 95% confidence interval = ( 15.20259 , 19.12259 )
## Predicted value at location 54 : 22.66357 95% confidence interval = ( 20.70357 , 24.62357 )
## Predicted value at location 55 : 31.41278 95% confidence interval = ( 29.45278 , 33.37278 )
## Predicted value at location 56 : 28.56537 95% confidence interval = ( 26.60537 , 30.52537 )
## Predicted value at location 57 : 32.47781 95% confidence interval = ( 30.51781 , 34.43781 )
## Predicted value at location 58 : 39.21029 95% confidence interval = ( 37.25029 , 41.17029 )
## Predicted value at location 59 : 31.71067 95% confidence interval = ( 29.75067 , 33.67067 )
## Predicted value at location 60 : 29.46727 95% confidence interval = ( 27.50727 , 31.42727 )
## Predicted value at location 61 : 28.06809 95% confidence interval = ( 26.10809 , 30.02809 )
## Predicted value at location 62 : 29.9774 95% confidence interval = ( 28.0174 , 31.9374 )
## Predicted value at location 63 : 23.27445 95% confidence interval = ( 21.31445 , 25.23445 )
## Predicted value at location 64 : 23.72079 95% confidence interval = ( 21.76079 , 25.68079 )
## Predicted value at location 65 : 27.96598 95% confidence interval = ( 26.00598 , 29.92598 )
## Predicted value at location 66 : 50.47777 95% confidence interval = ( 48.51777 , 52.43777 )
## Predicted value at location 67 : 41.0676 95% confidence interval = ( 39.1076 , 43.0276 )
## Predicted value at location 68 : 27.80255 95% confidence interval = ( 25.84255 , 29.76255 )
## Predicted value at location 69 : 34.46943 95% confidence interval = ( 32.50943 , 36.42943 )
## Predicted value at location 70 : 29.56731 95% confidence interval = ( 27.60731 , 31.52731 )
## Predicted value at location 71 : 25.20236 95% confidence interval = ( 23.24236 , 27.16236 )
## Predicted value at location 72 : 24.68092 95% confidence interval = ( 22.72092 , 26.64092 )
## Predicted value at location 73 : 18.56539 95% confidence interval = ( 16.60539 , 20.52539 )
## Predicted value at location 74 : 32.39989 95% confidence interval = ( 30.43989 , 34.35989 )
## Predicted value at location 75 : 23.28937 95% confidence interval = ( 21.32937 , 25.24937 )
## Predicted value at location 76 : 27.2788 95% confidence interval = ( 25.3188 , 29.2388 )
## Predicted value at location 77 : 35.08212 95% confidence interval = ( 33.12212 , 37.04212 )
## Predicted value at location 78 : 22.37381 95% confidence interval = ( 20.41381 , 24.33381 )
## Predicted value at location 79 : 27.95529 95% confidence interval = ( 25.99529 , 29.91529 )
## Predicted value at location 80 : 20.9207 95% confidence interval = ( 18.9607 , 22.8807 )
## Predicted value at location 81 : 35.24413 95% confidence interval = ( 33.28413 , 37.20413 )
## Predicted value at location 82 : 18.53212 95% confidence interval = ( 16.57212 , 20.49212 )
## Predicted value at location 83 : 30.88871 95% confidence interval = ( 28.92871 , 32.84871 )
## Predicted value at location 84 : 24.00555 95% confidence interval = ( 22.04555 , 25.96555 )
## Predicted value at location 85 : 18.44806 95% confidence interval = ( 16.48806 , 20.40806 )
## Predicted value at location 86 : 28.46738 95% confidence interval = ( 26.50738 , 30.42738 )
## Predicted value at location 87 : 29.24852 95% confidence interval = ( 27.28852 , 31.20852 )
## Predicted value at location 88 : 29.43688 95% confidence interval = ( 27.47688 , 31.39688 )
## Predicted value at location 89 : 22.23968 95% confidence interval = ( 20.27968 , 24.19968 )
## Predicted value at location 90 : 25.90018 95% confidence interval = ( 23.94018 , 27.86018 )
## Predicted value at location 91 : 41.2251 95% confidence interval = ( 39.2651 , 43.1851 )
## Predicted value at location 92 : 23.61383 95% confidence interval = ( 21.65383 , 25.57383 )
## Predicted value at location 93 : 29.19054 95% confidence interval = ( 27.23054 , 31.15054 )
## Predicted value at location 94 : 31.87818 95% confidence interval = ( 29.91818 , 33.83818 )
## Predicted value at location 95 : 41.88757 95% confidence interval = ( 39.92757 , 43.84757 )
## Predicted value at location 96 : 31.7696 95% confidence interval = ( 29.8096 , 33.7296 )
## Predicted value at location 97 : 23.83781 95% confidence interval = ( 21.87781 , 25.79781 )
## Predicted value at location 98 : 24.1341 95% confidence interval = ( 22.1741 , 26.0941 )
## Predicted value at location 99 : 34.63893 95% confidence interval = ( 32.67893 , 36.59893 )
## Predicted value at location 100 : 32.37082 95% confidence interval = ( 30.41082 , 34.33082 )
## Predicted value at location 101 : 41.6057 95% confidence interval = ( 39.6457 , 43.5657 )
## Predicted value at location 102 : 40.08031 95% confidence interval = ( 38.12031 , 42.04031 )
## Predicted value at location 103 : 28.70402 95% confidence interval = ( 26.74402 , 30.66402 )
## Predicted value at location 104 : 30.05844 95% confidence interval = ( 28.09844 , 32.01844 )
## Predicted value at location 105 : 25.63195 95% confidence interval = ( 23.67195 , 27.59195 )
## Predicted value at location 106 : 28.06617 95% confidence interval = ( 26.10617 , 30.02617 )
## Predicted value at location 107 : 22.92874 95% confidence interval = ( 20.96874 , 24.88874 )
## Predicted value at location 108 : 29.72827 95% confidence interval = ( 27.76827 , 31.68827 )
## Predicted value at location 109 : 30.69506 95% confidence interval = ( 28.73506 , 32.65506 )
## Predicted value at location 110 : 29.63387 95% confidence interval = ( 27.67387 , 31.59387 )
## Predicted value at location 111 : 32.04697 95% confidence interval = ( 30.08697 , 34.00697 )
## Predicted value at location 112 : 33.92682 95% confidence interval = ( 31.96682 , 35.88682 )
## Predicted value at location 113 : 35.81832 95% confidence interval = ( 33.85832 , 37.77832 )
## Predicted value at location 114 : 23.19584 95% confidence interval = ( 21.23584 , 25.15584 )
## Predicted value at location 115 : 33.90997 95% confidence interval = ( 31.94997 , 35.86997 )
## Predicted value at location 116 : 31.91173 95% confidence interval = ( 29.95173 , 33.87173 )
## Predicted value at location 117 : 27.4129 95% confidence interval = ( 25.4529 , 29.3729 )
## Predicted value at location 118 : 39.30946 95% confidence interval = ( 37.34946 , 41.26946 )
## Predicted value at location 119 : 31.23737 95% confidence interval = ( 29.27737 , 33.19737 )
## Predicted value at location 120 : 36.99478 95% confidence interval = ( 35.03478 , 38.95478 )
## Predicted value at location 121 : 27.68947 95% confidence interval = ( 25.72947 , 29.64947 )
## Predicted value at location 122 : 33.37872 95% confidence interval = ( 31.41872 , 35.33872 )
## Predicted value at location 123 : 23.50956 95% confidence interval = ( 21.54956 , 25.46956 )
## Predicted value at location 124 : 35.31988 95% confidence interval = ( 33.35988 , 37.27988 )
## Predicted value at location 125 : 23.72261 95% confidence interval = ( 21.76261 , 25.68261 )
## Predicted value at location 126 : 49.00698 95% confidence interval = ( 47.04698 , 50.96698 )
## Predicted value at location 127 : 31.18273 95% confidence interval = ( 29.22273 , 33.14273 )
## Predicted value at location 128 : 25.27662 95% confidence interval = ( 23.31662 , 27.23662 )
## Predicted value at location 129 : 30.88547 95% confidence interval = ( 28.92547 , 32.84547 )
## Predicted value at location 130 : 30.80803 95% confidence interval = ( 28.84803 , 32.76803 )
## Predicted value at location 131 : 32.50601 95% confidence interval = ( 30.54601 , 34.46601 )
## Predicted value at location 132 : 34.77888 95% confidence interval = ( 32.81888 , 36.73888 )
## Predicted value at location 133 : 32.29498 95% confidence interval = ( 30.33498 , 34.25498 )
## Predicted value at location 134 : 29.34268 95% confidence interval = ( 27.38268 , 31.30268 )
## Predicted value at location 135 : 23.69529 95% confidence interval = ( 21.73529 , 25.65529 )
## Predicted value at location 136 : 30.72706 95% confidence interval = ( 28.76706 , 32.68706 )
## Predicted value at location 137 : 31.44014 95% confidence interval = ( 29.48014 , 33.40014 )
## Predicted value at location 138 : 35.07365 95% confidence interval = ( 33.11365 , 37.03365 )
## Predicted value at location 139 : 36.57133 95% confidence interval = ( 34.61133 , 38.53133 )
## Predicted value at location 140 : 33.61469 95% confidence interval = ( 31.65469 , 35.57469 )
## Predicted value at location 141 : 31.41935 95% confidence interval = ( 29.45935 , 33.37935 )
## Predicted value at location 142 : 31.91257 95% confidence interval = ( 29.95257 , 33.87257 )
## Predicted value at location 143 : 26.96392 95% confidence interval = ( 25.00392 , 28.92392 )
## Predicted value at location 144 : 23.40586 95% confidence interval = ( 21.44586 , 25.36586 )
## Predicted value at location 145 : 29.18536 95% confidence interval = ( 27.22536 , 31.14536 )
## Predicted value at location 146 : 27.79459 95% confidence interval = ( 25.83459 , 29.75459 )
## Predicted value at location 147 : 25.77448 95% confidence interval = ( 23.81448 , 27.73448 )
## Predicted value at location 148 : 29.74958 95% confidence interval = ( 27.78958 , 31.70958 )
## Predicted value at location 149 : 31.91038 95% confidence interval = ( 29.95038 , 33.87038 )
## Predicted value at location 150 : 30.65687 95% confidence interval = ( 28.69687 , 32.61687 )
## Predicted value at location 151 : 24.07663 95% confidence interval = ( 22.11663 , 26.03663 )
## Predicted value at location 152 : 36.86248 95% confidence interval = ( 34.90248 , 38.82248 )
## Predicted value at location 153 : 49.99032 95% confidence interval = ( 48.03032 , 51.95032 )
## Predicted value at location 154 : 23.64362 95% confidence interval = ( 21.68362 , 25.60362 )
## Predicted value at location 155 : 29.30133 95% confidence interval = ( 27.34133 , 31.26133 )
## Predicted value at location 156 : 42.60603 95% confidence interval = ( 40.64603 , 44.56603 )
## Predicted value at location 157 : 28.10241 95% confidence interval = ( 26.14241 , 30.06241 )
## Predicted value at location 158 : 35.02109 95% confidence interval = ( 33.06109 , 36.98109 )
## Predicted value at location 159 : 44.89608 95% confidence interval = ( 42.93608 , 46.85608 )
## Predicted value at location 160 : 34.5458 95% confidence interval = ( 32.5858 , 36.5058 )
## Predicted value at location 161 : 24.01931 95% confidence interval = ( 22.05931 , 25.97931 )
## Predicted value at location 162 : 28.24946 95% confidence interval = ( 26.28946 , 30.20946 )
## Predicted value at location 163 : 38.12299 95% confidence interval = ( 36.16299 , 40.08299 )
## Predicted value at location 164 : 31.49878 95% confidence interval = ( 29.53878 , 33.45878 )
## Predicted value at location 165 : 41.81825 95% confidence interval = ( 39.85825 , 43.77825 )
## Predicted value at location 166 : 28.14985 95% confidence interval = ( 26.18985 , 30.10985 )
## Predicted value at location 167 : 25.73949 95% confidence interval = ( 23.77949 , 27.69949 )
## Predicted value at location 168 : 23.32434 95% confidence interval = ( 21.36434 , 25.28434 )
## Predicted value at location 169 : 24.50809 95% confidence interval = ( 22.54809 , 26.46809 )
## Predicted value at location 170 : 27.07705 95% confidence interval = ( 25.11705 , 29.03705 )
## Predicted value at location 171 : 31.99711 95% confidence interval = ( 30.03711 , 33.95711 )
## Predicted value at location 172 : 30.9675 95% confidence interval = ( 29.0075 , 32.9275 )
## Predicted value at location 173 : 30.97076 95% confidence interval = ( 29.01076 , 32.93076 )
## Predicted value at location 174 : 48.56164 95% confidence interval = ( 46.60164 , 50.52164 )
## Predicted value at location 175 : 35.37533 95% confidence interval = ( 33.41533 , 37.33533 )
## Predicted value at location 176 : 28.55213 95% confidence interval = ( 26.59213 , 30.51213 )
## Predicted value at location 177 : 32.1114 95% confidence interval = ( 30.1514 , 34.0714 )
## Predicted value at location 178 : 27.52756 95% confidence interval = ( 25.56756 , 29.48756 )
## Predicted value at location 179 : 24.46681 95% confidence interval = ( 22.50681 , 26.42681 )
## Predicted value at location 180 : 37.54214 95% confidence interval = ( 35.58214 , 39.50214 )
## Predicted value at location 181 : 17.17844 95% confidence interval = ( 15.21844 , 19.13844 )
## Predicted value at location 182 : 24.15564 95% confidence interval = ( 22.19564 , 26.11564 )
## Predicted value at location 183 : 16.68412 95% confidence interval = ( 14.72412 , 18.64412 )
## Predicted value at location 184 : 31.37267 95% confidence interval = ( 29.41267 , 33.33267 )
## Predicted value at location 185 : 32.72442 95% confidence interval = ( 30.76442 , 34.68442 )
## Predicted value at location 186 : 29.53453 95% confidence interval = ( 27.57453 , 31.49453 )
## Predicted value at location 187 : 15.36682 95% confidence interval = ( 13.40682 , 17.32682 )
## Predicted value at location 188 : 31.92666 95% confidence interval = ( 29.96666 , 33.88666 )
## Predicted value at location 189 : 30.88818 95% confidence interval = ( 28.92818 , 32.84818 )
## Predicted value at location 190 : 33.01586 95% confidence interval = ( 31.05586 , 34.97586 )
## Predicted value at location 191 : 24.3329 95% confidence interval = ( 22.3729 , 26.2929 )
## Predicted value at location 192 : 34.16953 95% confidence interval = ( 32.20953 , 36.12953 )
## Predicted value at location 193 : 34.96968 95% confidence interval = ( 33.00968 , 36.92968 )
## Predicted value at location 194 : 21.80231 95% confidence interval = ( 19.84231 , 23.76231 )
## Predicted value at location 195 : 33.01399 95% confidence interval = ( 31.05399 , 34.97399 )
## Predicted value at location 196 : 37.72505 95% confidence interval = ( 35.76505 , 39.68505 )
## Predicted value at location 197 : 27.83772 95% confidence interval = ( 25.87772 , 29.79772 )
## Predicted value at location 198 : 25.10888 95% confidence interval = ( 23.14888 , 27.06888 )
## Predicted value at location 199 : 32.33668 95% confidence interval = ( 30.37668 , 34.29668 )
## Predicted value at location 200 : 24.08613 95% confidence interval = ( 22.12613 , 26.04613 )
## Predicted value at location 201 : 31.18227 95% confidence interval = ( 29.22227 , 33.14227 )
## Predicted value at location 202 : 31.63371 95% confidence interval = ( 29.67371 , 33.59371 )
## Predicted value at location 203 : 28.93524 95% confidence interval = ( 26.97524 , 30.89524 )
## Predicted value at location 204 : 24.79336 95% confidence interval = ( 22.83336 , 26.75336 )
## Predicted value at location 205 : 33.70202 95% confidence interval = ( 31.74202 , 35.66202 )
## Predicted value at location 206 : 30.02489 95% confidence interval = ( 28.06489 , 31.98489 )
## Predicted value at location 207 : 32.85534 95% confidence interval = ( 30.89534 , 34.81534 )
## Predicted value at location 208 : 49.62591 95% confidence interval = ( 47.66591 , 51.58591 )
## Predicted value at location 209 : 32.25833 95% confidence interval = ( 30.29833 , 34.21833 )
## Predicted value at location 210 : 27.746 95% confidence interval = ( 25.786 , 29.706 )
## Predicted value at location 211 : 34.50083 95% confidence interval = ( 32.54083 , 36.46083 )
## Predicted value at location 212 : 24.76435 95% confidence interval = ( 22.80435 , 26.72435 )
## Predicted value at location 213 : 36.81814 95% confidence interval = ( 34.85814 , 38.77814 )
## Predicted value at location 214 : 36.76351 95% confidence interval = ( 34.80351 , 38.72351 )
## Predicted value at location 215 : 30.52988 95% confidence interval = ( 28.56988 , 32.48988 )
## Predicted value at location 216 : 28.10757 95% confidence interval = ( 26.14757 , 30.06757 )
## Predicted value at location 217 : 40.61436 95% confidence interval = ( 38.65436 , 42.57436 )
## Predicted value at location 218 : 37.76699 95% confidence interval = ( 35.80699 , 39.72699 )
## Predicted value at location 219 : 41.92327 95% confidence interval = ( 39.96327 , 43.88327 )
## Predicted value at location 220 : 36.7474 95% confidence interval = ( 34.7874 , 38.7074 )
## Predicted value at location 221 : 35.85423 95% confidence interval = ( 33.89423 , 37.81423 )
## Predicted value at location 222 : 35.06256 95% confidence interval = ( 33.10256 , 37.02256 )
## Predicted value at location 223 : 37.0194 95% confidence interval = ( 35.0594 , 38.9794 )
## Predicted value at location 224 : 28.03227 95% confidence interval = ( 26.07227 , 29.99227 )
## Predicted value at location 225 : 27.59048 95% confidence interval = ( 25.63048 , 29.55048 )
## Predicted value at location 226 : 28.11412 95% confidence interval = ( 26.15412 , 30.07412 )
## Predicted value at location 227 : 50.32656 95% confidence interval = ( 48.36656 , 52.28656 )
## Predicted value at location 228 : 28.10458 95% confidence interval = ( 26.14458 , 30.06458 )
## Predicted value at location 229 : 35.7681 95% confidence interval = ( 33.8081 , 37.7281 )
## Predicted value at location 230 : 24.51024 95% confidence interval = ( 22.55024 , 26.47024 )
## Predicted value at location 231 : 37.71322 95% confidence interval = ( 35.75322 , 39.67322 )
## Predicted value at location 232 : 31.44113 95% confidence interval = ( 29.48113 , 33.40113 )
## Predicted value at location 233 : 18.43882 95% confidence interval = ( 16.47882 , 20.39882 )
## Predicted value at location 234 : 27.82144 95% confidence interval = ( 25.86144 , 29.78144 )
## Predicted value at location 235 : 32.09715 95% confidence interval = ( 30.13715 , 34.05715 )
## Predicted value at location 236 : 24.96648 95% confidence interval = ( 23.00648 , 26.92648 )
## Predicted value at location 237 : 32.10637 95% confidence interval = ( 30.14637 , 34.06637 )
## Predicted value at location 238 : 23.75023 95% confidence interval = ( 21.79023 , 25.71023 )
## Predicted value at location 239 : 21.91845 95% confidence interval = ( 19.95845 , 23.87845 )
## Predicted value at location 240 : 23.34812 95% confidence interval = ( 21.38812 , 25.30812 )
## Predicted value at location 241 : 31.35814 95% confidence interval = ( 29.39814 , 33.31814 )
## Predicted value at location 242 : 35.55182 95% confidence interval = ( 33.59182 , 37.51182 )
## Predicted value at location 243 : 32.33246 95% confidence interval = ( 30.37246 , 34.29246 )
## Predicted value at location 244 : 29.19285 95% confidence interval = ( 27.23285 , 31.15285 )
## Predicted value at location 245 : 35.33404 95% confidence interval = ( 33.37404 , 37.29404 )
## Predicted value at location 246 : 23.87871 95% confidence interval = ( 21.91871 , 25.83871 )
## Predicted value at location 247 : 30.07905 95% confidence interval = ( 28.11905 , 32.03905 )
## Predicted value at location 248 : 35.02037 95% confidence interval = ( 33.06037 , 36.98037 )
## Predicted value at location 249 : 30.67675 95% confidence interval = ( 28.71675 , 32.63675 )
## Predicted value at location 250 : 31.52536 95% confidence interval = ( 29.56536 , 33.48536 )
## Predicted value at location 251 : 36.16972 95% confidence interval = ( 34.20972 , 38.12972 )
## Predicted value at location 252 : 49.09233 95% confidence interval = ( 47.13233 , 51.05233 )
## Predicted value at location 253 : 29.08954 95% confidence interval = ( 27.12954 , 31.04954 )
## Predicted value at location 254 : 23.74388 95% confidence interval = ( 21.78388 , 25.70388 )
## Predicted value at location 255 : 22.61158 95% confidence interval = ( 20.65158 , 24.57158 )
## Predicted value at location 256 : 29.31414 95% confidence interval = ( 27.35414 , 31.27414 )
## Predicted value at location 257 : 36.3272 95% confidence interval = ( 34.3672 , 38.2872 )
## Predicted value at location 258 : 27.61556 95% confidence interval = ( 25.65556 , 29.57556 )
## Predicted value at location 259 : 37.79886 95% confidence interval = ( 35.83886 , 39.75886 )
## Predicted value at location 260 : 23.19812 95% confidence interval = ( 21.23812 , 25.15812 )
## Predicted value at location 261 : 32.79322 95% confidence interval = ( 30.83322 , 34.75322 )
## Predicted value at location 262 : 32.7096 95% confidence interval = ( 30.7496 , 34.6696 )
## Predicted value at location 263 : 34.38865 95% confidence interval = ( 32.42865 , 36.34865 )
## Predicted value at location 264 : 31.1928 95% confidence interval = ( 29.2328 , 33.1528 )
## Predicted value at location 265 : 29.49279 95% confidence interval = ( 27.53279 , 31.45279 )
## Predicted value at location 266 : 33.97469 95% confidence interval = ( 32.01469 , 35.93469 )
## Predicted value at location 267 : 27.82875 95% confidence interval = ( 25.86875 , 29.78875 )
## Predicted value at location 268 : 29.64025 95% confidence interval = ( 27.68025 , 31.60025 )
## Predicted value at location 269 : 25.03434 95% confidence interval = ( 23.07434 , 26.99434 )
## Predicted value at location 270 : 46.34709 95% confidence interval = ( 44.38709 , 48.30709 )
## Predicted value at location 271 : 30.32746 95% confidence interval = ( 28.36746 , 32.28746 )
## Predicted value at location 272 : 30.6353 95% confidence interval = ( 28.6753 , 32.5953 )
## Predicted value at location 273 : 27.53923 95% confidence interval = ( 25.57923 , 29.49923 )
## Predicted value at location 274 : 35.12594 95% confidence interval = ( 33.16594 , 37.08594 )
## Predicted value at location 275 : 36.57061 95% confidence interval = ( 34.61061 , 38.53061 )
## Predicted value at location 276 : 27.65127 95% confidence interval = ( 25.69127 , 29.61127 )
## Predicted value at location 277 : 43.53133 95% confidence interval = ( 41.57133 , 45.49133 )
## Predicted value at location 278 : 47.48674 95% confidence interval = ( 45.52674 , 49.44674 )
## Predicted value at location 279 : 33.52157 95% confidence interval = ( 31.56157 , 35.48157 )
## Predicted value at location 280 : 28.19338 95% confidence interval = ( 26.23338 , 30.15338 )
## Predicted value at location 281 : 22.53243 95% confidence interval = ( 20.57243 , 24.49243 )
## Predicted value at location 282 : 27.60397 95% confidence interval = ( 25.64397 , 29.56397 )
## Predicted value at location 283 : 29.40681 95% confidence interval = ( 27.44681 , 31.36681 )
## Predicted value at location 284 : 27.883 95% confidence interval = ( 25.923 , 29.843 )
## Predicted value at location 285 : 31.77717 95% confidence interval = ( 29.81717 , 33.73717 )
## Predicted value at location 286 : 25.31549 95% confidence interval = ( 23.35549 , 27.27549 )
## Predicted value at location 287 : 31.90093 95% confidence interval = ( 29.94093 , 33.86093 )
## Predicted value at location 288 : 32.70335 95% confidence interval = ( 30.74335 , 34.66335 )
## Predicted value at location 289 : 32.76831 95% confidence interval = ( 30.80831 , 34.72831 )
## Predicted value at location 290 : 30.46364 95% confidence interval = ( 28.50364 , 32.42364 )
## Predicted value at location 291 : 54.94382 95% confidence interval = ( 52.98382 , 56.90382 )
## Predicted value at location 292 : 30.204 95% confidence interval = ( 28.244 , 32.164 )
## Predicted value at location 293 : 23.44399 95% confidence interval = ( 21.48399 , 25.40399 )
## Predicted value at location 294 : 35.27128 95% confidence interval = ( 33.31128 , 37.23128 )
## Predicted value at location 295 : 29.95579 95% confidence interval = ( 27.99579 , 31.91579 )
## Predicted value at location 296 : 27.59341 95% confidence interval = ( 25.63341 , 29.55341 )
## Predicted value at location 297 : 35.12885 95% confidence interval = ( 33.16885 , 37.08885 )
## Predicted value at location 298 : 36.34103 95% confidence interval = ( 34.38103 , 38.30103 )
## Predicted value at location 299 : 40.28578 95% confidence interval = ( 38.32578 , 42.24578 )
## Predicted value at location 300 : 33.85466 95% confidence interval = ( 31.89466 , 35.81466 )
## Predicted value at location 301 : 30.49834 95% confidence interval = ( 28.53834 , 32.45834 )
## Predicted value at location 302 : 30.87406 95% confidence interval = ( 28.91406 , 32.83406 )
## Predicted value at location 303 : 31.65938 95% confidence interval = ( 29.69938 , 33.61938 )
## Predicted value at location 304 : 30.03244 95% confidence interval = ( 28.07244 , 31.99244 )
## Predicted value at location 305 : 35.86834 95% confidence interval = ( 33.90834 , 37.82834 )
## Predicted value at location 306 : 30.25404 95% confidence interval = ( 28.29404 , 32.21404 )
## Predicted value at location 307 : 32.37677 95% confidence interval = ( 30.41677 , 34.33677 )
## Predicted value at location 308 : 34.25772 95% confidence interval = ( 32.29772 , 36.21772 )
## Predicted value at location 309 : 29.37893 95% confidence interval = ( 27.41893 , 31.33893 )
## Predicted value at location 310 : 29.42539 95% confidence interval = ( 27.46539 , 31.38539 )
## Predicted value at location 311 : 29.87685 95% confidence interval = ( 27.91685 , 31.83685 )
## Predicted value at location 312 : 44.89947 95% confidence interval = ( 42.93947 , 46.85947 )
## Predicted value at location 313 : 30.8409 95% confidence interval = ( 28.8809 , 32.8009 )
## Predicted value at location 314 : 31.93039 95% confidence interval = ( 29.97039 , 33.89039 )
## Predicted value at location 315 : 46.33032 95% confidence interval = ( 44.37032 , 48.29032 )
## Predicted value at location 316 : 49.16648 95% confidence interval = ( 47.20648 , 51.12648 )
## Predicted value at location 317 : 50.50665 95% confidence interval = ( 48.54665 , 52.46665 )
## Predicted value at location 318 : 17.11577 95% confidence interval = ( 15.15577 , 19.07577 )
## Predicted value at location 319 : 22.89165 95% confidence interval = ( 20.93165 , 24.85165 )
## Predicted value at location 320 : 27.35703 95% confidence interval = ( 25.39703 , 29.31703 )
## Predicted value at location 321 : 34.77521 95% confidence interval = ( 32.81521 , 36.73521 )
## Predicted value at location 322 : 53.29944 95% confidence interval = ( 51.33944 , 55.25944 )
## Predicted value at location 323 : 41.99806 95% confidence interval = ( 40.03806 , 43.95806 )
## Predicted value at location 324 : 49.01845 95% confidence interval = ( 47.05845 , 50.97845 )
## Predicted value at location 325 : 27.07472 95% confidence interval = ( 25.11472 , 29.03472 )
## Predicted value at location 326 : 23.68379 95% confidence interval = ( 21.72379 , 25.64379 )
## Predicted value at location 327 : 27.29704 95% confidence interval = ( 25.33704 , 29.25704 )
## Predicted value at location 328 : 42.71877 95% confidence interval = ( 40.75877 , 44.67877 )
## Predicted value at location 329 : 29.57537 95% confidence interval = ( 27.61537 , 31.53537 )
## Predicted value at location 330 : 24.47401 95% confidence interval = ( 22.51401 , 26.43401 )
## Predicted value at location 331 : 23.84594 95% confidence interval = ( 21.88594 , 25.80594 )
## Predicted value at location 332 : 30.54715 95% confidence interval = ( 28.58715 , 32.50715 )
## Predicted value at location 333 : 29.08133 95% confidence interval = ( 27.12133 , 31.04133 )
## Predicted value at location 334 : 50.36641 95% confidence interval = ( 48.40641 , 52.32641 )
## Predicted value at location 335 : 34.9951 95% confidence interval = ( 33.0351 , 36.9551 )
## Predicted value at location 336 : 31.53834 95% confidence interval = ( 29.57834 , 33.49834 )
## Predicted value at location 337 : 23.20601 95% confidence interval = ( 21.24601 , 25.16601 )
## Predicted value at location 338 : 30.97099 95% confidence interval = ( 29.01099 , 32.93099 )
## Predicted value at location 339 : 28.75362 95% confidence interval = ( 26.79362 , 30.71362 )
## Predicted value at location 340 : 49.49202 95% confidence interval = ( 47.53202 , 51.45202 )
## Predicted value at location 341 : 17.35896 95% confidence interval = ( 15.39896 , 19.31896 )
## Predicted value at location 342 : 24.09472 95% confidence interval = ( 22.13472 , 26.05472 )
## Predicted value at location 343 : 27.70843 95% confidence interval = ( 25.74843 , 29.66843 )
## Predicted value at location 344 : 30.35225 95% confidence interval = ( 28.39225 , 32.31225 )
## Predicted value at location 345 : 30.85492 95% confidence interval = ( 28.89492 , 32.81492 )
## Predicted value at location 346 : 19.49673 95% confidence interval = ( 17.53673 , 21.45673 )
## Predicted value at location 347 : 38.95908 95% confidence interval = ( 36.99908 , 40.91908 )
## Predicted value at location 348 : 36.76032 95% confidence interval = ( 34.80032 , 38.72032 )
## Predicted value at location 349 : 27.90917 95% confidence interval = ( 25.94917 , 29.86917 )
## Predicted value at location 350 : 33.14967 95% confidence interval = ( 31.18967 , 35.10967 )
## Predicted value at location 351 : 23.41803 95% confidence interval = ( 21.45803 , 25.37803 )
## Predicted value at location 352 : 34.71378 95% confidence interval = ( 32.75378 , 36.67378 )
## Predicted value at location 353 : 18.62 95% confidence interval = ( 16.66 , 20.58 )
## Predicted value at location 354 : 28.59145 95% confidence interval = ( 26.63145 , 30.55145 )
## Predicted value at location 355 : 42.28342 95% confidence interval = ( 40.32342 , 44.24342 )
## Predicted value at location 356 : 29.37665 95% confidence interval = ( 27.41665 , 31.33665 )
## Predicted value at location 357 : 30.49428 95% confidence interval = ( 28.53428 , 32.45428 )
## Predicted value at location 358 : 29.82867 95% confidence interval = ( 27.86867 , 31.78867 )
## Predicted value at location 359 : 38.45499 95% confidence interval = ( 36.49499 , 40.41499 )
## Predicted value at location 360 : 35.79208 95% confidence interval = ( 33.83208 , 37.75208 )
## Predicted value at location 361 : 34.91586 95% confidence interval = ( 32.95586 , 36.87586 )
## Predicted value at location 362 : 27.93368 95% confidence interval = ( 25.97368 , 29.89368 )
## Predicted value at location 363 : 15.39401 95% confidence interval = ( 13.43401 , 17.35401 )
## Predicted value at location 364 : 17.74769 95% confidence interval = ( 15.78769 , 19.70769 )
## Predicted value at location 365 : 22.6611 95% confidence interval = ( 20.7011 , 24.6211 )
## Predicted value at location 366 : 29.10332 95% confidence interval = ( 27.14332 , 31.06332 )
## Predicted value at location 367 : 29.66755 95% confidence interval = ( 27.70755 , 31.62755 )
## Predicted value at location 368 : 34.67599 95% confidence interval = ( 32.71599 , 36.63599 )
## Predicted value at location 369 : 36.65425 95% confidence interval = ( 34.69425 , 38.61425 )
## Predicted value at location 370 : 28.95894 95% confidence interval = ( 26.99894 , 30.91894 )
## Predicted value at location 1 : 29.10365 95% confidence interval = ( 27.14365 , 31.06365 )
## Predicted value at location 2 : 22.67534 95% confidence interval = ( 20.71534 , 24.63534 )
## Predicted value at location 3 : 23.34302 95% confidence interval = ( 21.38302 , 25.30302 )
## Predicted value at location 4 : 35.22109 95% confidence interval = ( 33.26109 , 37.18109 )
## Predicted value at location 5 : 21.66809 95% confidence interval = ( 19.70809 , 23.62809 )
## Predicted value at location 6 : 36.8201 95% confidence interval = ( 34.8601 , 38.7801 )
## Predicted value at location 7 : 38.94422 95% confidence interval = ( 36.98422 , 40.90422 )
## Predicted value at location 8 : 28.21661 95% confidence interval = ( 26.25661 , 30.17661 )
## Predicted value at location 9 : 27.5321 95% confidence interval = ( 25.5721 , 29.4921 )
## Predicted value at location 10 : 22.3228 95% confidence interval = ( 20.3628 , 24.2828 )
## Predicted value at location 11 : 31.537 95% confidence interval = ( 29.577 , 33.497 )
## Predicted value at location 12 : 26.04503 95% confidence interval = ( 24.08503 , 28.00503 )
## Predicted value at location 13 : 43.60854 95% confidence interval = ( 41.64854 , 45.56854 )
## Predicted value at location 14 : 42.36586 95% confidence interval = ( 40.40586 , 44.32586 )
## Predicted value at location 15 : 18.58848 95% confidence interval = ( 16.62848 , 20.54848 )
## Predicted value at location 16 : 33.25844 95% confidence interval = ( 31.29844 , 35.21844 )
## Predicted value at location 17 : 31.53565 95% confidence interval = ( 29.57565 , 33.49565 )
## Predicted value at location 18 : 26.70979 95% confidence interval = ( 24.74979 , 28.66979 )
## Predicted value at location 19 : 29.39497 95% confidence interval = ( 27.43497 , 31.35497 )
## Predicted value at location 20 : 30.84523 95% confidence interval = ( 28.88523 , 32.80523 )
## Predicted value at location 21 : 24.66578 95% confidence interval = ( 22.70578 , 26.62578 )
## Predicted value at location 22 : 28.08698 95% confidence interval = ( 26.12698 , 30.04698 )
## Predicted value at location 23 : 21.37889 95% confidence interval = ( 19.41889 , 23.33889 )
## Predicted value at location 24 : 22.48933 95% confidence interval = ( 20.52933 , 24.44933 )
## Predicted value at location 25 : 25.83384 95% confidence interval = ( 23.87384 , 27.79384 )
## Predicted value at location 26 : 36.71312 95% confidence interval = ( 34.75312 , 38.67312 )
## Predicted value at location 27 : 27.69272 95% confidence interval = ( 25.73272 , 29.65272 )
## Predicted value at location 28 : 27.51454 95% confidence interval = ( 25.55454 , 29.47454 )
## Predicted value at location 29 : 19.33225 95% confidence interval = ( 17.37225 , 21.29225 )
## Predicted value at location 30 : 22.7565 95% confidence interval = ( 20.7965 , 24.7165 )
## Predicted value at location 31 : 38.375 95% confidence interval = ( 36.415 , 40.335 )
## Predicted value at location 32 : 23.17422 95% confidence interval = ( 21.21422 , 25.13422 )
## Predicted value at location 33 : 23.57261 95% confidence interval = ( 21.61261 , 25.53261 )
## Predicted value at location 34 : 37.82785 95% confidence interval = ( 35.86785 , 39.78785 )
## Predicted value at location 35 : 22.97117 95% confidence interval = ( 21.01117 , 24.93117 )
## Predicted value at location 36 : 43.50497 95% confidence interval = ( 41.54497 , 45.46497 )
## Predicted value at location 37 : 30.57568 95% confidence interval = ( 28.61568 , 32.53568 )
## Predicted value at location 38 : 25.1855 95% confidence interval = ( 23.2255 , 27.1455 )
## Predicted value at location 39 : 22.41913 95% confidence interval = ( 20.45913 , 24.37913 )
## Predicted value at location 40 : 23.87033 95% confidence interval = ( 21.91033 , 25.83033 )
## Predicted value at location 41 : 27.14794 95% confidence interval = ( 25.18794 , 29.10794 )
## Predicted value at location 42 : 36.54297 95% confidence interval = ( 34.58297 , 38.50297 )
## Predicted value at location 43 : 36.10763 95% confidence interval = ( 34.14763 , 38.06763 )
## Predicted value at location 44 : 33.2153 95% confidence interval = ( 31.2553 , 35.1753 )
## Predicted value at location 45 : 33.77837 95% confidence interval = ( 31.81837 , 35.73837 )
## Predicted value at location 46 : 31.54649 95% confidence interval = ( 29.58649 , 33.50649 )
## Predicted value at location 47 : 32.15854 95% confidence interval = ( 30.19854 , 34.11854 )
## Predicted value at location 48 : 34.72605 95% confidence interval = ( 32.76605 , 36.68605 )
## Predicted value at location 49 : 32.4698 95% confidence interval = ( 30.5098 , 34.4298 )
## Predicted value at location 50 : 32.86416 95% confidence interval = ( 30.90416 , 34.82416 )
## Predicted value at location 51 : 31.80454 95% confidence interval = ( 29.84454 , 33.76454 )
## Predicted value at location 52 : 37.40252 95% confidence interval = ( 35.44252 , 39.36252 )
## Predicted value at location 53 : 19.39797 95% confidence interval = ( 17.43797 , 21.35797 )
## Predicted value at location 54 : 19.90734 95% confidence interval = ( 17.94734 , 21.86734 )
## Predicted value at location 55 : 23.83384 95% confidence interval = ( 21.87384 , 25.79384 )
## Predicted value at location 56 : 28.23202 95% confidence interval = ( 26.27202 , 30.19202 )
## Predicted value at location 57 : 32.59085 95% confidence interval = ( 30.63085 , 34.55085 )
## Predicted value at location 58 : 28.82502 95% confidence interval = ( 26.86502 , 30.78502 )
## Predicted value at location 59 : 32.98318 95% confidence interval = ( 31.02318 , 34.94318 )
## Predicted value at location 60 : 31.24215 95% confidence interval = ( 29.28215 , 33.20215 )
## Predicted value at location 61 : 28.43961 95% confidence interval = ( 26.47961 , 30.39961 )
## Predicted value at location 62 : 28.06671 95% confidence interval = ( 26.10671 , 30.02671 )
## Predicted value at location 63 : 17.93051 95% confidence interval = ( 15.97051 , 19.89051 )
## Predicted value at location 64 : 23.41486 95% confidence interval = ( 21.45486 , 25.37486 )
## Predicted value at location 65 : 30.37404 95% confidence interval = ( 28.41404 , 32.33404 )
## Predicted value at location 66 : 36.53734 95% confidence interval = ( 34.57734 , 38.49734 )
## Predicted value at location 67 : 31.87089 95% confidence interval = ( 29.91089 , 33.83089 )
## Predicted value at location 68 : 34.12679 95% confidence interval = ( 32.16679 , 36.08679 )
## Predicted value at location 69 : 22.69641 95% confidence interval = ( 20.73641 , 24.65641 )
## Predicted value at location 70 : 30.43874 95% confidence interval = ( 28.47874 , 32.39874 )
## Predicted value at location 71 : 39.49643 95% confidence interval = ( 37.53643 , 41.45643 )
## Predicted value at location 72 : 26.72843 95% confidence interval = ( 24.76843 , 28.68843 )
## Predicted value at location 73 : 27.9198 95% confidence interval = ( 25.9598 , 29.8798 )
## Predicted value at location 74 : 26.0773 95% confidence interval = ( 24.1173 , 28.0373 )
## Predicted value at location 75 : 20.03885 95% confidence interval = ( 18.07885 , 21.99885 )
## Predicted value at location 76 : 22.24034 95% confidence interval = ( 20.28034 , 24.20034 )
## Predicted value at location 77 : 25.4795 95% confidence interval = ( 23.5195 , 27.4395 )
## Predicted value at location 78 : 32.61255 95% confidence interval = ( 30.65255 , 34.57255 )
## Predicted value at location 79 : 25.98566 95% confidence interval = ( 24.02566 , 27.94566 )
## Predicted value at location 80 : 30.43839 95% confidence interval = ( 28.47839 , 32.39839 )
## Predicted value at location 81 : 30.79306 95% confidence interval = ( 28.83306 , 32.75306 )
## Predicted value at location 82 : 22.69343 95% confidence interval = ( 20.73343 , 24.65343 )
## Predicted value at location 83 : 30.40961 95% confidence interval = ( 28.44961 , 32.36961 )
## Predicted value at location 84 : 29.24654 95% confidence interval = ( 27.28654 , 31.20654 )
## Predicted value at location 85 : 19.95433 95% confidence interval = ( 17.99433 , 21.91433 )
## Predicted value at location 86 : 35.24729 95% confidence interval = ( 33.28729 , 37.20729 )
## Predicted value at location 87 : 28.21089 95% confidence interval = ( 26.25089 , 30.17089 )
## Predicted value at location 88 : 24.39129 95% confidence interval = ( 22.43129 , 26.35129 )
## Predicted value at location 89 : 24.6023 95% confidence interval = ( 22.6423 , 26.5623 )
## Predicted value at location 90 : 28.40591 95% confidence interval = ( 26.44591 , 30.36591 )
## Predicted value at location 91 : 24.74918 95% confidence interval = ( 22.78918 , 26.70918 )
## Predicted value at location 92 : 20.85441 95% confidence interval = ( 18.89441 , 22.81441 )
## Predicted value at location 93 : 29.09217 95% confidence interval = ( 27.13217 , 31.05217 )
## Predicted value at location 94 : 26.28145 95% confidence interval = ( 24.32145 , 28.24145 )
## Predicted value at location 95 : 30.12011 95% confidence interval = ( 28.16011 , 32.08011 )
## Predicted value at location 96 : 19.83578 95% confidence interval = ( 17.87578 , 21.79578 )
## Predicted value at location 97 : 28.08524 95% confidence interval = ( 26.12524 , 30.04524 )
## Predicted value at location 98 : 18.21465 95% confidence interval = ( 16.25465 , 20.17465 )
## Predicted value at location 99 : 32.55838 95% confidence interval = ( 30.59838 , 34.51838 )
## Predicted value at location 100 : 28.28403 95% confidence interval = ( 26.32403 , 30.24403 )
## Predicted value at location 101 : 37.59578 95% confidence interval = ( 35.63578 , 39.55578 )
## Predicted value at location 102 : 33.80544 95% confidence interval = ( 31.84544 , 35.76544 )
## Predicted value at location 103 : 29.58895 95% confidence interval = ( 27.62895 , 31.54895 )
## Predicted value at location 104 : 25.98008 95% confidence interval = ( 24.02008 , 27.94008 )
## Predicted value at location 105 : 30.68588 95% confidence interval = ( 28.72588 , 32.64588 )
## Predicted value at location 106 : 28.78006 95% confidence interval = ( 26.82006 , 30.74006 )
## Predicted value at location 107 : 26.32274 95% confidence interval = ( 24.36274 , 28.28274 )
## Predicted value at location 108 : 29.12656 95% confidence interval = ( 27.16656 , 31.08656 )
## Predicted value at location 109 : 24.02052 95% confidence interval = ( 22.06052 , 25.98052 )
## Predicted value at location 110 : 25.31574 95% confidence interval = ( 23.35574 , 27.27574 )
## Predicted value at location 111 : 23.95229 95% confidence interval = ( 21.99229 , 25.91229 )
## Predicted value at location 112 : 23.13934 95% confidence interval = ( 21.17934 , 25.09934 )
## Predicted value at location 113 : 36.45846 95% confidence interval = ( 34.49846 , 38.41846 )
## Predicted value at location 114 : 19.89766 95% confidence interval = ( 17.93766 , 21.85766 )
## Predicted value at location 115 : 33.01553 95% confidence interval = ( 31.05553 , 34.97553 )
## Predicted value at location 116 : 28.39444 95% confidence interval = ( 26.43444 , 30.35444 )
## Predicted value at location 117 : 20.1008 95% confidence interval = ( 18.1408 , 22.0608 )
## Predicted value at location 118 : 30.83136 95% confidence interval = ( 28.87136 , 32.79136 )
## Predicted value at location 119 : 26.82566 95% confidence interval = ( 24.86566 , 28.78566 )
## Predicted value at location 120 : 35.1927 95% confidence interval = ( 33.2327 , 37.1527 )
## Predicted value at location 121 : 31.74161 95% confidence interval = ( 29.78161 , 33.70161 )
## Predicted value at location 122 : 25.91859 95% confidence interval = ( 23.95859 , 27.87859 )
## Predicted value at location 123 : 34.62846 95% confidence interval = ( 32.66846 , 36.58846 )
## Predicted value at location 124 : 28.88706 95% confidence interval = ( 26.92706 , 30.84706 )
## Predicted value at location 125 : 35.13804 95% confidence interval = ( 33.17804 , 37.09804 )
## Predicted value at location 126 : 23.66829 95% confidence interval = ( 21.70829 , 25.62829 )
## Predicted value at location 127 : 24.93178 95% confidence interval = ( 22.97178 , 26.89178 )
## Predicted value at location 128 : 25.77348 95% confidence interval = ( 23.81348 , 27.73348 )
## Predicted value at location 129 : 30.49216 95% confidence interval = ( 28.53216 , 32.45216 )
## Predicted value at location 130 : 37.92491 95% confidence interval = ( 35.96491 , 39.88491 )
## Predicted value at location 131 : 21.56627 95% confidence interval = ( 19.60627 , 23.52627 )
## Predicted value at location 132 : 28.99189 95% confidence interval = ( 27.03189 , 30.95189 )
## Predicted value at location 133 : 33.23318 95% confidence interval = ( 31.27318 , 35.19318 )
## Predicted value at location 134 : 24.25669 95% confidence interval = ( 22.29669 , 26.21669 )
## Predicted value at location 135 : 33.27182 95% confidence interval = ( 31.31182 , 35.23182 )
## Predicted value at location 136 : 29.17562 95% confidence interval = ( 27.21562 , 31.13562 )
## Predicted value at location 137 : 37.87549 95% confidence interval = ( 35.91549 , 39.83549 )
## Predicted value at location 138 : 25.36884 95% confidence interval = ( 23.40884 , 27.32884 )
## Predicted value at location 139 : 23.13511 95% confidence interval = ( 21.17511 , 25.09511 )
## Predicted value at location 140 : 20.84667 95% confidence interval = ( 18.88667 , 22.80667 )
## Predicted value at location 141 : 23.88365 95% confidence interval = ( 21.92365 , 25.84365 )
## Predicted value at location 142 : 26.09668 95% confidence interval = ( 24.13668 , 28.05668 )
## Predicted value at location 143 : 23.70433 95% confidence interval = ( 21.74433 , 25.66433 )
## Predicted value at location 144 : 22.49642 95% confidence interval = ( 20.53642 , 24.45642 )
## Predicted value at location 145 : 19.11131 95% confidence interval = ( 17.15131 , 21.07131 )
## Predicted value at location 146 : 29.6874 95% confidence interval = ( 27.7274 , 31.6474 )
## Predicted value at location 147 : 36.22471 95% confidence interval = ( 34.26471 , 38.18471 )
## Predicted value at location 148 : 21.11716 95% confidence interval = ( 19.15716 , 23.07716 )
## Predicted value at location 149 : 37.1434 95% confidence interval = ( 35.1834 , 39.1034 )
## Predicted value at location 150 : 27.24721 95% confidence interval = ( 25.28721 , 29.20721 )
## Predicted value at location 151 : 35.28732 95% confidence interval = ( 33.32732 , 37.24732 )
## Predicted value at location 152 : 42.43722 95% confidence interval = ( 40.47722 , 44.39722 )
## Predicted value at location 153 : 34.97402 95% confidence interval = ( 33.01402 , 36.93402 )
## Predicted value at location 154 : 40.09528 95% confidence interval = ( 38.13528 , 42.05528 )
## Predicted value at location 155 : 20.99856 95% confidence interval = ( 19.03856 , 22.95856 )
## Predicted value at location 156 : 28.08853 95% confidence interval = ( 26.12853 , 30.04853 )
## Predicted value at location 157 : 29.7972 95% confidence interval = ( 27.8372 , 31.7572 )
## Predicted value at location 158 : 28.41447 95% confidence interval = ( 26.45447 , 30.37447 )
## Predicted value at location 159 : 37.74385 95% confidence interval = ( 35.78385 , 39.70385 )
## Predicted value at location 160 : 21.52299 95% confidence interval = ( 19.56299 , 23.48299 )
## Predicted value at location 161 : 27.92363 95% confidence interval = ( 25.96363 , 29.88363 )
## Predicted value at location 162 : 27.57092 95% confidence interval = ( 25.61092 , 29.53092 )
## Predicted value at location 163 : 18.92711 95% confidence interval = ( 16.96711 , 20.88711 )
## Predicted value at location 164 : 18.47403 95% confidence interval = ( 16.51403 , 20.43403 )
## Predicted value at location 165 : 25.87887 95% confidence interval = ( 23.91887 , 27.83887 )
## Predicted value at location 166 : 33.38613 95% confidence interval = ( 31.42613 , 35.34613 )
## Predicted value at location 167 : 28.7788 95% confidence interval = ( 26.8188 , 30.7388 )
## Predicted value at location 168 : 27.34065 95% confidence interval = ( 25.38065 , 29.30065 )
## Predicted value at location 169 : 31.07701 95% confidence interval = ( 29.11701 , 33.03701 )
## Predicted value at location 170 : 32.80838 95% confidence interval = ( 30.84838 , 34.76838 )
## Predicted value at location 171 : 28.94615 95% confidence interval = ( 26.98615 , 30.90615 )
## Predicted value at location 172 : 22.21396 95% confidence interval = ( 20.25396 , 24.17396 )
## Predicted value at location 173 : 26.13 95% confidence interval = ( 24.17 , 28.09 )
## Predicted value at location 174 : 37.43449 95% confidence interval = ( 35.47449 , 39.39449 )
## Predicted value at location 175 : 19.39546 95% confidence interval = ( 17.43546 , 21.35546 )
## Predicted value at location 176 : 18.31241 95% confidence interval = ( 16.35241 , 20.27241 )
## Predicted value at location 177 : 19.97971 95% confidence interval = ( 18.01971 , 21.93971 )
## Predicted value at location 178 : 25.7411 95% confidence interval = ( 23.7811 , 27.7011 )
## Predicted value at location 179 : 29.57429 95% confidence interval = ( 27.61429 , 31.53429 )
## Predicted value at location 180 : 26.63129 95% confidence interval = ( 24.67129 , 28.59129 )
## Predicted value at location 181 : 35.62397 95% confidence interval = ( 33.66397 , 37.58397 )
## Predicted value at location 182 : 34.36269 95% confidence interval = ( 32.40269 , 36.32269 )
## Predicted value at location 183 : 33.69219 95% confidence interval = ( 31.73219 , 35.65219 )
## Predicted value at location 184 : 25.80925 95% confidence interval = ( 23.84925 , 27.76925 )
## Predicted value at location 185 : 30.7767 95% confidence interval = ( 28.8167 , 32.7367 )
## Predicted value at location 186 : 33.3298 95% confidence interval = ( 31.3698 , 35.2898 )
## Predicted value at location 187 : 29.62576 95% confidence interval = ( 27.66576 , 31.58576 )
## Predicted value at location 188 : 24.55745 95% confidence interval = ( 22.59745 , 26.51745 )
## Predicted value at location 189 : 30.9033 95% confidence interval = ( 28.9433 , 32.8633 )
## Predicted value at location 190 : 29.1154 95% confidence interval = ( 27.1554 , 31.0754 )
## Predicted value at location 191 : 22.17925 95% confidence interval = ( 20.21925 , 24.13925 )
## Predicted value at location 192 : 21.62196 95% confidence interval = ( 19.66196 , 23.58196 )
## Predicted value at location 193 : 38.73212 95% confidence interval = ( 36.77212 , 40.69212 )
## Predicted value at location 194 : 29.93407 95% confidence interval = ( 27.97407 , 31.89407 )
## Predicted value at location 195 : 22.57631 95% confidence interval = ( 20.61631 , 24.53631 )
## Predicted value at location 196 : 30.96629 95% confidence interval = ( 29.00629 , 32.92629 )
## Predicted value at location 197 : 26.41528 95% confidence interval = ( 24.45528 , 28.37528 )
## Predicted value at location 198 : 29.84253 95% confidence interval = ( 27.88253 , 31.80253 )
## Predicted value at location 199 : 23.54815 95% confidence interval = ( 21.58815 , 25.50815 )
## Predicted value at location 200 : 39.82212 95% confidence interval = ( 37.86212 , 41.78212 )
## Predicted value at location 201 : 26.11491 95% confidence interval = ( 24.15491 , 28.07491 )
## Predicted value at location 202 : 37.72915 95% confidence interval = ( 35.76915 , 39.68915 )
## Predicted value at location 203 : 31.4343 95% confidence interval = ( 29.4743 , 33.3943 )
## Predicted value at location 204 : 29.18748 95% confidence interval = ( 27.22748 , 31.14748 )
## Predicted value at location 205 : 25.86107 95% confidence interval = ( 23.90107 , 27.82107 )
## Predicted value at location 206 : 29.22046 95% confidence interval = ( 27.26046 , 31.18046 )
## Predicted value at location 207 : 22.37293 95% confidence interval = ( 20.41293 , 24.33293 )
## Predicted value at location 208 : 28.00292 95% confidence interval = ( 26.04292 , 29.96292 )
## Predicted value at location 209 : 26.24275 95% confidence interval = ( 24.28275 , 28.20275 )
## Predicted value at location 210 : 36.54174 95% confidence interval = ( 34.58174 , 38.50174 )
## Predicted value at location 211 : 28.5021 95% confidence interval = ( 26.5421 , 30.4621 )
## Predicted value at location 212 : 31.17964 95% confidence interval = ( 29.21964 , 33.13964 )
## Predicted value at location 213 : 18.47732 95% confidence interval = ( 16.51732 , 20.43732 )
## Predicted value at location 214 : 26.44329 95% confidence interval = ( 24.48329 , 28.40329 )
## Predicted value at location 215 : 28.25375 95% confidence interval = ( 26.29375 , 30.21375 )
## Predicted value at location 216 : 18.89611 95% confidence interval = ( 16.93611 , 20.85611 )
## Predicted value at location 217 : 25.16543 95% confidence interval = ( 23.20543 , 27.12543 )
## Predicted value at location 218 : 26.09708 95% confidence interval = ( 24.13708 , 28.05708 )
## Predicted value at location 219 : 25.87035 95% confidence interval = ( 23.91035 , 27.83035 )
## Predicted value at location 220 : 38.2389 95% confidence interval = ( 36.2789 , 40.1989 )
## Predicted value at location 221 : 21.44939 95% confidence interval = ( 19.48939 , 23.40939 )
## Predicted value at location 222 : 33.81674 95% confidence interval = ( 31.85674 , 35.77674 )
## Predicted value at location 223 : 23.83366 95% confidence interval = ( 21.87366 , 25.79366 )
## Predicted value at location 224 : 22.54315 95% confidence interval = ( 20.58315 , 24.50315 )
## Predicted value at location 225 : 23.96696 95% confidence interval = ( 22.00696 , 25.92696 )
## Predicted value at location 226 : 36.43361 95% confidence interval = ( 34.47361 , 38.39361 )
## Predicted value at location 227 : 32.29958 95% confidence interval = ( 30.33958 , 34.25958 )
## Predicted value at location 228 : 27.25303 95% confidence interval = ( 25.29303 , 29.21303 )
## Predicted value at location 229 : 33.28197 95% confidence interval = ( 31.32197 , 35.24197 )
## Predicted value at location 230 : 31.30974 95% confidence interval = ( 29.34974 , 33.26974 )
## Predicted value at location 231 : 27.46141 95% confidence interval = ( 25.50141 , 29.42141 )
## Predicted value at location 232 : 31.50417 95% confidence interval = ( 29.54417 , 33.46417 )
## Predicted value at location 233 : 25.86852 95% confidence interval = ( 23.90852 , 27.82852 )
## Predicted value at location 234 : 36.38597 95% confidence interval = ( 34.42597 , 38.34597 )
## Predicted value at location 235 : 24.16908 95% confidence interval = ( 22.20908 , 26.12908 )
## Predicted value at location 236 : 35.28424 95% confidence interval = ( 33.32424 , 37.24424 )
## Predicted value at location 237 : 26.4726 95% confidence interval = ( 24.5126 , 28.4326 )
## Predicted value at location 238 : 33.20699 95% confidence interval = ( 31.24699 , 35.16699 )
## Predicted value at location 239 : 36.0696 95% confidence interval = ( 34.1096 , 38.0296 )
## Predicted value at location 240 : 36.51404 95% confidence interval = ( 34.55404 , 38.47404 )
## Predicted value at location 241 : 29.93803 95% confidence interval = ( 27.97803 , 31.89803 )
## Predicted value at location 242 : 35.32317 95% confidence interval = ( 33.36317 , 37.28317 )
## Predicted value at location 243 : 25.97144 95% confidence interval = ( 24.01144 , 27.93144 )
## Predicted value at location 244 : 27.58902 95% confidence interval = ( 25.62902 , 29.54902 )
## Predicted value at location 245 : 31.31886 95% confidence interval = ( 29.35886 , 33.27886 )
## Predicted value at location 246 : 27.70302 95% confidence interval = ( 25.74302 , 29.66302 )
## Predicted value at location 247 : 30.4516 95% confidence interval = ( 28.4916 , 32.4116 )
## Predicted value at location 248 : 28.72972 95% confidence interval = ( 26.76972 , 30.68972 )
## Predicted value at location 249 : 29.83671 95% confidence interval = ( 27.87671 , 31.79671 )
## Predicted value at location 250 : 30.717 95% confidence interval = ( 28.757 , 32.677 )
## Predicted value at location 251 : 35.77615 95% confidence interval = ( 33.81615 , 37.73615 )
## Predicted value at location 252 : 28.43032 95% confidence interval = ( 26.47032 , 30.39032 )
## Predicted value at location 253 : 33.29128 95% confidence interval = ( 31.33128 , 35.25128 )
## Predicted value at location 254 : 21.38555 95% confidence interval = ( 19.42555 , 23.34555 )
## Predicted value at location 255 : 24.42143 95% confidence interval = ( 22.46143 , 26.38143 )
## Predicted value at location 256 : 22.67443 95% confidence interval = ( 20.71443 , 24.63443 )
## Predicted value at location 257 : 23.6916 95% confidence interval = ( 21.7316 , 25.6516 )
## Predicted value at location 258 : 28.0838 95% confidence interval = ( 26.1238 , 30.0438 )
## Predicted value at location 259 : 22.89345 95% confidence interval = ( 20.93345 , 24.85345 )
## Predicted value at location 260 : 30.59571 95% confidence interval = ( 28.63571 , 32.55571 )
## Predicted value at location 261 : 22.61341 95% confidence interval = ( 20.65341 , 24.57341 )
## Predicted value at location 262 : 27.13329 95% confidence interval = ( 25.17329 , 29.09329 )
## Predicted value at location 263 : 40.45874 95% confidence interval = ( 38.49874 , 42.41874 )
## Predicted value at location 264 : 30.79515 95% confidence interval = ( 28.83515 , 32.75515 )
## Predicted value at location 265 : 33.22524 95% confidence interval = ( 31.26524 , 35.18524 )
## Predicted value at location 266 : 35.31969 95% confidence interval = ( 33.35969 , 37.27969 )
## Predicted value at location 267 : 25.9615 95% confidence interval = ( 24.0015 , 27.9215 )
## Predicted value at location 268 : 21.48728 95% confidence interval = ( 19.52728 , 23.44728 )
## Predicted value at location 269 : 20.87592 95% confidence interval = ( 18.91592 , 22.83592 )
## Predicted value at location 270 : 31.41487 95% confidence interval = ( 29.45487 , 33.37487 )
## Predicted value at location 271 : 25.90538 95% confidence interval = ( 23.94538 , 27.86538 )
## Predicted value at location 272 : 29.77792 95% confidence interval = ( 27.81792 , 31.73792 )
## Predicted value at location 273 : 23.16199 95% confidence interval = ( 21.20199 , 25.12199 )
## Predicted value at location 274 : 29.9581 95% confidence interval = ( 27.9981 , 31.9181 )
## Predicted value at location 275 : 30.82124 95% confidence interval = ( 28.86124 , 32.78124 )
## Predicted value at location 276 : 31.90534 95% confidence interval = ( 29.94534 , 33.86534 )
## Predicted value at location 277 : 38.1179 95% confidence interval = ( 36.1579 , 40.0779 )
## Predicted value at location 278 : 38.33345 95% confidence interval = ( 36.37345 , 40.29345 )
## Predicted value at location 279 : 32.56913 95% confidence interval = ( 30.60913 , 34.52913 )
## Predicted value at location 280 : 31.78081 95% confidence interval = ( 29.82081 , 33.74081 )
## Predicted value at location 281 : 20.9935 95% confidence interval = ( 19.0335 , 22.9535 )
## Predicted value at location 282 : 33.70809 95% confidence interval = ( 31.74809 , 35.66809 )
## Predicted value at location 283 : 27.51924 95% confidence interval = ( 25.55924 , 29.47924 )
## Predicted value at location 284 : 20.8271 95% confidence interval = ( 18.8671 , 22.7871 )
## Predicted value at location 285 : 36.02438 95% confidence interval = ( 34.06438 , 37.98438 )
## Predicted value at location 286 : 32.09821 95% confidence interval = ( 30.13821 , 34.05821 )
## Predicted value at location 287 : 39.61435 95% confidence interval = ( 37.65435 , 41.57435 )
## Predicted value at location 288 : 33.01362 95% confidence interval = ( 31.05362 , 34.97362 )
## Predicted value at location 289 : 31.99511 95% confidence interval = ( 30.03511 , 33.95511 )
## Predicted value at location 290 : 31.10526 95% confidence interval = ( 29.14526 , 33.06526 )
## Predicted value at location 291 : 26.40243 95% confidence interval = ( 24.44243 , 28.36243 )
## Predicted value at location 292 : 29.37657 95% confidence interval = ( 27.41657 , 31.33657 )
## Predicted value at location 293 : 29.99978 95% confidence interval = ( 28.03978 , 31.95978 )
## Predicted value at location 294 : 31.09562 95% confidence interval = ( 29.13562 , 33.05562 )
## Predicted value at location 295 : 29.97413 95% confidence interval = ( 28.01413 , 31.93413 )
## Predicted value at location 296 : 31.15646 95% confidence interval = ( 29.19646 , 33.11646 )
## Predicted value at location 297 : 36.56043 95% confidence interval = ( 34.60043 , 38.52043 )
## Predicted value at location 298 : 36.17376 95% confidence interval = ( 34.21376 , 38.13376 )
## Predicted value at location 299 : 28.11487 95% confidence interval = ( 26.15487 , 30.07487 )
## Predicted value at location 300 : 21.99476 95% confidence interval = ( 20.03476 , 23.95476 )
## Predicted value at location 301 : 31.24639 95% confidence interval = ( 29.28639 , 33.20639 )
## Predicted value at location 302 : 31.21638 95% confidence interval = ( 29.25638 , 33.17638 )
## Predicted value at location 303 : 31.42133 95% confidence interval = ( 29.46133 , 33.38133 )
## Predicted value at location 304 : 43.59792 95% confidence interval = ( 41.63792 , 45.55792 )
## Predicted value at location 305 : 19.92104 95% confidence interval = ( 17.96104 , 21.88104 )
## Predicted value at location 306 : 29.17809 95% confidence interval = ( 27.21809 , 31.13809 )
## Predicted value at location 307 : 33.42922 95% confidence interval = ( 31.46922 , 35.38922 )
## Predicted value at location 308 : 33.04024 95% confidence interval = ( 31.08024 , 35.00024 )
## Predicted value at location 309 : 36.45164 95% confidence interval = ( 34.49164 , 38.41164 )
## Predicted value at location 310 : 34.39494 95% confidence interval = ( 32.43494 , 36.35494 )
## Predicted value at location 311 : 39.92052 95% confidence interval = ( 37.96052 , 41.88052 )
## Predicted value at location 312 : 36.83333 95% confidence interval = ( 34.87333 , 38.79333 )
## Predicted value at location 313 : 25.76648 95% confidence interval = ( 23.80648 , 27.72648 )
## Predicted value at location 314 : 19.17696 95% confidence interval = ( 17.21696 , 21.13696 )
## Predicted value at location 315 : 24.23883 95% confidence interval = ( 22.27883 , 26.19883 )
## Predicted value at location 316 : 25.55668 95% confidence interval = ( 23.59668 , 27.51668 )
## Predicted value at location 317 : 31.33815 95% confidence interval = ( 29.37815 , 33.29815 )
## Predicted value at location 318 : 35.80292 95% confidence interval = ( 33.84292 , 37.76292 )
## Predicted value at location 319 : 25.5809 95% confidence interval = ( 23.6209 , 27.5409 )
## Predicted value at location 320 : 20.817 95% confidence interval = ( 18.857 , 22.777 )
## Predicted value at location 321 : 35.01419 95% confidence interval = ( 33.05419 , 36.97419 )
## Predicted value at location 322 : 36.72764 95% confidence interval = ( 34.76764 , 38.68764 )
## Predicted value at location 323 : 43.54941 95% confidence interval = ( 41.58941 , 45.50941 )
## Predicted value at location 324 : 23.01925 95% confidence interval = ( 21.05925 , 24.97925 )
## Predicted value at location 325 : 28.55332 95% confidence interval = ( 26.59332 , 30.51332 )
## Predicted value at location 326 : 26.2082 95% confidence interval = ( 24.2482 , 28.1682 )
## Predicted value at location 327 : 16.98608 95% confidence interval = ( 15.02608 , 18.94608 )
## Predicted value at location 328 : 28.34197 95% confidence interval = ( 26.38197 , 30.30197 )
## Predicted value at location 329 : 36.56296 95% confidence interval = ( 34.60296 , 38.52296 )
## Predicted value at location 330 : 30.54898 95% confidence interval = ( 28.58898 , 32.50898 )
## Predicted value at location 331 : 40.46819 95% confidence interval = ( 38.50819 , 42.42819 )
## Predicted value at location 332 : 18.42666 95% confidence interval = ( 16.46666 , 20.38666 )
## Predicted value at location 333 : 22.00317 95% confidence interval = ( 20.04317 , 23.96317 )
## Predicted value at location 334 : 21.51276 95% confidence interval = ( 19.55276 , 23.47276 )
## Predicted value at location 335 : 36.22985 95% confidence interval = ( 34.26985 , 38.18985 )
## Predicted value at location 336 : 19.47623 95% confidence interval = ( 17.51623 , 21.43623 )
## Predicted value at location 337 : 20.29149 95% confidence interval = ( 18.33149 , 22.25149 )
## Predicted value at location 338 : 30.41747 95% confidence interval = ( 28.45747 , 32.37747 )
## Predicted value at location 339 : 20.13387 95% confidence interval = ( 18.17387 , 22.09387 )
## Predicted value at location 340 : 34.77307 95% confidence interval = ( 32.81307 , 36.73307 )
## Predicted value at location 341 : 35.42603 95% confidence interval = ( 33.46603 , 37.38603 )
## Predicted value at location 342 : 19.95913 95% confidence interval = ( 17.99913 , 21.91913 )
## Predicted value at location 343 : 35.98655 95% confidence interval = ( 34.02655 , 37.94655 )
## Predicted value at location 344 : 39.70071 95% confidence interval = ( 37.74071 , 41.66071 )
## Predicted value at location 345 : 23.35613 95% confidence interval = ( 21.39613 , 25.31613 )
## Predicted value at location 346 : 30.88799 95% confidence interval = ( 28.92799 , 32.84799 )
## Predicted value at location 347 : 21.5149 95% confidence interval = ( 19.5549 , 23.4749 )
## Predicted value at location 348 : 32.41141 95% confidence interval = ( 30.45141 , 34.37141 )
## Predicted value at location 349 : 23.05176 95% confidence interval = ( 21.09176 , 25.01176 )
## Predicted value at location 350 : 27.93595 95% confidence interval = ( 25.97595 , 29.89595 )
## Predicted value at location 351 : 28.53174 95% confidence interval = ( 26.57174 , 30.49174 )
## Predicted value at location 352 : 23.71061 95% confidence interval = ( 21.75061 , 25.67061 )
## Predicted value at location 353 : 32.85159 95% confidence interval = ( 30.89159 , 34.81159 )
## Predicted value at location 354 : 21.68641 95% confidence interval = ( 19.72641 , 23.64641 )
## Predicted value at location 355 : 29.90588 95% confidence interval = ( 27.94588 , 31.86588 )
## Predicted value at location 356 : 32.90229 95% confidence interval = ( 30.94229 , 34.86229 )
## Predicted value at location 357 : 31.78065 95% confidence interval = ( 29.82065 , 33.74065 )
## Predicted value at location 358 : 25.95152 95% confidence interval = ( 23.99152 , 27.91152 )
## Predicted value at location 359 : 20.45003 95% confidence interval = ( 18.49003 , 22.41003 )
## Predicted value at location 360 : 30.83024 95% confidence interval = ( 28.87024 , 32.79024 )
## Predicted value at location 361 : 25.85075 95% confidence interval = ( 23.89075 , 27.81075 )
## Predicted value at location 362 : 21.43856 95% confidence interval = ( 19.47856 , 23.39856 )
## Predicted value at location 363 : 27.02343 95% confidence interval = ( 25.06343 , 28.98343 )
## Predicted value at location 364 : 31.37484 95% confidence interval = ( 29.41484 , 33.33484 )
## Predicted value at location 365 : 40.67314 95% confidence interval = ( 38.71314 , 42.63314 )
## Predicted value at location 366 : 31.23294 95% confidence interval = ( 29.27294 , 33.19294 )
## Predicted value at location 1 : 26.9392 95% confidence interval = ( 24.9792 , 28.8992 )
## Predicted value at location 2 : 28.70988 95% confidence interval = ( 26.74988 , 30.66988 )
## Predicted value at location 3 : 31.27205 95% confidence interval = ( 29.31205 , 33.23205 )
## Predicted value at location 4 : 32.83638 95% confidence interval = ( 30.87638 , 34.79638 )
## Predicted value at location 5 : 32.99619 95% confidence interval = ( 31.03619 , 34.95619 )
## Predicted value at location 6 : 25.81099 95% confidence interval = ( 23.85099 , 27.77099 )
## Predicted value at location 7 : 23.85603 95% confidence interval = ( 21.89603 , 25.81603 )
## Predicted value at location 8 : 36.43612 95% confidence interval = ( 34.47612 , 38.39612 )
## Predicted value at location 9 : 37.2526 95% confidence interval = ( 35.2926 , 39.2126 )
## Predicted value at location 10 : 33.518 95% confidence interval = ( 31.558 , 35.478 )
## Predicted value at location 11 : 24.33208 95% confidence interval = ( 22.37208 , 26.29208 )
## Predicted value at location 12 : 25.27226 95% confidence interval = ( 23.31226 , 27.23226 )
## Predicted value at location 13 : 43.45287 95% confidence interval = ( 41.49287 , 45.41287 )
## Predicted value at location 14 : 20.81154 95% confidence interval = ( 18.85154 , 22.77154 )
## Predicted value at location 15 : 44.09103 95% confidence interval = ( 42.13103 , 46.05103 )
## Predicted value at location 16 : 42.18769 95% confidence interval = ( 40.22769 , 44.14769 )
## Predicted value at location 17 : 29.98101 95% confidence interval = ( 28.02101 , 31.94101 )
## Predicted value at location 18 : 29.81112 95% confidence interval = ( 27.85112 , 31.77112 )
## Predicted value at location 19 : 29.76148 95% confidence interval = ( 27.80148 , 31.72148 )
## Predicted value at location 20 : 26.28152 95% confidence interval = ( 24.32152 , 28.24152 )
## Predicted value at location 21 : 25.73721 95% confidence interval = ( 23.77721 , 27.69721 )
## Predicted value at location 22 : 23.93419 95% confidence interval = ( 21.97419 , 25.89419 )
## Predicted value at location 23 : 35.78563 95% confidence interval = ( 33.82563 , 37.74563 )
## Predicted value at location 24 : 37.08867 95% confidence interval = ( 35.12867 , 39.04867 )
## Predicted value at location 25 : 27.28833 95% confidence interval = ( 25.32833 , 29.24833 )
## Predicted value at location 26 : 25.80918 95% confidence interval = ( 23.84918 , 27.76918 )
## Predicted value at location 27 : 29.14907 95% confidence interval = ( 27.18907 , 31.10907 )
## Predicted value at location 28 : 31.29332 95% confidence interval = ( 29.33332 , 33.25332 )
## Predicted value at location 29 : 36.112 95% confidence interval = ( 34.152 , 38.072 )
## Predicted value at location 30 : 29.67423 95% confidence interval = ( 27.71423 , 31.63423 )
## Predicted value at location 31 : 30.69238 95% confidence interval = ( 28.73238 , 32.65238 )
## Predicted value at location 32 : 30.6379 95% confidence interval = ( 28.6779 , 32.5979 )
## Predicted value at location 33 : 29.36867 95% confidence interval = ( 27.40867 , 31.32867 )
## Predicted value at location 34 : 44.01643 95% confidence interval = ( 42.05643 , 45.97643 )
## Predicted value at location 35 : 30.85674 95% confidence interval = ( 28.89674 , 32.81674 )
## Predicted value at location 36 : 30.72417 95% confidence interval = ( 28.76417 , 32.68417 )
## Predicted value at location 37 : 23.85001 95% confidence interval = ( 21.89001 , 25.81001 )
## Predicted value at location 38 : 22.79906 95% confidence interval = ( 20.83906 , 24.75906 )
## Predicted value at location 39 : 25.82627 95% confidence interval = ( 23.86627 , 27.78627 )
## Predicted value at location 40 : 35.90695 95% confidence interval = ( 33.94695 , 37.86695 )
## Predicted value at location 41 : 37.49303 95% confidence interval = ( 35.53303 , 39.45303 )
## Predicted value at location 42 : 40.49797 95% confidence interval = ( 38.53797 , 42.45797 )
## Predicted value at location 43 : 38.34253 95% confidence interval = ( 36.38253 , 40.30253 )
## Predicted value at location 44 : 46.26792 95% confidence interval = ( 44.30792 , 48.22792 )
## Predicted value at location 45 : 34.56122 95% confidence interval = ( 32.60122 , 36.52122 )
## Predicted value at location 46 : 38.22306 95% confidence interval = ( 36.26306 , 40.18306 )
## Predicted value at location 47 : 41.3119 95% confidence interval = ( 39.3519 , 43.2719 )
## Predicted value at location 48 : 32.55324 95% confidence interval = ( 30.59324 , 34.51324 )
## Predicted value at location 49 : 40.78611 95% confidence interval = ( 38.82611 , 42.74611 )
## Predicted value at location 50 : 39.06118 95% confidence interval = ( 37.10118 , 41.02118 )
## Predicted value at location 51 : 20.21588 95% confidence interval = ( 18.25588 , 22.17588 )
## Predicted value at location 52 : 21.60139 95% confidence interval = ( 19.64139 , 23.56139 )
## Predicted value at location 53 : 24.76046 95% confidence interval = ( 22.80046 , 26.72046 )
## Predicted value at location 54 : 37.14917 95% confidence interval = ( 35.18917 , 39.10917 )
## Predicted value at location 55 : 23.78464 95% confidence interval = ( 21.82464 , 25.74464 )
## Predicted value at location 56 : 30.6803 95% confidence interval = ( 28.7203 , 32.6403 )
## Predicted value at location 57 : 38.73033 95% confidence interval = ( 36.77033 , 40.69033 )
## Predicted value at location 58 : 28.60157 95% confidence interval = ( 26.64157 , 30.56157 )
## Predicted value at location 59 : 20.73728 95% confidence interval = ( 18.77728 , 22.69728 )
## Predicted value at location 60 : 25.04975 95% confidence interval = ( 23.08975 , 27.00975 )
## Predicted value at location 61 : 38.75304 95% confidence interval = ( 36.79304 , 40.71304 )
## Predicted value at location 62 : 37.73107 95% confidence interval = ( 35.77107 , 39.69107 )
## Predicted value at location 63 : 31.43983 95% confidence interval = ( 29.47983 , 33.39983 )
## Predicted value at location 64 : 36.66684 95% confidence interval = ( 34.70684 , 38.62684 )
## Predicted value at location 65 : 25.69742 95% confidence interval = ( 23.73742 , 27.65742 )
## Predicted value at location 66 : 25.2649 95% confidence interval = ( 23.3049 , 27.2249 )
## Predicted value at location 67 : 20.79441 95% confidence interval = ( 18.83441 , 22.75441 )
## Predicted value at location 68 : 29.97672 95% confidence interval = ( 28.01672 , 31.93672 )
## Predicted value at location 69 : 24.04739 95% confidence interval = ( 22.08739 , 26.00739 )
## Predicted value at location 70 : 29.8914 95% confidence interval = ( 27.9314 , 31.8514 )
## Predicted value at location 71 : 26.25713 95% confidence interval = ( 24.29713 , 28.21713 )
## Predicted value at location 72 : 30.24844 95% confidence interval = ( 28.28844 , 32.20844 )
## Predicted value at location 73 : 39.93354 95% confidence interval = ( 37.97354 , 41.89354 )
## Predicted value at location 74 : 29.54897 95% confidence interval = ( 27.58897 , 31.50897 )
## Predicted value at location 75 : 38.79986 95% confidence interval = ( 36.83986 , 40.75986 )
## Predicted value at location 76 : 33.96448 95% confidence interval = ( 32.00448 , 35.92448 )
## Predicted value at location 77 : 20.69274 95% confidence interval = ( 18.73274 , 22.65274 )
## Predicted value at location 78 : 32.86982 95% confidence interval = ( 30.90982 , 34.82982 )
## Predicted value at location 79 : 24.27128 95% confidence interval = ( 22.31128 , 26.23128 )
## Predicted value at location 80 : 22.28394 95% confidence interval = ( 20.32394 , 24.24394 )
## Predicted value at location 81 : 20.55221 95% confidence interval = ( 18.59221 , 22.51221 )
## Predicted value at location 82 : 24.01124 95% confidence interval = ( 22.05124 , 25.97124 )
## Predicted value at location 83 : 25.64732 95% confidence interval = ( 23.68732 , 27.60732 )
## Predicted value at location 84 : 30.07871 95% confidence interval = ( 28.11871 , 32.03871 )
## Predicted value at location 85 : 24.24656 95% confidence interval = ( 22.28656 , 26.20656 )
## Predicted value at location 86 : 29.86396 95% confidence interval = ( 27.90396 , 31.82396 )
## Predicted value at location 87 : 40.68284 95% confidence interval = ( 38.72284 , 42.64284 )
## Predicted value at location 88 : 25.82911 95% confidence interval = ( 23.86911 , 27.78911 )
## Predicted value at location 89 : 29.90707 95% confidence interval = ( 27.94707 , 31.86707 )
## Predicted value at location 90 : 26.58075 95% confidence interval = ( 24.62075 , 28.54075 )
## Predicted value at location 91 : 29.75868 95% confidence interval = ( 27.79868 , 31.71868 )
## Predicted value at location 92 : 26.24764 95% confidence interval = ( 24.28764 , 28.20764 )
## Predicted value at location 93 : 35.36312 95% confidence interval = ( 33.40312 , 37.32312 )
## Predicted value at location 94 : 29.7797 95% confidence interval = ( 27.8197 , 31.7397 )
## Predicted value at location 95 : 23.43634 95% confidence interval = ( 21.47634 , 25.39634 )
## Predicted value at location 96 : 21.72063 95% confidence interval = ( 19.76063 , 23.68063 )
## Predicted value at location 97 : 30.67354 95% confidence interval = ( 28.71354 , 32.63354 )
## Predicted value at location 98 : 27.672 95% confidence interval = ( 25.712 , 29.632 )
## Predicted value at location 99 : 35.3391 95% confidence interval = ( 33.3791 , 37.2991 )
## Predicted value at location 100 : 22.82981 95% confidence interval = ( 20.86981 , 24.78981 )
## Predicted value at location 101 : 27.57 95% confidence interval = ( 25.61 , 29.53 )
## Predicted value at location 102 : 27.18164 95% confidence interval = ( 25.22164 , 29.14164 )
## Predicted value at location 103 : 33.42559 95% confidence interval = ( 31.46559 , 35.38559 )
## Predicted value at location 104 : 24.44184 95% confidence interval = ( 22.48184 , 26.40184 )
## Predicted value at location 105 : 27.05328 95% confidence interval = ( 25.09328 , 29.01328 )
## Predicted value at location 106 : 29.0302 95% confidence interval = ( 27.0702 , 30.9902 )
## Predicted value at location 107 : 39.47001 95% confidence interval = ( 37.51001 , 41.43001 )
## Predicted value at location 108 : 30.33171 95% confidence interval = ( 28.37171 , 32.29171 )
## Predicted value at location 109 : 28.75989 95% confidence interval = ( 26.79989 , 30.71989 )
## Predicted value at location 110 : 31.00978 95% confidence interval = ( 29.04978 , 32.96978 )
## Predicted value at location 111 : 25.63326 95% confidence interval = ( 23.67326 , 27.59326 )
## Predicted value at location 112 : 24.19969 95% confidence interval = ( 22.23969 , 26.15969 )
## Predicted value at location 113 : 28.59351 95% confidence interval = ( 26.63351 , 30.55351 )
## Predicted value at location 114 : 39.66817 95% confidence interval = ( 37.70817 , 41.62817 )
## Predicted value at location 115 : 30.78097 95% confidence interval = ( 28.82097 , 32.74097 )
## Predicted value at location 116 : 22.40643 95% confidence interval = ( 20.44643 , 24.36643 )
## Predicted value at location 117 : 37.65852 95% confidence interval = ( 35.69852 , 39.61852 )
## Predicted value at location 118 : 32.79884 95% confidence interval = ( 30.83884 , 34.75884 )
## Predicted value at location 119 : 32.62382 95% confidence interval = ( 30.66382 , 34.58382 )
## Predicted value at location 120 : 35.38104 95% confidence interval = ( 33.42104 , 37.34104 )
## Predicted value at location 121 : 25.31299 95% confidence interval = ( 23.35299 , 27.27299 )
## Predicted value at location 122 : 33.27116 95% confidence interval = ( 31.31116 , 35.23116 )
## Predicted value at location 123 : 31.07842 95% confidence interval = ( 29.11842 , 33.03842 )
## Predicted value at location 124 : 44.47603 95% confidence interval = ( 42.51603 , 46.43603 )
## Predicted value at location 125 : 26.69121 95% confidence interval = ( 24.73121 , 28.65121 )
## Predicted value at location 126 : 33.66266 95% confidence interval = ( 31.70266 , 35.62266 )
## Predicted value at location 127 : 25.71917 95% confidence interval = ( 23.75917 , 27.67917 )
## Predicted value at location 128 : 30.44501 95% confidence interval = ( 28.48501 , 32.40501 )
## Predicted value at location 129 : 29.71676 95% confidence interval = ( 27.75676 , 31.67676 )
## Predicted value at location 130 : 28.79581 95% confidence interval = ( 26.83581 , 30.75581 )
## Predicted value at location 131 : 29.73395 95% confidence interval = ( 27.77395 , 31.69395 )
## Predicted value at location 132 : 22.04506 95% confidence interval = ( 20.08506 , 24.00506 )
## Predicted value at location 133 : 27.67249 95% confidence interval = ( 25.71249 , 29.63249 )
## Predicted value at location 134 : 26.17421 95% confidence interval = ( 24.21421 , 28.13421 )
## Predicted value at location 135 : 33.2171 95% confidence interval = ( 31.2571 , 35.1771 )
## Predicted value at location 136 : 35.16278 95% confidence interval = ( 33.20278 , 37.12278 )
## Predicted value at location 137 : 29.20819 95% confidence interval = ( 27.24819 , 31.16819 )
## Predicted value at location 138 : 27.644 95% confidence interval = ( 25.684 , 29.604 )
## Predicted value at location 139 : 28.5945 95% confidence interval = ( 26.6345 , 30.5545 )
## Predicted value at location 140 : 30.69881 95% confidence interval = ( 28.73881 , 32.65881 )
## Predicted value at location 141 : 22.41386 95% confidence interval = ( 20.45386 , 24.37386 )
## Predicted value at location 142 : 30.91263 95% confidence interval = ( 28.95263 , 32.87263 )
## Predicted value at location 143 : 21.87276 95% confidence interval = ( 19.91276 , 23.83276 )
## Predicted value at location 144 : 24.57947 95% confidence interval = ( 22.61947 , 26.53947 )
## Predicted value at location 145 : 23.01987 95% confidence interval = ( 21.05987 , 24.97987 )
## Predicted value at location 146 : 31.83025 95% confidence interval = ( 29.87025 , 33.79025 )
## Predicted value at location 147 : 29.23789 95% confidence interval = ( 27.27789 , 31.19789 )
## Predicted value at location 148 : 20.08376 95% confidence interval = ( 18.12376 , 22.04376 )
## Predicted value at location 149 : 20.46204 95% confidence interval = ( 18.50204 , 22.42204 )
## Predicted value at location 150 : 39.18631 95% confidence interval = ( 37.22631 , 41.14631 )
## Predicted value at location 151 : 23.83072 95% confidence interval = ( 21.87072 , 25.79072 )
## Predicted value at location 152 : 28.02248 95% confidence interval = ( 26.06248 , 29.98248 )
## Predicted value at location 153 : 38.53664 95% confidence interval = ( 36.57664 , 40.49664 )
## Predicted value at location 154 : 28.30201 95% confidence interval = ( 26.34201 , 30.26201 )
## Predicted value at location 155 : 43.51112 95% confidence interval = ( 41.55112 , 45.47112 )
## Predicted value at location 156 : 30.81777 95% confidence interval = ( 28.85777 , 32.77777 )
## Predicted value at location 157 : 28.53036 95% confidence interval = ( 26.57036 , 30.49036 )
## Predicted value at location 158 : 22.26834 95% confidence interval = ( 20.30834 , 24.22834 )
## Predicted value at location 159 : 31.68971 95% confidence interval = ( 29.72971 , 33.64971 )
## Predicted value at location 160 : 27.23035 95% confidence interval = ( 25.27035 , 29.19035 )
## Predicted value at location 161 : 25.82041 95% confidence interval = ( 23.86041 , 27.78041 )
## Predicted value at location 162 : 35.37298 95% confidence interval = ( 33.41298 , 37.33298 )
## Predicted value at location 163 : 22.51062 95% confidence interval = ( 20.55062 , 24.47062 )
## Predicted value at location 164 : 26.65413 95% confidence interval = ( 24.69413 , 28.61413 )
## Predicted value at location 165 : 21.9841 95% confidence interval = ( 20.0241 , 23.9441 )
## Predicted value at location 166 : 31.72994 95% confidence interval = ( 29.76994 , 33.68994 )
## Predicted value at location 167 : 29.90209 95% confidence interval = ( 27.94209 , 31.86209 )
## Predicted value at location 168 : 30.38225 95% confidence interval = ( 28.42225 , 32.34225 )
## Predicted value at location 169 : 40.91972 95% confidence interval = ( 38.95972 , 42.87972 )
## Predicted value at location 170 : 32.48463 95% confidence interval = ( 30.52463 , 34.44463 )
## Predicted value at location 171 : 28.70714 95% confidence interval = ( 26.74714 , 30.66714 )
## Predicted value at location 172 : 29.43485 95% confidence interval = ( 27.47485 , 31.39485 )
## Predicted value at location 173 : 25.61465 95% confidence interval = ( 23.65465 , 27.57465 )
## Predicted value at location 174 : 25.87898 95% confidence interval = ( 23.91898 , 27.83898 )
## Predicted value at location 175 : 39.94974 95% confidence interval = ( 37.98974 , 41.90974 )
## Predicted value at location 176 : 20.23597 95% confidence interval = ( 18.27597 , 22.19597 )
## Predicted value at location 177 : 24.41058 95% confidence interval = ( 22.45058 , 26.37058 )
## Predicted value at location 178 : 20.75022 95% confidence interval = ( 18.79022 , 22.71022 )
## Predicted value at location 179 : 22.51591 95% confidence interval = ( 20.55591 , 24.47591 )
## Predicted value at location 180 : 26.18443 95% confidence interval = ( 24.22443 , 28.14443 )
## Predicted value at location 181 : 29.5352 95% confidence interval = ( 27.5752 , 31.4952 )
## Predicted value at location 182 : 32.00247 95% confidence interval = ( 30.04247 , 33.96247 )
## Predicted value at location 183 : 37.21566 95% confidence interval = ( 35.25566 , 39.17566 )
## Predicted value at location 184 : 35.9897 95% confidence interval = ( 34.0297 , 37.9497 )
## Predicted value at location 185 : 22.76809 95% confidence interval = ( 20.80809 , 24.72809 )
## Predicted value at location 186 : 28.61292 95% confidence interval = ( 26.65292 , 30.57292 )
## Predicted value at location 187 : 31.7388 95% confidence interval = ( 29.7788 , 33.6988 )
## Predicted value at location 188 : 31.04168 95% confidence interval = ( 29.08168 , 33.00168 )
## Predicted value at location 189 : 28.32949 95% confidence interval = ( 26.36949 , 30.28949 )
## Predicted value at location 190 : 30.22594 95% confidence interval = ( 28.26594 , 32.18594 )
## Predicted value at location 191 : 30.92256 95% confidence interval = ( 28.96256 , 32.88256 )
## Predicted value at location 192 : 26.20975 95% confidence interval = ( 24.24975 , 28.16975 )
## Predicted value at location 193 : 40.31707 95% confidence interval = ( 38.35707 , 42.27707 )
## Predicted value at location 194 : 30.45785 95% confidence interval = ( 28.49785 , 32.41785 )
## Predicted value at location 195 : 30.58348 95% confidence interval = ( 28.62348 , 32.54348 )
## Predicted value at location 196 : 29.56447 95% confidence interval = ( 27.60447 , 31.52447 )
## Predicted value at location 197 : 31.82011 95% confidence interval = ( 29.86011 , 33.78011 )
## Predicted value at location 198 : 30.5667 95% confidence interval = ( 28.6067 , 32.5267 )
## Predicted value at location 199 : 28.90569 95% confidence interval = ( 26.94569 , 30.86569 )
## Predicted value at location 200 : 23.00676 95% confidence interval = ( 21.04676 , 24.96676 )
## Predicted value at location 201 : 38.21416 95% confidence interval = ( 36.25416 , 40.17416 )
## Predicted value at location 202 : 31.0991 95% confidence interval = ( 29.1391 , 33.0591 )
## Predicted value at location 203 : 29.76442 95% confidence interval = ( 27.80442 , 31.72442 )
## Predicted value at location 204 : 37.89897 95% confidence interval = ( 35.93897 , 39.85897 )
## Predicted value at location 205 : 33.00829 95% confidence interval = ( 31.04829 , 34.96829 )
## Predicted value at location 206 : 26.50031 95% confidence interval = ( 24.54031 , 28.46031 )
## Predicted value at location 207 : 30.85716 95% confidence interval = ( 28.89716 , 32.81716 )
## Predicted value at location 208 : 41.57937 95% confidence interval = ( 39.61937 , 43.53937 )
## Predicted value at location 209 : 30.4162 95% confidence interval = ( 28.4562 , 32.3762 )
## Predicted value at location 210 : 39.90319 95% confidence interval = ( 37.94319 , 41.86319 )
## Predicted value at location 211 : 34.86761 95% confidence interval = ( 32.90761 , 36.82761 )
## Predicted value at location 212 : 34.69602 95% confidence interval = ( 32.73602 , 36.65602 )
## Predicted value at location 213 : 29.97897 95% confidence interval = ( 28.01897 , 31.93897 )
## Predicted value at location 214 : 27.57208 95% confidence interval = ( 25.61208 , 29.53208 )
## Predicted value at location 215 : 39.26744 95% confidence interval = ( 37.30744 , 41.22744 )
## Predicted value at location 216 : 30.49457 95% confidence interval = ( 28.53457 , 32.45457 )
## Predicted value at location 217 : 38.5888 95% confidence interval = ( 36.6288 , 40.5488 )
## Predicted value at location 218 : 26.03343 95% confidence interval = ( 24.07343 , 27.99343 )
## Predicted value at location 219 : 27.99159 95% confidence interval = ( 26.03159 , 29.95159 )
## Predicted value at location 220 : 21.4833 95% confidence interval = ( 19.5233 , 23.4433 )
## Predicted value at location 221 : 30.62884 95% confidence interval = ( 28.66884 , 32.58884 )
## Predicted value at location 222 : 26.97885 95% confidence interval = ( 25.01885 , 28.93885 )
## Predicted value at location 223 : 26.21204 95% confidence interval = ( 24.25204 , 28.17204 )
## Predicted value at location 224 : 30.27964 95% confidence interval = ( 28.31964 , 32.23964 )
## Predicted value at location 225 : 30.01901 95% confidence interval = ( 28.05901 , 31.97901 )
## Predicted value at location 226 : 23.74194 95% confidence interval = ( 21.78194 , 25.70194 )
## Predicted value at location 227 : 27.44013 95% confidence interval = ( 25.48013 , 29.40013 )
## Predicted value at location 228 : 24.95484 95% confidence interval = ( 22.99484 , 26.91484 )
## Predicted value at location 229 : 22.65853 95% confidence interval = ( 20.69853 , 24.61853 )
## Predicted value at location 230 : 25.89368 95% confidence interval = ( 23.93368 , 27.85368 )
## Predicted value at location 231 : 35.85721 95% confidence interval = ( 33.89721 , 37.81721 )
## Predicted value at location 232 : 32.85585 95% confidence interval = ( 30.89585 , 34.81585 )
## Predicted value at location 233 : 32.28742 95% confidence interval = ( 30.32742 , 34.24742 )
## Predicted value at location 234 : 31.30299 95% confidence interval = ( 29.34299 , 33.26299 )
## Predicted value at location 235 : 30.24767 95% confidence interval = ( 28.28767 , 32.20767 )
## Predicted value at location 236 : 31.02999 95% confidence interval = ( 29.06999 , 32.98999 )
## Predicted value at location 237 : 30.07394 95% confidence interval = ( 28.11394 , 32.03394 )
## Predicted value at location 238 : 21.71849 95% confidence interval = ( 19.75849 , 23.67849 )
## Predicted value at location 239 : 25.99715 95% confidence interval = ( 24.03715 , 27.95715 )
## Predicted value at location 240 : 35.34227 95% confidence interval = ( 33.38227 , 37.30227 )
## Predicted value at location 241 : 30.63171 95% confidence interval = ( 28.67171 , 32.59171 )
## Predicted value at location 242 : 37.43378 95% confidence interval = ( 35.47378 , 39.39378 )
## Predicted value at location 243 : 32.55795 95% confidence interval = ( 30.59795 , 34.51795 )
## Predicted value at location 244 : 27.61846 95% confidence interval = ( 25.65846 , 29.57846 )
## Predicted value at location 245 : 26.22183 95% confidence interval = ( 24.26183 , 28.18183 )
## Predicted value at location 246 : 41.749 95% confidence interval = ( 39.789 , 43.709 )
## Predicted value at location 247 : 33.97001 95% confidence interval = ( 32.01001 , 35.93001 )
## Predicted value at location 248 : 30.39558 95% confidence interval = ( 28.43558 , 32.35558 )
## Predicted value at location 249 : 30.06418 95% confidence interval = ( 28.10418 , 32.02418 )
## Predicted value at location 250 : 38.76943 95% confidence interval = ( 36.80943 , 40.72943 )
## Predicted value at location 251 : 27.15408 95% confidence interval = ( 25.19408 , 29.11408 )
## Predicted value at location 252 : 36.10201 95% confidence interval = ( 34.14201 , 38.06201 )
## Predicted value at location 253 : 33.57887 95% confidence interval = ( 31.61887 , 35.53887 )
## Predicted value at location 254 : 32.79878 95% confidence interval = ( 30.83878 , 34.75878 )
## Predicted value at location 255 : 37.07396 95% confidence interval = ( 35.11396 , 39.03396 )
## Predicted value at location 256 : 30.10371 95% confidence interval = ( 28.14371 , 32.06371 )
## Predicted value at location 257 : 36.14056 95% confidence interval = ( 34.18056 , 38.10056 )
## Predicted value at location 258 : 27.60692 95% confidence interval = ( 25.64692 , 29.56692 )
## Predicted value at location 259 : 24.67738 95% confidence interval = ( 22.71738 , 26.63738 )
## Predicted value at location 260 : 39.45734 95% confidence interval = ( 37.49734 , 41.41734 )
## Predicted value at location 261 : 23.35964 95% confidence interval = ( 21.39964 , 25.31964 )
## Predicted value at location 262 : 44.02054 95% confidence interval = ( 42.06054 , 45.98054 )
## Predicted value at location 263 : 23.74914 95% confidence interval = ( 21.78914 , 25.70914 )
## Predicted value at location 264 : 38.80189 95% confidence interval = ( 36.84189 , 40.76189 )
## Predicted value at location 265 : 25.55814 95% confidence interval = ( 23.59814 , 27.51814 )
## Predicted value at location 266 : 29.78022 95% confidence interval = ( 27.82022 , 31.74022 )
## Predicted value at location 267 : 28.83942 95% confidence interval = ( 26.87942 , 30.79942 )
## Predicted value at location 268 : 33.41863 95% confidence interval = ( 31.45863 , 35.37863 )
## Predicted value at location 269 : 29.49728 95% confidence interval = ( 27.53728 , 31.45728 )
## Predicted value at location 270 : 39.9488 95% confidence interval = ( 37.9888 , 41.9088 )
## Predicted value at location 271 : 36.11591 95% confidence interval = ( 34.15591 , 38.07591 )
## Predicted value at location 272 : 33.74136 95% confidence interval = ( 31.78136 , 35.70136 )
## Predicted value at location 273 : 23.77697 95% confidence interval = ( 21.81697 , 25.73697 )
## Predicted value at location 274 : 31.06595 95% confidence interval = ( 29.10595 , 33.02595 )
## Predicted value at location 275 : 26.82208 95% confidence interval = ( 24.86208 , 28.78208 )
## Predicted value at location 276 : 25.2035 95% confidence interval = ( 23.2435 , 27.1635 )
## Predicted value at location 277 : 27.02493 95% confidence interval = ( 25.06493 , 28.98493 )
## Predicted value at location 278 : 29.45902 95% confidence interval = ( 27.49902 , 31.41902 )
## Predicted value at location 279 : 34.37406 95% confidence interval = ( 32.41406 , 36.33406 )
## Predicted value at location 280 : 29.01525 95% confidence interval = ( 27.05525 , 30.97525 )
## Predicted value at location 281 : 27.76362 95% confidence interval = ( 25.80362 , 29.72362 )
## Predicted value at location 282 : 33.7578 95% confidence interval = ( 31.7978 , 35.7178 )
## Predicted value at location 283 : 41.45234 95% confidence interval = ( 39.49234 , 43.41234 )
## Predicted value at location 284 : 27.2267 95% confidence interval = ( 25.2667 , 29.1867 )
## Predicted value at location 285 : 25.30098 95% confidence interval = ( 23.34098 , 27.26098 )
## Predicted value at location 286 : 35.80302 95% confidence interval = ( 33.84302 , 37.76302 )
## Predicted value at location 287 : 23.45892 95% confidence interval = ( 21.49892 , 25.41892 )
## Predicted value at location 288 : 37.5698 95% confidence interval = ( 35.6098 , 39.5298 )
## Predicted value at location 289 : 40.05838 95% confidence interval = ( 38.09838 , 42.01838 )
## Predicted value at location 290 : 30.57056 95% confidence interval = ( 28.61056 , 32.53056 )
## Predicted value at location 291 : 30.0851 95% confidence interval = ( 28.1251 , 32.0451 )
## Predicted value at location 292 : 26.47074 95% confidence interval = ( 24.51074 , 28.43074 )
## Predicted value at location 293 : 27.56343 95% confidence interval = ( 25.60343 , 29.52343 )
## Predicted value at location 294 : 31.06973 95% confidence interval = ( 29.10973 , 33.02973 )
## Predicted value at location 295 : 27.16117 95% confidence interval = ( 25.20117 , 29.12117 )
## Predicted value at location 296 : 33.3426 95% confidence interval = ( 31.3826 , 35.3026 )
## Predicted value at location 297 : 31.13238 95% confidence interval = ( 29.17238 , 33.09238 )
## Predicted value at location 298 : 42.06484 95% confidence interval = ( 40.10484 , 44.02484 )
## Predicted value at location 299 : 30.431 95% confidence interval = ( 28.471 , 32.391 )
## Predicted value at location 300 : 24.24184 95% confidence interval = ( 22.28184 , 26.20184 )
## Predicted value at location 301 : 31.08569 95% confidence interval = ( 29.12569 , 33.04569 )
## Predicted value at location 302 : 31.08505 95% confidence interval = ( 29.12505 , 33.04505 )
## Predicted value at location 303 : 31.06446 95% confidence interval = ( 29.10446 , 33.02446 )
## Predicted value at location 304 : 45.27966 95% confidence interval = ( 43.31966 , 47.23966 )
## Predicted value at location 305 : 21.73048 95% confidence interval = ( 19.77048 , 23.69048 )
## Predicted value at location 306 : 27.06673 95% confidence interval = ( 25.10673 , 29.02673 )
## Predicted value at location 307 : 30.76863 95% confidence interval = ( 28.80863 , 32.72863 )
## Predicted value at location 308 : 33.63289 95% confidence interval = ( 31.67289 , 35.59289 )
## Predicted value at location 309 : 35.86536 95% confidence interval = ( 33.90536 , 37.82536 )
## Predicted value at location 310 : 28.61953 95% confidence interval = ( 26.65953 , 30.57953 )
## Predicted value at location 311 : 38.48743 95% confidence interval = ( 36.52743 , 40.44743 )
## Predicted value at location 312 : 34.26464 95% confidence interval = ( 32.30464 , 36.22464 )
## Predicted value at location 313 : 37.73163 95% confidence interval = ( 35.77163 , 39.69163 )
## Predicted value at location 314 : 38.62381 95% confidence interval = ( 36.66381 , 40.58381 )
## Predicted value at location 315 : 26.45544 95% confidence interval = ( 24.49544 , 28.41544 )
## Predicted value at location 316 : 20.49777 95% confidence interval = ( 18.53777 , 22.45777 )
## Predicted value at location 317 : 30.65781 95% confidence interval = ( 28.69781 , 32.61781 )
## Predicted value at location 318 : 37.0139 95% confidence interval = ( 35.0539 , 38.9739 )
## Predicted value at location 319 : 38.70138 95% confidence interval = ( 36.74138 , 40.66138 )
## Predicted value at location 320 : 37.23602 95% confidence interval = ( 35.27602 , 39.19602 )
## Predicted value at location 321 : 27.7984 95% confidence interval = ( 25.8384 , 29.7584 )
## Predicted value at location 322 : 34.49524 95% confidence interval = ( 32.53524 , 36.45524 )
## Predicted value at location 323 : 35.00932 95% confidence interval = ( 33.04932 , 36.96932 )
## Predicted value at location 324 : 43.98573 95% confidence interval = ( 42.02573 , 45.94573 )
## Predicted value at location 325 : 30.80234 95% confidence interval = ( 28.84234 , 32.76234 )
## Predicted value at location 326 : 35.68052 95% confidence interval = ( 33.72052 , 37.64052 )
## Predicted value at location 327 : 25.9209 95% confidence interval = ( 23.9609 , 27.8809 )
## Predicted value at location 328 : 22.19367 95% confidence interval = ( 20.23367 , 24.15367 )
## Predicted value at location 329 : 37.52082 95% confidence interval = ( 35.56082 , 39.48082 )
## Predicted value at location 330 : 29.71228 95% confidence interval = ( 27.75228 , 31.67228 )
## Predicted value at location 331 : 38.61327 95% confidence interval = ( 36.65327 , 40.57327 )
## Predicted value at location 332 : 30.82166 95% confidence interval = ( 28.86166 , 32.78166 )
## Predicted value at location 333 : 31.73487 95% confidence interval = ( 29.77487 , 33.69487 )
## Predicted value at location 334 : 23.14508 95% confidence interval = ( 21.18508 , 25.10508 )
## Predicted value at location 335 : 23.0655 95% confidence interval = ( 21.1055 , 25.0255 )
## Predicted value at location 336 : 21.62146 95% confidence interval = ( 19.66146 , 23.58146 )
## Predicted value at location 337 : 38.79834 95% confidence interval = ( 36.83834 , 40.75834 )
## Predicted value at location 338 : 26.44045 95% confidence interval = ( 24.48045 , 28.40045 )
## Predicted value at location 339 : 32.1258 95% confidence interval = ( 30.1658 , 34.0858 )
## Predicted value at location 340 : 32.59018 95% confidence interval = ( 30.63018 , 34.55018 )
## Predicted value at location 341 : 34.67695 95% confidence interval = ( 32.71695 , 36.63695 )
## Predicted value at location 342 : 34.26573 95% confidence interval = ( 32.30573 , 36.22573 )
## Predicted value at location 343 : 24.28056 95% confidence interval = ( 22.32056 , 26.24056 )
## Predicted value at location 344 : 25.27499 95% confidence interval = ( 23.31499 , 27.23499 )
## Predicted value at location 345 : 31.01405 95% confidence interval = ( 29.05405 , 32.97405 )
## Predicted value at location 346 : 20.41068 95% confidence interval = ( 18.45068 , 22.37068 )
## Predicted value at location 347 : 22.9939 95% confidence interval = ( 21.0339 , 24.9539 )
## Predicted value at location 348 : 35.42336 95% confidence interval = ( 33.46336 , 37.38336 )
## Predicted value at location 349 : 26.12617 95% confidence interval = ( 24.16617 , 28.08617 )
## Predicted value at location 350 : 25.76278 95% confidence interval = ( 23.80278 , 27.72278 )
## Predicted value at location 351 : 29.17543 95% confidence interval = ( 27.21543 , 31.13543 )
## Predicted value at location 352 : 24.23344 95% confidence interval = ( 22.27344 , 26.19344 )
## Predicted value at location 353 : 31.45254 95% confidence interval = ( 29.49254 , 33.41254 )
## Predicted value at location 354 : 30.83932 95% confidence interval = ( 28.87932 , 32.79932 )
## Predicted value at location 355 : 31.29323 95% confidence interval = ( 29.33323 , 33.25323 )
## Predicted value at location 356 : 23.57305 95% confidence interval = ( 21.61305 , 25.53305 )
## Predicted value at location 357 : 27.03984 95% confidence interval = ( 25.07984 , 28.99984 )
## Predicted value at location 358 : 21.01331 95% confidence interval = ( 19.05331 , 22.97331 )
## Predicted value at location 359 : 26.60323 95% confidence interval = ( 24.64323 , 28.56323 )
## Predicted value at location 360 : 22.16801 95% confidence interval = ( 20.20801 , 24.12801 )
## Predicted value at location 361 : 34.995 95% confidence interval = ( 33.035 , 36.955 )
## Predicted value at location 362 : 31.09688 95% confidence interval = ( 29.13688 , 33.05688 )
## Predicted value at location 363 : 32.70099 95% confidence interval = ( 30.74099 , 34.66099 )
## Predicted value at location 364 : 29.87319 95% confidence interval = ( 27.91319 , 31.83319 )
## Predicted value at location 1 : 29.45381 95% confidence interval = ( 27.49381 , 31.41381 )
## Predicted value at location 2 : 27.48227 95% confidence interval = ( 25.52227 , 29.44227 )
## Predicted value at location 3 : 32.02869 95% confidence interval = ( 30.06869 , 33.98869 )
## Predicted value at location 4 : 25.52039 95% confidence interval = ( 23.56039 , 27.48039 )
## Predicted value at location 5 : 21.38051 95% confidence interval = ( 19.42051 , 23.34051 )
## Predicted value at location 6 : 29.64021 95% confidence interval = ( 27.68021 , 31.60021 )
## Predicted value at location 7 : 28.54234 95% confidence interval = ( 26.58234 , 30.50234 )
## Predicted value at location 8 : 28.22429 95% confidence interval = ( 26.26429 , 30.18429 )
## Predicted value at location 9 : 28.84765 95% confidence interval = ( 26.88765 , 30.80765 )
## Predicted value at location 10 : 33.06 95% confidence interval = ( 31.1 , 35.02 )
## Predicted value at location 11 : 25.51749 95% confidence interval = ( 23.55749 , 27.47749 )
## Predicted value at location 12 : 47.71992 95% confidence interval = ( 45.75992 , 49.67992 )
## Predicted value at location 13 : 41.44298 95% confidence interval = ( 39.48298 , 43.40298 )
## Predicted value at location 14 : 33.21103 95% confidence interval = ( 31.25103 , 35.17103 )
## Predicted value at location 15 : 28.84743 95% confidence interval = ( 26.88743 , 30.80743 )
## Predicted value at location 16 : 25.59777 95% confidence interval = ( 23.63777 , 27.55777 )
## Predicted value at location 17 : 32.89155 95% confidence interval = ( 30.93155 , 34.85155 )
## Predicted value at location 18 : 33.27538 95% confidence interval = ( 31.31538 , 35.23538 )
## Predicted value at location 19 : 31.27975 95% confidence interval = ( 29.31975 , 33.23975 )
## Predicted value at location 20 : 24.90222 95% confidence interval = ( 22.94222 , 26.86222 )
## Predicted value at location 21 : 17.64177 95% confidence interval = ( 15.68177 , 19.60177 )
## Predicted value at location 22 : 27.32449 95% confidence interval = ( 25.36449 , 29.28449 )
## Predicted value at location 23 : 32.89401 95% confidence interval = ( 30.93401 , 34.85401 )
## Predicted value at location 24 : 31.94605 95% confidence interval = ( 29.98605 , 33.90605 )
## Predicted value at location 25 : 18.58587 95% confidence interval = ( 16.62587 , 20.54587 )
## Predicted value at location 26 : 30.86639 95% confidence interval = ( 28.90639 , 32.82639 )
## Predicted value at location 27 : 27.65958 95% confidence interval = ( 25.69958 , 29.61958 )
## Predicted value at location 28 : 31.97855 95% confidence interval = ( 30.01855 , 33.93855 )
## Predicted value at location 29 : 22.1644 95% confidence interval = ( 20.2044 , 24.1244 )
## Predicted value at location 30 : 29.62189 95% confidence interval = ( 27.66189 , 31.58189 )
## Predicted value at location 31 : 34.27991 95% confidence interval = ( 32.31991 , 36.23991 )
## Predicted value at location 32 : 27.09277 95% confidence interval = ( 25.13277 , 29.05277 )
## Predicted value at location 33 : 33.1102 95% confidence interval = ( 31.1502 , 35.0702 )
## Predicted value at location 34 : 47.30593 95% confidence interval = ( 45.34593 , 49.26593 )
## Predicted value at location 35 : 27.88871 95% confidence interval = ( 25.92871 , 29.84871 )
## Predicted value at location 36 : 27.00143 95% confidence interval = ( 25.04143 , 28.96143 )
## Predicted value at location 37 : 30.94948 95% confidence interval = ( 28.98948 , 32.90948 )
## Predicted value at location 38 : 25.52081 95% confidence interval = ( 23.56081 , 27.48081 )
## Predicted value at location 39 : 42.74989 95% confidence interval = ( 40.78989 , 44.70989 )
## Predicted value at location 40 : 37.57989 95% confidence interval = ( 35.61989 , 39.53989 )
## Predicted value at location 41 : 42.1455 95% confidence interval = ( 40.1855 , 44.1055 )
## Predicted value at location 42 : 24.60094 95% confidence interval = ( 22.64094 , 26.56094 )
## Predicted value at location 43 : 35.04758 95% confidence interval = ( 33.08758 , 37.00758 )
## Predicted value at location 44 : 44.10441 95% confidence interval = ( 42.14441 , 46.06441 )
## Predicted value at location 45 : 31.27102 95% confidence interval = ( 29.31102 , 33.23102 )
## Predicted value at location 46 : 45.56006 95% confidence interval = ( 43.60006 , 47.52006 )
## Predicted value at location 47 : 17.71147 95% confidence interval = ( 15.75147 , 19.67147 )
## Predicted value at location 48 : 19.31879 95% confidence interval = ( 17.35879 , 21.27879 )
## Predicted value at location 49 : 22.21142 95% confidence interval = ( 20.25142 , 24.17142 )
## Predicted value at location 50 : 31.38607 95% confidence interval = ( 29.42607 , 33.34607 )
## Predicted value at location 51 : 32.25633 95% confidence interval = ( 30.29633 , 34.21633 )
## Predicted value at location 52 : 34.28157 95% confidence interval = ( 32.32157 , 36.24157 )
## Predicted value at location 53 : 32.48585 95% confidence interval = ( 30.52585 , 34.44585 )
## Predicted value at location 54 : 33.15149 95% confidence interval = ( 31.19149 , 35.11149 )
## Predicted value at location 55 : 30.84503 95% confidence interval = ( 28.88503 , 32.80503 )
## Predicted value at location 56 : 28.42347 95% confidence interval = ( 26.46347 , 30.38347 )
## Predicted value at location 57 : 31.6012 95% confidence interval = ( 29.6412 , 33.5612 )
## Predicted value at location 58 : 37.95248 95% confidence interval = ( 35.99248 , 39.91248 )
## Predicted value at location 59 : 22.78579 95% confidence interval = ( 20.82579 , 24.74579 )
## Predicted value at location 60 : 35.49399 95% confidence interval = ( 33.53399 , 37.45399 )
## Predicted value at location 61 : 36.78557 95% confidence interval = ( 34.82557 , 38.74557 )
## Predicted value at location 62 : 32.04904 95% confidence interval = ( 30.08904 , 34.00904 )
## Predicted value at location 63 : 33.01022 95% confidence interval = ( 31.05022 , 34.97022 )
## Predicted value at location 64 : 33.66301 95% confidence interval = ( 31.70301 , 35.62301 )
## Predicted value at location 65 : 18.60985 95% confidence interval = ( 16.64985 , 20.56985 )
## Predicted value at location 66 : 24.73616 95% confidence interval = ( 22.77616 , 26.69616 )
## Predicted value at location 67 : 23.54611 95% confidence interval = ( 21.58611 , 25.50611 )
## Predicted value at location 68 : 20.16973 95% confidence interval = ( 18.20973 , 22.12973 )
## Predicted value at location 69 : 29.3806 95% confidence interval = ( 27.4206 , 31.3406 )
## Predicted value at location 70 : 26.99256 95% confidence interval = ( 25.03256 , 28.95256 )
## Predicted value at location 71 : 31.31573 95% confidence interval = ( 29.35573 , 33.27573 )
## Predicted value at location 72 : 22.7637 95% confidence interval = ( 20.8037 , 24.7237 )
## Predicted value at location 73 : 44.00667 95% confidence interval = ( 42.04667 , 45.96667 )
## Predicted value at location 74 : 29.19675 95% confidence interval = ( 27.23675 , 31.15675 )
## Predicted value at location 75 : 37.21303 95% confidence interval = ( 35.25303 , 39.17303 )
## Predicted value at location 76 : 19.98951 95% confidence interval = ( 18.02951 , 21.94951 )
## Predicted value at location 77 : 30.16745 95% confidence interval = ( 28.20745 , 32.12745 )
## Predicted value at location 78 : 30.87144 95% confidence interval = ( 28.91144 , 32.83144 )
## Predicted value at location 79 : 29.765 95% confidence interval = ( 27.805 , 31.725 )
## Predicted value at location 80 : 17.35463 95% confidence interval = ( 15.39463 , 19.31463 )
## Predicted value at location 81 : 19.70921 95% confidence interval = ( 17.74921 , 21.66921 )
## Predicted value at location 82 : 29.68991 95% confidence interval = ( 27.72991 , 31.64991 )
## Predicted value at location 83 : 22.03482 95% confidence interval = ( 20.07482 , 23.99482 )
## Predicted value at location 84 : 27.30451 95% confidence interval = ( 25.34451 , 29.26451 )
## Predicted value at location 85 : 22.75893 95% confidence interval = ( 20.79893 , 24.71893 )
## Predicted value at location 86 : 26.02323 95% confidence interval = ( 24.06323 , 27.98323 )
## Predicted value at location 87 : 41.76353 95% confidence interval = ( 39.80353 , 43.72353 )
## Predicted value at location 88 : 36.57812 95% confidence interval = ( 34.61812 , 38.53812 )
## Predicted value at location 89 : 24.80614 95% confidence interval = ( 22.84614 , 26.76614 )
## Predicted value at location 90 : 31.30074 95% confidence interval = ( 29.34074 , 33.26074 )
## Predicted value at location 91 : 34.89727 95% confidence interval = ( 32.93727 , 36.85727 )
## Predicted value at location 92 : 29.39608 95% confidence interval = ( 27.43608 , 31.35608 )
## Predicted value at location 93 : 19.33726 95% confidence interval = ( 17.37726 , 21.29726 )
## Predicted value at location 94 : 30.72759 95% confidence interval = ( 28.76759 , 32.68759 )
## Predicted value at location 95 : 34.77463 95% confidence interval = ( 32.81463 , 36.73463 )
## Predicted value at location 96 : 32.73222 95% confidence interval = ( 30.77222 , 34.69222 )
## Predicted value at location 97 : 27.28165 95% confidence interval = ( 25.32165 , 29.24165 )
## Predicted value at location 98 : 22.41048 95% confidence interval = ( 20.45048 , 24.37048 )
## Predicted value at location 99 : 21.40122 95% confidence interval = ( 19.44122 , 23.36122 )
## Predicted value at location 100 : 30.26681 95% confidence interval = ( 28.30681 , 32.22681 )
## Predicted value at location 101 : 31.47339 95% confidence interval = ( 29.51339 , 33.43339 )
## Predicted value at location 102 : 22.30166 95% confidence interval = ( 20.34166 , 24.26166 )
## Predicted value at location 103 : 31.39381 95% confidence interval = ( 29.43381 , 33.35381 )
## Predicted value at location 104 : 31.93872 95% confidence interval = ( 29.97872 , 33.89872 )
## Predicted value at location 105 : 33.45983 95% confidence interval = ( 31.49983 , 35.41983 )
## Predicted value at location 106 : 36.54746 95% confidence interval = ( 34.58746 , 38.50746 )
## Predicted value at location 107 : 29.60519 95% confidence interval = ( 27.64519 , 31.56519 )
## Predicted value at location 108 : 29.7616 95% confidence interval = ( 27.8016 , 31.7216 )
## Predicted value at location 109 : 34.72759 95% confidence interval = ( 32.76759 , 36.68759 )
## Predicted value at location 110 : 31.30218 95% confidence interval = ( 29.34218 , 33.26218 )
## Predicted value at location 111 : 37.72735 95% confidence interval = ( 35.76735 , 39.68735 )
## Predicted value at location 112 : 15.25383 95% confidence interval = ( 13.29383 , 17.21383 )
## Predicted value at location 113 : 30.54685 95% confidence interval = ( 28.58685 , 32.50685 )
## Predicted value at location 114 : 32.76722 95% confidence interval = ( 30.80722 , 34.72722 )
## Predicted value at location 115 : 21.77212 95% confidence interval = ( 19.81212 , 23.73212 )
## Predicted value at location 116 : 35.59678 95% confidence interval = ( 33.63678 , 37.55678 )
## Predicted value at location 117 : 39.40376 95% confidence interval = ( 37.44376 , 41.36376 )
## Predicted value at location 118 : 24.34214 95% confidence interval = ( 22.38214 , 26.30214 )
## Predicted value at location 119 : 31.45545 95% confidence interval = ( 29.49545 , 33.41545 )
## Predicted value at location 120 : 24.84867 95% confidence interval = ( 22.88867 , 26.80867 )
## Predicted value at location 121 : 35.92806 95% confidence interval = ( 33.96806 , 37.88806 )
## Predicted value at location 122 : 26.73593 95% confidence interval = ( 24.77593 , 28.69593 )
## Predicted value at location 123 : 28.00793 95% confidence interval = ( 26.04793 , 29.96793 )
## Predicted value at location 124 : 30.32357 95% confidence interval = ( 28.36357 , 32.28357 )
## Predicted value at location 125 : 35.53588 95% confidence interval = ( 33.57588 , 37.49588 )
## Predicted value at location 126 : 29.7662 95% confidence interval = ( 27.8062 , 31.7262 )
## Predicted value at location 127 : 32.06993 95% confidence interval = ( 30.10993 , 34.02993 )
## Predicted value at location 128 : 31.60363 95% confidence interval = ( 29.64363 , 33.56363 )
## Predicted value at location 129 : 27.03482 95% confidence interval = ( 25.07482 , 28.99482 )
## Predicted value at location 130 : 16.56249 95% confidence interval = ( 14.60249 , 18.52249 )
## Predicted value at location 131 : 25.23683 95% confidence interval = ( 23.27683 , 27.19683 )
## Predicted value at location 132 : 21.49589 95% confidence interval = ( 19.53589 , 23.45589 )
## Predicted value at location 133 : 35.33404 95% confidence interval = ( 33.37404 , 37.29404 )
## Predicted value at location 134 : 21.60516 95% confidence interval = ( 19.64516 , 23.56516 )
## Predicted value at location 135 : 33.11449 95% confidence interval = ( 31.15449 , 35.07449 )
## Predicted value at location 136 : 32.26721 95% confidence interval = ( 30.30721 , 34.22721 )
## Predicted value at location 137 : 16.68959 95% confidence interval = ( 14.72959 , 18.64959 )
## Predicted value at location 138 : 31.86581 95% confidence interval = ( 29.90581 , 33.82581 )
## Predicted value at location 139 : 38.85048 95% confidence interval = ( 36.89048 , 40.81048 )
## Predicted value at location 140 : 33.52012 95% confidence interval = ( 31.56012 , 35.48012 )
## Predicted value at location 141 : 31.51059 95% confidence interval = ( 29.55059 , 33.47059 )
## Predicted value at location 142 : 38.35995 95% confidence interval = ( 36.39995 , 40.31995 )
## Predicted value at location 143 : 31.8479 95% confidence interval = ( 29.8879 , 33.8079 )
## Predicted value at location 144 : 35.8791 95% confidence interval = ( 33.9191 , 37.8391 )
## Predicted value at location 145 : 17.36244 95% confidence interval = ( 15.40244 , 19.32244 )
## Predicted value at location 146 : 33.07048 95% confidence interval = ( 31.11048 , 35.03048 )
## Predicted value at location 147 : 30.51061 95% confidence interval = ( 28.55061 , 32.47061 )
## Predicted value at location 148 : 40.07035 95% confidence interval = ( 38.11035 , 42.03035 )
## Predicted value at location 149 : 31.31549 95% confidence interval = ( 29.35549 , 33.27549 )
## Predicted value at location 150 : 19.5322 95% confidence interval = ( 17.5722 , 21.4922 )
## Predicted value at location 151 : 24.7547 95% confidence interval = ( 22.7947 , 26.7147 )
## Predicted value at location 152 : 18.48292 95% confidence interval = ( 16.52292 , 20.44292 )
## Predicted value at location 153 : 31.73348 95% confidence interval = ( 29.77348 , 33.69348 )
## Predicted value at location 154 : 30.37448 95% confidence interval = ( 28.41448 , 32.33448 )
## Predicted value at location 155 : 32.93993 95% confidence interval = ( 30.97993 , 34.89993 )
## Predicted value at location 156 : 31.29023 95% confidence interval = ( 29.33023 , 33.25023 )
## Predicted value at location 157 : 29.77213 95% confidence interval = ( 27.81213 , 31.73213 )
## Predicted value at location 158 : 34.32796 95% confidence interval = ( 32.36796 , 36.28796 )
## Predicted value at location 159 : 17.74978 95% confidence interval = ( 15.78978 , 19.70978 )
## Predicted value at location 160 : 21.2549 95% confidence interval = ( 19.2949 , 23.2149 )
## Predicted value at location 161 : 16.56814 95% confidence interval = ( 14.60814 , 18.52814 )
## Predicted value at location 162 : 22.64713 95% confidence interval = ( 20.68713 , 24.60713 )
## Predicted value at location 163 : 32.80094 95% confidence interval = ( 30.84094 , 34.76094 )
## Predicted value at location 164 : 31.40232 95% confidence interval = ( 29.44232 , 33.36232 )
## Predicted value at location 165 : 38.41054 95% confidence interval = ( 36.45054 , 40.37054 )
## Predicted value at location 166 : 15.00711 95% confidence interval = ( 13.04711 , 16.96711 )
## Predicted value at location 167 : 23.73799 95% confidence interval = ( 21.77799 , 25.69799 )
## Predicted value at location 168 : 25.7849 95% confidence interval = ( 23.8249 , 27.7449 )
## Predicted value at location 169 : 34.23943 95% confidence interval = ( 32.27943 , 36.19943 )
## Predicted value at location 170 : 32.23498 95% confidence interval = ( 30.27498 , 34.19498 )
## Predicted value at location 171 : 22.68027 95% confidence interval = ( 20.72027 , 24.64027 )
## Predicted value at location 172 : 41.39611 95% confidence interval = ( 39.43611 , 43.35611 )
## Predicted value at location 173 : 31.53014 95% confidence interval = ( 29.57014 , 33.49014 )
## Predicted value at location 174 : 29.70872 95% confidence interval = ( 27.74872 , 31.66872 )
## Predicted value at location 175 : 39.02799 95% confidence interval = ( 37.06799 , 40.98799 )
## Predicted value at location 176 : 24.32702 95% confidence interval = ( 22.36702 , 26.28702 )
## Predicted value at location 177 : 32.81926 95% confidence interval = ( 30.85926 , 34.77926 )
## Predicted value at location 178 : 40.47533 95% confidence interval = ( 38.51533 , 42.43533 )
## Predicted value at location 179 : 27.41206 95% confidence interval = ( 25.45206 , 29.37206 )
## Predicted value at location 180 : 28.11252 95% confidence interval = ( 26.15252 , 30.07252 )
## Predicted value at location 181 : 26.77626 95% confidence interval = ( 24.81626 , 28.73626 )
## Predicted value at location 182 : 35.02271 95% confidence interval = ( 33.06271 , 36.98271 )
## Predicted value at location 183 : 27.70741 95% confidence interval = ( 25.74741 , 29.66741 )
## Predicted value at location 184 : 32.99198 95% confidence interval = ( 31.03198 , 34.95198 )
## Predicted value at location 185 : 44.20437 95% confidence interval = ( 42.24437 , 46.16437 )
## Predicted value at location 186 : 26.31194 95% confidence interval = ( 24.35194 , 28.27194 )
## Predicted value at location 187 : 32.3129 95% confidence interval = ( 30.3529 , 34.2729 )
## Predicted value at location 188 : 31.55516 95% confidence interval = ( 29.59516 , 33.51516 )
## Predicted value at location 189 : 25.32252 95% confidence interval = ( 23.36252 , 27.28252 )
## Predicted value at location 190 : 37.10296 95% confidence interval = ( 35.14296 , 39.06296 )
## Predicted value at location 191 : 34.48196 95% confidence interval = ( 32.52196 , 36.44196 )
## Predicted value at location 192 : 32.48988 95% confidence interval = ( 30.52988 , 34.44988 )
## Predicted value at location 193 : 27.67887 95% confidence interval = ( 25.71887 , 29.63887 )
## Predicted value at location 194 : 34.91928 95% confidence interval = ( 32.95928 , 36.87928 )
## Predicted value at location 195 : 34.25756 95% confidence interval = ( 32.29756 , 36.21756 )
## Predicted value at location 196 : 31.97325 95% confidence interval = ( 30.01325 , 33.93325 )
## Predicted value at location 197 : 37.25054 95% confidence interval = ( 35.29054 , 39.21054 )
## Predicted value at location 198 : 23.16144 95% confidence interval = ( 21.20144 , 25.12144 )
## Predicted value at location 199 : 30.70253 95% confidence interval = ( 28.74253 , 32.66253 )
## Predicted value at location 200 : 31.95569 95% confidence interval = ( 29.99569 , 33.91569 )
## Predicted value at location 201 : 31.55394 95% confidence interval = ( 29.59394 , 33.51394 )
## Predicted value at location 202 : 38.11036 95% confidence interval = ( 36.15036 , 40.07036 )
## Predicted value at location 203 : 28.20721 95% confidence interval = ( 26.24721 , 30.16721 )
## Predicted value at location 204 : 24.07621 95% confidence interval = ( 22.11621 , 26.03621 )
## Predicted value at location 205 : 34.28598 95% confidence interval = ( 32.32598 , 36.24598 )
## Predicted value at location 206 : 38.0334 95% confidence interval = ( 36.0734 , 39.9934 )
## Predicted value at location 207 : 31.40916 95% confidence interval = ( 29.44916 , 33.36916 )
## Predicted value at location 208 : 16.33605 95% confidence interval = ( 14.37605 , 18.29605 )
## Predicted value at location 209 : 29.82407 95% confidence interval = ( 27.86407 , 31.78407 )
## Predicted value at location 210 : 24.57205 95% confidence interval = ( 22.61205 , 26.53205 )
## Predicted value at location 211 : 38.09445 95% confidence interval = ( 36.13445 , 40.05445 )
## Predicted value at location 212 : 26.6654 95% confidence interval = ( 24.7054 , 28.6254 )
## Predicted value at location 213 : 30.72222 95% confidence interval = ( 28.76222 , 32.68222 )
## Predicted value at location 214 : 21.38502 95% confidence interval = ( 19.42502 , 23.34502 )
## Predicted value at location 215 : 23.62033 95% confidence interval = ( 21.66033 , 25.58033 )
## Predicted value at location 216 : 31.83404 95% confidence interval = ( 29.87404 , 33.79404 )
## Predicted value at location 217 : 36.1451 95% confidence interval = ( 34.1851 , 38.1051 )
## Predicted value at location 218 : 32.78872 95% confidence interval = ( 30.82872 , 34.74872 )
## Predicted value at location 219 : 29.98429 95% confidence interval = ( 28.02429 , 31.94429 )
## Predicted value at location 220 : 32.80035 95% confidence interval = ( 30.84035 , 34.76035 )
## Predicted value at location 221 : 32.88406 95% confidence interval = ( 30.92406 , 34.84406 )
## Predicted value at location 222 : 25.87026 95% confidence interval = ( 23.91026 , 27.83026 )
## Predicted value at location 223 : 26.73628 95% confidence interval = ( 24.77628 , 28.69628 )
## Predicted value at location 224 : 35.82051 95% confidence interval = ( 33.86051 , 37.78051 )
## Predicted value at location 225 : 16.96261 95% confidence interval = ( 15.00261 , 18.92261 )
## Predicted value at location 226 : 21.40907 95% confidence interval = ( 19.44907 , 23.36907 )
## Predicted value at location 227 : 32.74678 95% confidence interval = ( 30.78678 , 34.70678 )
## Predicted value at location 228 : 32.14828 95% confidence interval = ( 30.18828 , 34.10828 )
## Predicted value at location 229 : 38.88383 95% confidence interval = ( 36.92383 , 40.84383 )
## Predicted value at location 230 : 33.21295 95% confidence interval = ( 31.25295 , 35.17295 )
## Predicted value at location 231 : 31.24119 95% confidence interval = ( 29.28119 , 33.20119 )
## Predicted value at location 232 : 27.96946 95% confidence interval = ( 26.00946 , 29.92946 )
## Predicted value at location 233 : 31.32869 95% confidence interval = ( 29.36869 , 33.28869 )
## Predicted value at location 234 : 37.54716 95% confidence interval = ( 35.58716 , 39.50716 )
## Predicted value at location 235 : 37.60413 95% confidence interval = ( 35.64413 , 39.56413 )
## Predicted value at location 236 : 24.03281 95% confidence interval = ( 22.07281 , 25.99281 )
## Predicted value at location 237 : 33.47664 95% confidence interval = ( 31.51664 , 35.43664 )
## Predicted value at location 238 : 29.19457 95% confidence interval = ( 27.23457 , 31.15457 )
## Predicted value at location 239 : 31.22884 95% confidence interval = ( 29.26884 , 33.18884 )
## Predicted value at location 240 : 32.31103 95% confidence interval = ( 30.35103 , 34.27103 )
## Predicted value at location 241 : 27.36747 95% confidence interval = ( 25.40747 , 29.32747 )
## Predicted value at location 242 : 44.62794 95% confidence interval = ( 42.66794 , 46.58794 )
## Predicted value at location 243 : 31.82168 95% confidence interval = ( 29.86168 , 33.78168 )
## Predicted value at location 244 : 31.42932 95% confidence interval = ( 29.46932 , 33.38932 )
## Predicted value at location 245 : 22.70312 95% confidence interval = ( 20.74312 , 24.66312 )
## Predicted value at location 246 : 47.19245 95% confidence interval = ( 45.23245 , 49.15245 )
## Predicted value at location 247 : 37.20928 95% confidence interval = ( 35.24928 , 39.16928 )
## Predicted value at location 248 : 34.41687 95% confidence interval = ( 32.45687 , 36.37687 )
## Predicted value at location 249 : 29.38648 95% confidence interval = ( 27.42648 , 31.34648 )
## Predicted value at location 250 : 29.16798 95% confidence interval = ( 27.20798 , 31.12798 )
## Predicted value at location 251 : 29.8848 95% confidence interval = ( 27.9248 , 31.8448 )
## Predicted value at location 252 : 43.53017 95% confidence interval = ( 41.57017 , 45.49017 )
## Predicted value at location 253 : 44.03006 95% confidence interval = ( 42.07006 , 45.99006 )
## Predicted value at location 254 : 29.20597 95% confidence interval = ( 27.24597 , 31.16597 )
## Predicted value at location 255 : 36.51267 95% confidence interval = ( 34.55267 , 38.47267 )
## Predicted value at location 256 : 19.52821 95% confidence interval = ( 17.56821 , 21.48821 )
## Predicted value at location 257 : 28.66741 95% confidence interval = ( 26.70741 , 30.62741 )
## Predicted value at location 258 : 29.72224 95% confidence interval = ( 27.76224 , 31.68224 )
## Predicted value at location 259 : 35.6957 95% confidence interval = ( 33.7357 , 37.6557 )
## Predicted value at location 260 : 32.80396 95% confidence interval = ( 30.84396 , 34.76396 )
## Predicted value at location 261 : 30.3784 95% confidence interval = ( 28.4184 , 32.3384 )
## Predicted value at location 262 : 30.78137 95% confidence interval = ( 28.82137 , 32.74137 )
## Predicted value at location 263 : 22.65202 95% confidence interval = ( 20.69202 , 24.61202 )
## Predicted value at location 264 : 33.75335 95% confidence interval = ( 31.79335 , 35.71335 )
## Predicted value at location 265 : 21.91871 95% confidence interval = ( 19.95871 , 23.87871 )
## Predicted value at location 266 : 31.4445 95% confidence interval = ( 29.4845 , 33.4045 )
## Predicted value at location 267 : 19.50245 95% confidence interval = ( 17.54245 , 21.46245 )
## Predicted value at location 268 : 37.7311 95% confidence interval = ( 35.7711 , 39.6911 )
## Predicted value at location 269 : 34.79726 95% confidence interval = ( 32.83726 , 36.75726 )
## Predicted value at location 270 : 37.72565 95% confidence interval = ( 35.76565 , 39.68565 )
## Predicted value at location 271 : 34.03591 95% confidence interval = ( 32.07591 , 35.99591 )
## Predicted value at location 272 : 27.76712 95% confidence interval = ( 25.80712 , 29.72712 )
## Predicted value at location 273 : 33.58495 95% confidence interval = ( 31.62495 , 35.54495 )
## Predicted value at location 274 : 27.07735 95% confidence interval = ( 25.11735 , 29.03735 )
## Predicted value at location 275 : 38.54493 95% confidence interval = ( 36.58493 , 40.50493 )
## Predicted value at location 276 : 31.34215 95% confidence interval = ( 29.38215 , 33.30215 )
## Predicted value at location 277 : 32.67338 95% confidence interval = ( 30.71338 , 34.63338 )
## Predicted value at location 278 : 22.7674 95% confidence interval = ( 20.8074 , 24.7274 )
## Predicted value at location 279 : 28.39379 95% confidence interval = ( 26.43379 , 30.35379 )
## Predicted value at location 280 : 19.15295 95% confidence interval = ( 17.19295 , 21.11295 )
## Predicted value at location 281 : 27.72957 95% confidence interval = ( 25.76957 , 29.68957 )
## Predicted value at location 282 : 36.28642 95% confidence interval = ( 34.32642 , 38.24642 )
## Predicted value at location 283 : 36.15172 95% confidence interval = ( 34.19172 , 38.11172 )
## Predicted value at location 284 : 23.75908 95% confidence interval = ( 21.79908 , 25.71908 )
## Predicted value at location 285 : 43.03938 95% confidence interval = ( 41.07938 , 44.99938 )
## Predicted value at location 286 : 36.66756 95% confidence interval = ( 34.70756 , 38.62756 )
## Predicted value at location 287 : 44.15333 95% confidence interval = ( 42.19333 , 46.11333 )
## Predicted value at location 288 : 23.06219 95% confidence interval = ( 21.10219 , 25.02219 )
## Predicted value at location 289 : 16.59223 95% confidence interval = ( 14.63223 , 18.55223 )
## Predicted value at location 290 : 22.73527 95% confidence interval = ( 20.77527 , 24.69527 )
## Predicted value at location 291 : 26.86012 95% confidence interval = ( 24.90012 , 28.82012 )
## Predicted value at location 292 : 28.62239 95% confidence interval = ( 26.66239 , 30.58239 )
## Predicted value at location 293 : 31.09152 95% confidence interval = ( 29.13152 , 33.05152 )
## Predicted value at location 294 : 37.51134 95% confidence interval = ( 35.55134 , 39.47134 )
## Predicted value at location 295 : 21.2711 95% confidence interval = ( 19.3111 , 23.2311 )
## Predicted value at location 296 : 33.63094 95% confidence interval = ( 31.67094 , 35.59094 )
## Predicted value at location 297 : 34.86712 95% confidence interval = ( 32.90712 , 36.82712 )
## Predicted value at location 298 : 47.08117 95% confidence interval = ( 45.12117 , 49.04117 )
## Predicted value at location 299 : 35.36528 95% confidence interval = ( 33.40528 , 37.32528 )
## Predicted value at location 300 : 28.20432 95% confidence interval = ( 26.24432 , 30.16432 )
## Predicted value at location 301 : 17.26008 95% confidence interval = ( 15.30008 , 19.22008 )
## Predicted value at location 302 : 33.21435 95% confidence interval = ( 31.25435 , 35.17435 )
## Predicted value at location 303 : 27.32967 95% confidence interval = ( 25.36967 , 29.28967 )
## Predicted value at location 304 : 41.04404 95% confidence interval = ( 39.08404 , 43.00404 )
## Predicted value at location 305 : 33.05318 95% confidence interval = ( 31.09318 , 35.01318 )
## Predicted value at location 306 : 17.03997 95% confidence interval = ( 15.07997 , 18.99997 )
## Predicted value at location 307 : 26.96485 95% confidence interval = ( 25.00485 , 28.92485 )
## Predicted value at location 308 : 38.57881 95% confidence interval = ( 36.61881 , 40.53881 )
## Predicted value at location 309 : 17.93692 95% confidence interval = ( 15.97692 , 19.89692 )
## Predicted value at location 310 : 18.79163 95% confidence interval = ( 16.83163 , 20.75163 )
## Predicted value at location 311 : 17.49377 95% confidence interval = ( 15.53377 , 19.45377 )
## Predicted value at location 312 : 37.24857 95% confidence interval = ( 35.28857 , 39.20857 )
## Predicted value at location 313 : 31.35406 95% confidence interval = ( 29.39406 , 33.31406 )
## Predicted value at location 314 : 31.65444 95% confidence interval = ( 29.69444 , 33.61444 )
## Predicted value at location 315 : 19.34988 95% confidence interval = ( 17.38988 , 21.30988 )
## Predicted value at location 316 : 37.27463 95% confidence interval = ( 35.31463 , 39.23463 )
## Predicted value at location 317 : 34.47885 95% confidence interval = ( 32.51885 , 36.43885 )
## Predicted value at location 318 : 34.47774 95% confidence interval = ( 32.51774 , 36.43774 )
## Predicted value at location 319 : 34.94752 95% confidence interval = ( 32.98752 , 36.90752 )
## Predicted value at location 320 : 21.96724 95% confidence interval = ( 20.00724 , 23.92724 )
## Predicted value at location 321 : 28.94433 95% confidence interval = ( 26.98433 , 30.90433 )
## Predicted value at location 322 : 19.56624 95% confidence interval = ( 17.60624 , 21.52624 )
## Predicted value at location 323 : 35.10616 95% confidence interval = ( 33.14616 , 37.06616 )
## Predicted value at location 324 : 25.10725 95% confidence interval = ( 23.14725 , 27.06725 )
## Predicted value at location 325 : 25.17758 95% confidence interval = ( 23.21758 , 27.13758 )
## Predicted value at location 326 : 20.24743 95% confidence interval = ( 18.28743 , 22.20743 )
## Predicted value at location 327 : 40.42716 95% confidence interval = ( 38.46716 , 42.38716 )
## Predicted value at location 328 : 36.10438 95% confidence interval = ( 34.14438 , 38.06438 )
## Predicted value at location 329 : 31.39782 95% confidence interval = ( 29.43782 , 33.35782 )
## Predicted value at location 330 : 29.81654 95% confidence interval = ( 27.85654 , 31.77654 )
## Predicted value at location 331 : 27.62349 95% confidence interval = ( 25.66349 , 29.58349 )
## Predicted value at location 332 : 18.77473 95% confidence interval = ( 16.81473 , 20.73473 )
## Predicted value at location 333 : 24.40279 95% confidence interval = ( 22.44279 , 26.36279 )
## Predicted value at location 334 : 18.27847 95% confidence interval = ( 16.31847 , 20.23847 )
## Predicted value at location 335 : 26.83906 95% confidence interval = ( 24.87906 , 28.79906 )
## Predicted value at location 336 : 31.36683 95% confidence interval = ( 29.40683 , 33.32683 )
## Predicted value at location 337 : 36.48259 95% confidence interval = ( 34.52259 , 38.44259 )
## Predicted value at location 1 : 26.10043 95% confidence interval = ( 24.14043 , 28.06043 )
## Predicted value at location 2 : 33.20907 95% confidence interval = ( 31.24907 , 35.16907 )
## Predicted value at location 3 : 26.79729 95% confidence interval = ( 24.83729 , 28.75729 )
## Predicted value at location 4 : 33.43683 95% confidence interval = ( 31.47683 , 35.39683 )
## Predicted value at location 5 : 33.24388 95% confidence interval = ( 31.28388 , 35.20388 )
## Predicted value at location 6 : 25.42925 95% confidence interval = ( 23.46925 , 27.38925 )
## Predicted value at location 7 : 36.39931 95% confidence interval = ( 34.43931 , 38.35931 )
## Predicted value at location 8 : 32.5173 95% confidence interval = ( 30.5573 , 34.4773 )
## Predicted value at location 9 : 30.27315 95% confidence interval = ( 28.31315 , 32.23315 )
## Predicted value at location 10 : 23.02056 95% confidence interval = ( 21.06056 , 24.98056 )
## Predicted value at location 11 : 29.84343 95% confidence interval = ( 27.88343 , 31.80343 )
## Predicted value at location 12 : 21.75072 95% confidence interval = ( 19.79072 , 23.71072 )
## Predicted value at location 13 : 31.94683 95% confidence interval = ( 29.98683 , 33.90683 )
## Predicted value at location 14 : 32.32237 95% confidence interval = ( 30.36237 , 34.28237 )
## Predicted value at location 15 : 20.56227 95% confidence interval = ( 18.60227 , 22.52227 )
## Predicted value at location 16 : 41.42444 95% confidence interval = ( 39.46444 , 43.38444 )
## Predicted value at location 17 : 42.08707 95% confidence interval = ( 40.12707 , 44.04707 )
## Predicted value at location 18 : 29.84283 95% confidence interval = ( 27.88283 , 31.80283 )
## Predicted value at location 19 : 28.13335 95% confidence interval = ( 26.17335 , 30.09335 )
## Predicted value at location 20 : 35.87916 95% confidence interval = ( 33.91916 , 37.83916 )
## Predicted value at location 21 : 30.48771 95% confidence interval = ( 28.52771 , 32.44771 )
## Predicted value at location 22 : 25.35963 95% confidence interval = ( 23.39963 , 27.31963 )
## Predicted value at location 23 : 30.12666 95% confidence interval = ( 28.16666 , 32.08666 )
## Predicted value at location 24 : 21.31683 95% confidence interval = ( 19.35683 , 23.27683 )
## Predicted value at location 25 : 23.20443 95% confidence interval = ( 21.24443 , 25.16443 )
## Predicted value at location 26 : 29.69983 95% confidence interval = ( 27.73983 , 31.65983 )
## Predicted value at location 27 : 24.69323 95% confidence interval = ( 22.73323 , 26.65323 )
## Predicted value at location 28 : 18.52528 95% confidence interval = ( 16.56528 , 20.48528 )
## Predicted value at location 29 : 26.16744 95% confidence interval = ( 24.20744 , 28.12744 )
## Predicted value at location 30 : 26.85407 95% confidence interval = ( 24.89407 , 28.81407 )
## Predicted value at location 31 : 33.47325 95% confidence interval = ( 31.51325 , 35.43325 )
## Predicted value at location 32 : 24.89889 95% confidence interval = ( 22.93889 , 26.85889 )
## Predicted value at location 33 : 27.88272 95% confidence interval = ( 25.92272 , 29.84272 )
## Predicted value at location 34 : 32.71944 95% confidence interval = ( 30.75944 , 34.67944 )
## Predicted value at location 35 : 30.17755 95% confidence interval = ( 28.21755 , 32.13755 )
## Predicted value at location 36 : 32.87544 95% confidence interval = ( 30.91544 , 34.83544 )
## Predicted value at location 37 : 32.20335 95% confidence interval = ( 30.24335 , 34.16335 )
## Predicted value at location 38 : 29.69994 95% confidence interval = ( 27.73994 , 31.65994 )
## Predicted value at location 39 : 27.51502 95% confidence interval = ( 25.55502 , 29.47502 )
## Predicted value at location 40 : 30.29572 95% confidence interval = ( 28.33572 , 32.25572 )
## Predicted value at location 41 : 24.89137 95% confidence interval = ( 22.93137 , 26.85137 )
## Predicted value at location 42 : 33.20074 95% confidence interval = ( 31.24074 , 35.16074 )
## Predicted value at location 43 : 33.96799 95% confidence interval = ( 32.00799 , 35.92799 )
## Predicted value at location 44 : 33.67212 95% confidence interval = ( 31.71212 , 35.63212 )
## Predicted value at location 45 : 41.60509 95% confidence interval = ( 39.64509 , 43.56509 )
## Predicted value at location 46 : 38.87148 95% confidence interval = ( 36.91148 , 40.83148 )
## Predicted value at location 47 : 31.32097 95% confidence interval = ( 29.36097 , 33.28097 )
## Predicted value at location 48 : 32.03169 95% confidence interval = ( 30.07169 , 33.99169 )
## Predicted value at location 49 : 38.82433 95% confidence interval = ( 36.86433 , 40.78433 )
## Predicted value at location 50 : 40.36237 95% confidence interval = ( 38.40237 , 42.32237 )
## Predicted value at location 51 : 40.55281 95% confidence interval = ( 38.59281 , 42.51281 )
## Predicted value at location 52 : 42.39257 95% confidence interval = ( 40.43257 , 44.35257 )
## Predicted value at location 53 : 14.17435 95% confidence interval = ( 12.21435 , 16.13435 )
## Predicted value at location 54 : 24.24 95% confidence interval = ( 22.28 , 26.2 )
## Predicted value at location 55 : 32.75479 95% confidence interval = ( 30.79479 , 34.71479 )
## Predicted value at location 56 : 32.38906 95% confidence interval = ( 30.42906 , 34.34906 )
## Predicted value at location 57 : 39.41655 95% confidence interval = ( 37.45655 , 41.37655 )
## Predicted value at location 58 : 32.90458 95% confidence interval = ( 30.94458 , 34.86458 )
## Predicted value at location 59 : 29.80031 95% confidence interval = ( 27.84031 , 31.76031 )
## Predicted value at location 60 : 32.14719 95% confidence interval = ( 30.18719 , 34.10719 )
## Predicted value at location 61 : 21.02276 95% confidence interval = ( 19.06276 , 22.98276 )
## Predicted value at location 62 : 23.38859 95% confidence interval = ( 21.42859 , 25.34859 )
## Predicted value at location 63 : 30.58137 95% confidence interval = ( 28.62137 , 32.54137 )
## Predicted value at location 64 : 40.87878 95% confidence interval = ( 38.91878 , 42.83878 )
## Predicted value at location 65 : 36.83714 95% confidence interval = ( 34.87714 , 38.79714 )
## Predicted value at location 66 : 41.41757 95% confidence interval = ( 39.45757 , 43.37757 )
## Predicted value at location 67 : 22.4051 95% confidence interval = ( 20.4451 , 24.3651 )
## Predicted value at location 68 : 32.67541 95% confidence interval = ( 30.71541 , 34.63541 )
## Predicted value at location 69 : 24.53678 95% confidence interval = ( 22.57678 , 26.49678 )
## Predicted value at location 70 : 30.94693 95% confidence interval = ( 28.98693 , 32.90693 )
## Predicted value at location 71 : 25.31784 95% confidence interval = ( 23.35784 , 27.27784 )
## Predicted value at location 72 : 30.23379 95% confidence interval = ( 28.27379 , 32.19379 )
## Predicted value at location 73 : 22.48318 95% confidence interval = ( 20.52318 , 24.44318 )
## Predicted value at location 74 : 30.26599 95% confidence interval = ( 28.30599 , 32.22599 )
## Predicted value at location 75 : 21.8808 95% confidence interval = ( 19.9208 , 23.8408 )
## Predicted value at location 76 : 42.23638 95% confidence interval = ( 40.27638 , 44.19638 )
## Predicted value at location 77 : 30.57865 95% confidence interval = ( 28.61865 , 32.53865 )
## Predicted value at location 78 : 41.86053 95% confidence interval = ( 39.90053 , 43.82053 )
## Predicted value at location 79 : 33.88767 95% confidence interval = ( 31.92767 , 35.84767 )
## Predicted value at location 80 : 35.3502 95% confidence interval = ( 33.3902 , 37.3102 )
## Predicted value at location 81 : 33.2699 95% confidence interval = ( 31.3099 , 35.2299 )
## Predicted value at location 82 : 30.35234 95% confidence interval = ( 28.39234 , 32.31234 )
## Predicted value at location 83 : 25.88205 95% confidence interval = ( 23.92205 , 27.84205 )
## Predicted value at location 84 : 23.19949 95% confidence interval = ( 21.23949 , 25.15949 )
## Predicted value at location 85 : 10.83333 95% confidence interval = ( 8.873334 , 12.79333 )
## Predicted value at location 86 : 25.28444 95% confidence interval = ( 23.32444 , 27.24444 )
## Predicted value at location 87 : 22.11945 95% confidence interval = ( 20.15945 , 24.07945 )
## Predicted value at location 88 : 31.24259 95% confidence interval = ( 29.28259 , 33.20259 )
## Predicted value at location 89 : 21.76344 95% confidence interval = ( 19.80344 , 23.72344 )
## Predicted value at location 90 : 36.20095 95% confidence interval = ( 34.24095 , 38.16095 )
## Predicted value at location 91 : 33.6224 95% confidence interval = ( 31.6624 , 35.5824 )
## Predicted value at location 92 : 30.51726 95% confidence interval = ( 28.55726 , 32.47726 )
## Predicted value at location 93 : 31.59466 95% confidence interval = ( 29.63466 , 33.55466 )
## Predicted value at location 94 : 18.38387 95% confidence interval = ( 16.42387 , 20.34387 )
## Predicted value at location 95 : 22.53177 95% confidence interval = ( 20.57177 , 24.49177 )
## Predicted value at location 96 : 32.74527 95% confidence interval = ( 30.78527 , 34.70527 )
## Predicted value at location 97 : 40.41841 95% confidence interval = ( 38.45841 , 42.37841 )
## Predicted value at location 98 : 21.41303 95% confidence interval = ( 19.45303 , 23.37303 )
## Predicted value at location 99 : 29.1961 95% confidence interval = ( 27.2361 , 31.1561 )
## Predicted value at location 100 : 26.50802 95% confidence interval = ( 24.54802 , 28.46802 )
## Predicted value at location 101 : 31.9181 95% confidence interval = ( 29.9581 , 33.8781 )
## Predicted value at location 102 : 27.08638 95% confidence interval = ( 25.12638 , 29.04638 )
## Predicted value at location 103 : 22.65676 95% confidence interval = ( 20.69676 , 24.61676 )
## Predicted value at location 104 : 30.75238 95% confidence interval = ( 28.79238 , 32.71238 )
## Predicted value at location 105 : 35.01002 95% confidence interval = ( 33.05002 , 36.97002 )
## Predicted value at location 106 : 31.20582 95% confidence interval = ( 29.24582 , 33.16582 )
## Predicted value at location 107 : 36.59718 95% confidence interval = ( 34.63718 , 38.55718 )
## Predicted value at location 108 : 25.47846 95% confidence interval = ( 23.51846 , 27.43846 )
## Predicted value at location 109 : 27.21681 95% confidence interval = ( 25.25681 , 29.17681 )
## Predicted value at location 110 : 25.42573 95% confidence interval = ( 23.46573 , 27.38573 )
## Predicted value at location 111 : 28.78775 95% confidence interval = ( 26.82775 , 30.74775 )
## Predicted value at location 112 : 44.7646 95% confidence interval = ( 42.8046 , 46.7246 )
## Predicted value at location 113 : 30.60208 95% confidence interval = ( 28.64208 , 32.56208 )
## Predicted value at location 114 : 39.69928 95% confidence interval = ( 37.73928 , 41.65928 )
## Predicted value at location 115 : 30.68577 95% confidence interval = ( 28.72577 , 32.64577 )
## Predicted value at location 116 : 17.94971 95% confidence interval = ( 15.98971 , 19.90971 )
## Predicted value at location 117 : 32.6772 95% confidence interval = ( 30.7172 , 34.6372 )
## Predicted value at location 118 : 28.73366 95% confidence interval = ( 26.77366 , 30.69366 )
## Predicted value at location 119 : 33.27557 95% confidence interval = ( 31.31557 , 35.23557 )
## Predicted value at location 120 : 23.44977 95% confidence interval = ( 21.48977 , 25.40977 )
## Predicted value at location 121 : 29.70538 95% confidence interval = ( 27.74538 , 31.66538 )
## Predicted value at location 122 : 26.74157 95% confidence interval = ( 24.78157 , 28.70157 )
## Predicted value at location 123 : 26.7917 95% confidence interval = ( 24.8317 , 28.7517 )
## Predicted value at location 124 : 32.70592 95% confidence interval = ( 30.74592 , 34.66592 )
## Predicted value at location 125 : 25.38818 95% confidence interval = ( 23.42818 , 27.34818 )
## Predicted value at location 126 : 32.93576 95% confidence interval = ( 30.97576 , 34.89576 )
## Predicted value at location 127 : 26.86825 95% confidence interval = ( 24.90825 , 28.82825 )
## Predicted value at location 128 : 28.27187 95% confidence interval = ( 26.31187 , 30.23187 )
## Predicted value at location 129 : 27.70888 95% confidence interval = ( 25.74888 , 29.66888 )
## Predicted value at location 130 : 21.34482 95% confidence interval = ( 19.38482 , 23.30482 )
## Predicted value at location 131 : 29.77505 95% confidence interval = ( 27.81505 , 31.73505 )
## Predicted value at location 132 : 32.15659 95% confidence interval = ( 30.19659 , 34.11659 )
## Predicted value at location 133 : 33.39853 95% confidence interval = ( 31.43853 , 35.35853 )
## Predicted value at location 134 : 40.35531 95% confidence interval = ( 38.39531 , 42.31531 )
## Predicted value at location 135 : 26.33476 95% confidence interval = ( 24.37476 , 28.29476 )
## Predicted value at location 136 : 28.78693 95% confidence interval = ( 26.82693 , 30.74693 )
## Predicted value at location 137 : 30.26378 95% confidence interval = ( 28.30378 , 32.22378 )
## Predicted value at location 138 : 21.7822 95% confidence interval = ( 19.8222 , 23.7422 )
## Predicted value at location 139 : 31.89837 95% confidence interval = ( 29.93837 , 33.85837 )
## Predicted value at location 140 : 14.88685 95% confidence interval = ( 12.92685 , 16.84685 )
## Predicted value at location 141 : 26.74269 95% confidence interval = ( 24.78269 , 28.70269 )
## Predicted value at location 142 : 24.38368 95% confidence interval = ( 22.42368 , 26.34368 )
## Predicted value at location 143 : 30.08123 95% confidence interval = ( 28.12123 , 32.04123 )
## Predicted value at location 144 : 35.08376 95% confidence interval = ( 33.12376 , 37.04376 )
## Predicted value at location 145 : 23.17871 95% confidence interval = ( 21.21871 , 25.13871 )
## Predicted value at location 146 : 17.00623 95% confidence interval = ( 15.04623 , 18.96623 )
## Predicted value at location 147 : 33.57893 95% confidence interval = ( 31.61893 , 35.53893 )
## Predicted value at location 148 : 21.69673 95% confidence interval = ( 19.73673 , 23.65673 )
## Predicted value at location 149 : 27.70986 95% confidence interval = ( 25.74986 , 29.66986 )
## Predicted value at location 150 : 29.81638 95% confidence interval = ( 27.85638 , 31.77638 )
## Predicted value at location 151 : 32.46241 95% confidence interval = ( 30.50241 , 34.42241 )
## Predicted value at location 152 : 32.3078 95% confidence interval = ( 30.3478 , 34.2678 )
## Predicted value at location 153 : 29.44738 95% confidence interval = ( 27.48738 , 31.40738 )
## Predicted value at location 154 : 33.03093 95% confidence interval = ( 31.07093 , 34.99093 )
## Predicted value at location 155 : 23.1855 95% confidence interval = ( 21.2255 , 25.1455 )
## Predicted value at location 156 : 30.18261 95% confidence interval = ( 28.22261 , 32.14261 )
## Predicted value at location 157 : 31.61959 95% confidence interval = ( 29.65959 , 33.57959 )
## Predicted value at location 158 : 30.12452 95% confidence interval = ( 28.16452 , 32.08452 )
## Predicted value at location 159 : 37.74413 95% confidence interval = ( 35.78413 , 39.70413 )
## Predicted value at location 160 : 31.06056 95% confidence interval = ( 29.10056 , 33.02056 )
## Predicted value at location 161 : 31.59223 95% confidence interval = ( 29.63223 , 33.55223 )
## Predicted value at location 162 : 21.17762 95% confidence interval = ( 19.21762 , 23.13762 )
## Predicted value at location 163 : 30.23353 95% confidence interval = ( 28.27353 , 32.19353 )
## Predicted value at location 164 : 23.44678 95% confidence interval = ( 21.48678 , 25.40678 )
## Predicted value at location 165 : 21.42486 95% confidence interval = ( 19.46486 , 23.38486 )
## Predicted value at location 166 : 22.98847 95% confidence interval = ( 21.02847 , 24.94847 )
## Predicted value at location 167 : 29.75426 95% confidence interval = ( 27.79426 , 31.71426 )
## Predicted value at location 168 : 27.82997 95% confidence interval = ( 25.86997 , 29.78997 )
## Predicted value at location 169 : 40.64746 95% confidence interval = ( 38.68746 , 42.60746 )
## Predicted value at location 170 : 32.35111 95% confidence interval = ( 30.39111 , 34.31111 )
## Predicted value at location 171 : 28.38539 95% confidence interval = ( 26.42539 , 30.34539 )
## Predicted value at location 172 : 25.24449 95% confidence interval = ( 23.28449 , 27.20449 )
## Predicted value at location 173 : 34.00291 95% confidence interval = ( 32.04291 , 35.96291 )
## Predicted value at location 174 : 23.75859 95% confidence interval = ( 21.79859 , 25.71859 )
## Predicted value at location 175 : 19.44789 95% confidence interval = ( 17.48789 , 21.40789 )
## Predicted value at location 176 : 19.6317 95% confidence interval = ( 17.6717 , 21.5917 )
## Predicted value at location 177 : 20.84974 95% confidence interval = ( 18.88974 , 22.80974 )
## Predicted value at location 178 : 33.53196 95% confidence interval = ( 31.57196 , 35.49196 )
## Predicted value at location 179 : 30.84443 95% confidence interval = ( 28.88443 , 32.80443 )
## Predicted value at location 180 : 48.05672 95% confidence interval = ( 46.09672 , 50.01672 )
## Predicted value at location 181 : 18.95241 95% confidence interval = ( 16.99241 , 20.91241 )
## Predicted value at location 182 : 28.77393 95% confidence interval = ( 26.81393 , 30.73393 )
## Predicted value at location 183 : 32.90381 95% confidence interval = ( 30.94381 , 34.86381 )
## Predicted value at location 184 : 29.03291 95% confidence interval = ( 27.07291 , 30.99291 )
## Predicted value at location 185 : 24.8022 95% confidence interval = ( 22.8422 , 26.7622 )
## Predicted value at location 186 : 33.10653 95% confidence interval = ( 31.14653 , 35.06653 )
## Predicted value at location 187 : 29.71708 95% confidence interval = ( 27.75708 , 31.67708 )
## Predicted value at location 188 : 38.28717 95% confidence interval = ( 36.32717 , 40.24717 )
## Predicted value at location 189 : 28.96387 95% confidence interval = ( 27.00387 , 30.92387 )
## Predicted value at location 190 : 37.82469 95% confidence interval = ( 35.86469 , 39.78469 )
## Predicted value at location 191 : 26.82138 95% confidence interval = ( 24.86138 , 28.78138 )
## Predicted value at location 192 : 28.95833 95% confidence interval = ( 26.99833 , 30.91833 )
## Predicted value at location 193 : 29.89792 95% confidence interval = ( 27.93792 , 31.85792 )
## Predicted value at location 194 : 28.81085 95% confidence interval = ( 26.85085 , 30.77085 )
## Predicted value at location 195 : 30.24723 95% confidence interval = ( 28.28723 , 32.20723 )
## Predicted value at location 196 : 32.63821 95% confidence interval = ( 30.67821 , 34.59821 )
## Predicted value at location 197 : 24.73019 95% confidence interval = ( 22.77019 , 26.69019 )
## Predicted value at location 198 : 22.88284 95% confidence interval = ( 20.92284 , 24.84284 )
## Predicted value at location 199 : 24.04374 95% confidence interval = ( 22.08374 , 26.00374 )
## Predicted value at location 200 : 32.63238 95% confidence interval = ( 30.67238 , 34.59238 )
## Predicted value at location 201 : 33.72189 95% confidence interval = ( 31.76189 , 35.68189 )
## Predicted value at location 202 : 39.80499 95% confidence interval = ( 37.84499 , 41.76499 )
## Predicted value at location 203 : 29.99323 95% confidence interval = ( 28.03323 , 31.95323 )
## Predicted value at location 204 : 22.19842 95% confidence interval = ( 20.23842 , 24.15842 )
## Predicted value at location 205 : 36.38014 95% confidence interval = ( 34.42014 , 38.34014 )
## Predicted value at location 206 : 24.69803 95% confidence interval = ( 22.73803 , 26.65803 )
## Predicted value at location 207 : 22.12534 95% confidence interval = ( 20.16534 , 24.08534 )
## Predicted value at location 208 : 32.99978 95% confidence interval = ( 31.03978 , 34.95978 )
## Predicted value at location 209 : 33.00933 95% confidence interval = ( 31.04933 , 34.96933 )
## Predicted value at location 210 : 33.02338 95% confidence interval = ( 31.06338 , 34.98338 )
## Predicted value at location 211 : 34.64964 95% confidence interval = ( 32.68964 , 36.60964 )
## Predicted value at location 212 : 31.59401 95% confidence interval = ( 29.63401 , 33.55401 )
## Predicted value at location 213 : 32.36866 95% confidence interval = ( 30.40866 , 34.32866 )
## Predicted value at location 214 : 35.70269 95% confidence interval = ( 33.74269 , 37.66269 )
## Predicted value at location 215 : 34.39577 95% confidence interval = ( 32.43577 , 36.35577 )
## Predicted value at location 216 : 30.67013 95% confidence interval = ( 28.71013 , 32.63013 )
## Predicted value at location 217 : 26.66018 95% confidence interval = ( 24.70018 , 28.62018 )
## Predicted value at location 218 : 31.79852 95% confidence interval = ( 29.83852 , 33.75852 )
## Predicted value at location 219 : 34.70001 95% confidence interval = ( 32.74001 , 36.66001 )
## Predicted value at location 220 : 41.30911 95% confidence interval = ( 39.34911 , 43.26911 )
## Predicted value at location 221 : 29.76037 95% confidence interval = ( 27.80037 , 31.72037 )
## Predicted value at location 222 : 30.52066 95% confidence interval = ( 28.56066 , 32.48066 )
## Predicted value at location 223 : 30.12681 95% confidence interval = ( 28.16681 , 32.08681 )
## Predicted value at location 224 : 22.99244 95% confidence interval = ( 21.03244 , 24.95244 )
## Predicted value at location 225 : 32.53212 95% confidence interval = ( 30.57212 , 34.49212 )
## Predicted value at location 226 : 17.83817 95% confidence interval = ( 15.87817 , 19.79817 )
## Predicted value at location 227 : 25.91404 95% confidence interval = ( 23.95404 , 27.87404 )
## Predicted value at location 228 : 24.49105 95% confidence interval = ( 22.53105 , 26.45105 )
## Predicted value at location 229 : 34.55319 95% confidence interval = ( 32.59319 , 36.51319 )
## Predicted value at location 230 : 29.72214 95% confidence interval = ( 27.76214 , 31.68214 )
## Predicted value at location 231 : 32.66719 95% confidence interval = ( 30.70719 , 34.62719 )
## Predicted value at location 232 : 21.58465 95% confidence interval = ( 19.62465 , 23.54465 )
## Predicted value at location 233 : 28.06826 95% confidence interval = ( 26.10826 , 30.02826 )
## Predicted value at location 234 : 29.92552 95% confidence interval = ( 27.96552 , 31.88552 )
## Predicted value at location 235 : 23.67486 95% confidence interval = ( 21.71486 , 25.63486 )
## Predicted value at location 236 : 18.61907 95% confidence interval = ( 16.65907 , 20.57907 )
## Predicted value at location 237 : 25.73654 95% confidence interval = ( 23.77654 , 27.69654 )
## Predicted value at location 238 : 33.1306 95% confidence interval = ( 31.1706 , 35.0906 )
## Predicted value at location 239 : 33.54416 95% confidence interval = ( 31.58416 , 35.50416 )
## Predicted value at location 240 : 34.37645 95% confidence interval = ( 32.41645 , 36.33645 )
## Predicted value at location 241 : 30.19628 95% confidence interval = ( 28.23628 , 32.15628 )
## Predicted value at location 242 : 30.10443 95% confidence interval = ( 28.14443 , 32.06443 )
## Predicted value at location 243 : 29.40991 95% confidence interval = ( 27.44991 , 31.36991 )
## Predicted value at location 244 : 28.91625 95% confidence interval = ( 26.95625 , 30.87625 )
## Predicted value at location 245 : 22.16626 95% confidence interval = ( 20.20626 , 24.12626 )
## Predicted value at location 246 : 32.46605 95% confidence interval = ( 30.50605 , 34.42605 )
## Predicted value at location 247 : 36.62064 95% confidence interval = ( 34.66064 , 38.58064 )
## Predicted value at location 248 : 32.13625 95% confidence interval = ( 30.17625 , 34.09625 )
## Predicted value at location 249 : 36.52944 95% confidence interval = ( 34.56944 , 38.48944 )
## Predicted value at location 250 : 27.60333 95% confidence interval = ( 25.64333 , 29.56333 )
## Predicted value at location 251 : 33.3542 95% confidence interval = ( 31.3942 , 35.3142 )
## Predicted value at location 252 : 21.43705 95% confidence interval = ( 19.47705 , 23.39705 )
## Predicted value at location 253 : 20.92278 95% confidence interval = ( 18.96278 , 22.88278 )
## Predicted value at location 254 : 35.38739 95% confidence interval = ( 33.42739 , 37.34739 )
## Predicted value at location 255 : 22.54093 95% confidence interval = ( 20.58093 , 24.50093 )
## Predicted value at location 256 : 29.77798 95% confidence interval = ( 27.81798 , 31.73798 )
## Predicted value at location 257 : 33.2801 95% confidence interval = ( 31.3201 , 35.2401 )
## Predicted value at location 258 : 24.03059 95% confidence interval = ( 22.07059 , 25.99059 )
## Predicted value at location 259 : 33.45255 95% confidence interval = ( 31.49255 , 35.41255 )
## Predicted value at location 260 : 33.0958 95% confidence interval = ( 31.1358 , 35.0558 )
## Predicted value at location 261 : 30.08519 95% confidence interval = ( 28.12519 , 32.04519 )
## Predicted value at location 262 : 33.45268 95% confidence interval = ( 31.49268 , 35.41268 )
## Predicted value at location 263 : 32.12699 95% confidence interval = ( 30.16699 , 34.08699 )
## Predicted value at location 264 : 23.68366 95% confidence interval = ( 21.72366 , 25.64366 )
## Predicted value at location 265 : 30.76179 95% confidence interval = ( 28.80179 , 32.72179 )
## Predicted value at location 266 : 32.19623 95% confidence interval = ( 30.23623 , 34.15623 )
## Predicted value at location 267 : 25.33184 95% confidence interval = ( 23.37184 , 27.29184 )
## Predicted value at location 268 : 33.88491 95% confidence interval = ( 31.92491 , 35.84491 )
## Predicted value at location 269 : 21.67696 95% confidence interval = ( 19.71696 , 23.63696 )
## Predicted value at location 270 : 30.12406 95% confidence interval = ( 28.16406 , 32.08406 )
## Predicted value at location 271 : 33.34558 95% confidence interval = ( 31.38558 , 35.30558 )
## Predicted value at location 272 : 35.27987 95% confidence interval = ( 33.31987 , 37.23987 )
## Predicted value at location 273 : 16.85929 95% confidence interval = ( 14.89929 , 18.81929 )
## Predicted value at location 274 : 28.43684 95% confidence interval = ( 26.47684 , 30.39684 )
## Predicted value at location 275 : 33.90128 95% confidence interval = ( 31.94128 , 35.86128 )
## Predicted value at location 276 : 33.94493 95% confidence interval = ( 31.98493 , 35.90493 )
## Predicted value at location 277 : 32.69896 95% confidence interval = ( 30.73896 , 34.65896 )
## Predicted value at location 278 : 26.98352 95% confidence interval = ( 25.02352 , 28.94352 )
## Predicted value at location 279 : 21.60248 95% confidence interval = ( 19.64248 , 23.56248 )
## Predicted value at location 280 : 27.00868 95% confidence interval = ( 25.04868 , 28.96868 )
## Predicted value at location 281 : 26.9461 95% confidence interval = ( 24.9861 , 28.9061 )
## Predicted value at location 282 : 29.8659 95% confidence interval = ( 27.9059 , 31.8259 )
## Predicted value at location 283 : 25.18584 95% confidence interval = ( 23.22584 , 27.14584 )
## Predicted value at location 284 : 29.87401 95% confidence interval = ( 27.91401 , 31.83401 )
## Predicted value at location 285 : 37.33161 95% confidence interval = ( 35.37161 , 39.29161 )
## Predicted value at location 286 : 29.07096 95% confidence interval = ( 27.11096 , 31.03096 )
## Predicted value at location 287 : 27.88164 95% confidence interval = ( 25.92164 , 29.84164 )
## Predicted value at location 288 : 29.30777 95% confidence interval = ( 27.34777 , 31.26777 )
## Predicted value at location 289 : 31.22923 95% confidence interval = ( 29.26923 , 33.18923 )
## Predicted value at location 290 : 40.55297 95% confidence interval = ( 38.59297 , 42.51297 )
## Predicted value at location 291 : 31.61644 95% confidence interval = ( 29.65644 , 33.57644 )
## Predicted value at location 292 : 23.58298 95% confidence interval = ( 21.62298 , 25.54298 )
## Predicted value at location 293 : 34.1803 95% confidence interval = ( 32.2203 , 36.1403 )
## Predicted value at location 294 : 30.86564 95% confidence interval = ( 28.90564 , 32.82564 )
## Predicted value at location 295 : 34.37203 95% confidence interval = ( 32.41203 , 36.33203 )
## Predicted value at location 296 : 30.43504 95% confidence interval = ( 28.47504 , 32.39504 )
## Predicted value at location 297 : 28.54623 95% confidence interval = ( 26.58623 , 30.50623 )
## Predicted value at location 298 : 39.69512 95% confidence interval = ( 37.73512 , 41.65512 )
## Predicted value at location 299 : 30.63213 95% confidence interval = ( 28.67213 , 32.59213 )
## Predicted value at location 300 : 34.00969 95% confidence interval = ( 32.04969 , 35.96969 )
## Predicted value at location 301 : 29.72613 95% confidence interval = ( 27.76613 , 31.68613 )
## Predicted value at location 302 : 30.14309 95% confidence interval = ( 28.18309 , 32.10309 )
## Predicted value at location 303 : 37.84609 95% confidence interval = ( 35.88609 , 39.80609 )
## Predicted value at location 304 : 27.50638 95% confidence interval = ( 25.54638 , 29.46638 )
## Predicted value at location 305 : 32.68867 95% confidence interval = ( 30.72867 , 34.64867 )
## Predicted value at location 306 : 30.08955 95% confidence interval = ( 28.12955 , 32.04955 )
## Predicted value at location 307 : 29.97454 95% confidence interval = ( 28.01454 , 31.93454 )
## Predicted value at location 308 : 30.03332 95% confidence interval = ( 28.07332 , 31.99332 )
## Predicted value at location 309 : 22.11024 95% confidence interval = ( 20.15024 , 24.07024 )
## Predicted value at location 310 : 29.88447 95% confidence interval = ( 27.92447 , 31.84447 )
## Predicted value at location 311 : 30.16272 95% confidence interval = ( 28.20272 , 32.12272 )
## Predicted value at location 312 : 29.84114 95% confidence interval = ( 27.88114 , 31.80114 )
## Predicted value at location 313 : 31.94218 95% confidence interval = ( 29.98218 , 33.90218 )
## Predicted value at location 314 : 14.5956 95% confidence interval = ( 12.6356 , 16.5556 )
## Predicted value at location 315 : 25.35205 95% confidence interval = ( 23.39205 , 27.31205 )
## Predicted value at location 316 : 32.33887 95% confidence interval = ( 30.37887 , 34.29887 )
## Predicted value at location 317 : 42.44348 95% confidence interval = ( 40.48348 , 44.40348 )
## Predicted value at location 318 : 33.12614 95% confidence interval = ( 31.16614 , 35.08614 )
## Predicted value at location 319 : 28.77124 95% confidence interval = ( 26.81124 , 30.73124 )
## Predicted value at location 320 : 42.16131 95% confidence interval = ( 40.20131 , 44.12131 )
## Predicted value at location 321 : 36.36942 95% confidence interval = ( 34.40942 , 38.32942 )
## Predicted value at location 322 : 42.397 95% confidence interval = ( 40.437 , 44.357 )
## Predicted value at location 323 : 21.98993 95% confidence interval = ( 20.02993 , 23.94993 )
## Predicted value at location 324 : 24.85798 95% confidence interval = ( 22.89798 , 26.81798 )
## Predicted value at location 325 : 28.92567 95% confidence interval = ( 26.96567 , 30.88567 )
## Predicted value at location 326 : 30.99517 95% confidence interval = ( 29.03517 , 32.95517 )
## Predicted value at location 327 : 36.72705 95% confidence interval = ( 34.76705 , 38.68705 )
## Predicted value at location 328 : 42.28991 95% confidence interval = ( 40.32991 , 44.24991 )
## Predicted value at location 329 : 26.65649 95% confidence interval = ( 24.69649 , 28.61649 )
## Predicted value at location 330 : 21.5106 95% confidence interval = ( 19.5506 , 23.4706 )
## Predicted value at location 331 : 31.64575 95% confidence interval = ( 29.68575 , 33.60575 )
## Predicted value at location 332 : 31.62064 95% confidence interval = ( 29.66064 , 33.58064 )
## Predicted value at location 333 : 32.19714 95% confidence interval = ( 30.23714 , 34.15714 )
## Predicted value at location 334 : 30.42663 95% confidence interval = ( 28.46663 , 32.38663 )
## Predicted value at location 335 : 31.45714 95% confidence interval = ( 29.49714 , 33.41714 )
## Predicted value at location 336 : 29.7605 95% confidence interval = ( 27.8005 , 31.7205 )
## Predicted value at location 337 : 25.30952 95% confidence interval = ( 23.34952 , 27.26952 )
## Predicted value at location 338 : 32.51807 95% confidence interval = ( 30.55807 , 34.47807 )
## Predicted value at location 339 : 29.68884 95% confidence interval = ( 27.72884 , 31.64884 )
## Predicted value at location 340 : 20.88537 95% confidence interval = ( 18.92537 , 22.84537 )
## Predicted value at location 341 : 23.84076 95% confidence interval = ( 21.88076 , 25.80076 )
## Predicted value at location 342 : 21.90171 95% confidence interval = ( 19.94171 , 23.86171 )
## Predicted value at location 343 : 36.55301 95% confidence interval = ( 34.59301 , 38.51301 )
## Predicted value at location 344 : 12.27709 95% confidence interval = ( 10.31709 , 14.23709 )
## Predicted value at location 345 : 17.61523 95% confidence interval = ( 15.65523 , 19.57523 )
## Predicted value at location 346 : 22.44295 95% confidence interval = ( 20.48295 , 24.40295 )
## Predicted value at location 347 : 33.85793 95% confidence interval = ( 31.89793 , 35.81793 )
## Predicted value at location 348 : 33.12647 95% confidence interval = ( 31.16647 , 35.08647 )
## Predicted value at location 349 : 14.41302 95% confidence interval = ( 12.45302 , 16.37302 )
## Predicted value at location 350 : 31.84958 95% confidence interval = ( 29.88958 , 33.80958 )
## Predicted value at location 351 : 31.26112 95% confidence interval = ( 29.30112 , 33.22112 )
## Predicted value at location 352 : 32.99684 95% confidence interval = ( 31.03684 , 34.95684 )
## Predicted value at location 353 : 22.20917 95% confidence interval = ( 20.24917 , 24.16917 )
## Predicted value at location 354 : 37.52437 95% confidence interval = ( 35.56437 , 39.48437 )
## Predicted value at location 355 : 11.73002 95% confidence interval = ( 9.770018 , 13.69002 )
## Predicted value at location 356 : 24.07622 95% confidence interval = ( 22.11622 , 26.03622 )
## Predicted value at location 357 : 31.56424 95% confidence interval = ( 29.60424 , 33.52424 )
## Predicted value at location 358 : 30.07703 95% confidence interval = ( 28.11703 , 32.03703 )
## Predicted value at location 359 : 29.74629 95% confidence interval = ( 27.78629 , 31.70629 )
## Predicted value at location 360 : 24.68204 95% confidence interval = ( 22.72204 , 26.64204 )
## Predicted value at location 361 : 33.97972 95% confidence interval = ( 32.01972 , 35.93972 )
## Predicted value at location 362 : 28.00977 95% confidence interval = ( 26.04977 , 29.96977 )
## Predicted value at location 363 : 37.97307 95% confidence interval = ( 36.01307 , 39.93307 )
## Predicted value at location 364 : 29.1223 95% confidence interval = ( 27.1623 , 31.0823 )
## Predicted value at location 365 : 26.84513 95% confidence interval = ( 24.88513 , 28.80513 )
## Predicted value at location 366 : 18.56306 95% confidence interval = ( 16.60306 , 20.52306 )
## Predicted value at location 367 : 28.81086 95% confidence interval = ( 26.85086 , 30.77086 )
## Predicted value at location 368 : 12.943 95% confidence interval = ( 10.983 , 14.903 )
## Predicted value at location 369 : 22.34451 95% confidence interval = ( 20.38451 , 24.30451 )
## Predicted value at location 370 : 34.96614 95% confidence interval = ( 33.00614 , 36.92614 )
## Predicted value at location 371 : 30.9394 95% confidence interval = ( 28.9794 , 32.8994 )