library(nlme)
library(orcutt)
library(leaps)
library(lmtest)
## Loading required package: zoo
## Attaching package: 'zoo'
## The following object(s) are masked from 'package:base':
##
## as.Date, as.Date.numeric
afz_clust <- read.csv("/Users/telekineticturtle/Desktop/Colorado 13/Quant Methods/Project_Quant/AFZGrads_Clust_July_1979_2012.csv",
header = T)
names(afz_clust)
## [1] "Year" "TempGrad" "Cluster" "ClusterAB"
## [5] "Cluster1" "Cluster2" "Cluster3" "Cluster4"
## [9] "Cluster5" "Cluster6" "AO_Index" "AO_3LagAvg"
## [13] "AO_6LagAvg" "AO_12LagAvg" "AO_6Lag3Avg" "AO_2Lag3Avg"
## [17] "AO_5Lag6Avg" "AO_11Lag12Avg" "NAO_Index" "NAO_3LagAvg"
## [21] "NAO_6LagAvg" "NAO_12LagAvg" "NAO_6Lag3Avg" "NAO_2Lag3Avg"
## [25] "NAO_5Lag6Avg" "NAO_11Lag12Avg" "PNA_Index" "PNA_3LagAvg"
## [29] "PNA_6LagAvg" "PNA_12LagAvg" "PNA_6Lag3Avg" "PNA_2Lag3Avg"
## [33] "PNA_5Lag6Avg" "PNA_11Lag12Avg" "GlobalJulyTemp" "GT_3LagAvg"
## [37] "GT_6LagAvg" "GT_12LagAvg" "GT_6Lag3Avg" "GT_2Lag3Avg"
## [41] "GT_5Lag6Avg" "GT_11Lag12Avg"
summary(afz_clust$TempGrad)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0161 0.0369 0.0435 0.0445 0.0509 0.0735
length(afz_clust$TempGrad)
## [1] 204
# Create Subsets
afz_clust1 <- afz_clust[afz_clust$Cluster == 1, ]
afz_clust2 <- afz_clust[afz_clust$Cluster == 2, ]
afz_clust3 <- afz_clust[afz_clust$Cluster == 3, ]
afz_clust4 <- afz_clust[afz_clust$Cluster == 4, ]
afz_clust5 <- afz_clust[afz_clust$Cluster == 5, ]
afz_clust6 <- afz_clust[afz_clust$Cluster == 6, ]
# Cluster Plots:
plot(TempGrad ~ Year, data = afz_clust[1:34, ], main = "AFZ Cluster 1 Temperature Gradients 1979 to 2012",
ylab = "Temp Gradient (K/km)", xlab = "Year", type = "b", cex = 0.6, col = "blue",
ylim = c(0.01, 0.08))
plot(TempGrad ~ Year, data = afz_clust[35:68, ], main = "AFZ Cluster 2 Temperature Gradients 1979 to 2012",
ylab = "Temp Gradient (K/km)", xlab = "Year", type = "b", cex = 0.6, col = "red",
ylim = c(0.01, 0.08))
plot(TempGrad ~ Year, data = afz_clust[69:102, ], main = "AFZ Cluster 3 Temperature Gradients 1979 to 2012",
ylab = "Temp Gradient (K/km)", xlab = "Year", type = "b", cex = 0.6, col = "pink",
ylim = c(0.01, 0.08))
plot(TempGrad ~ Year, data = afz_clust[103:136, ], main = "AFZ Cluster 4 Temperature Gradients 1979 to 2012",
ylab = "Temp Gradient (K/km)", xlab = "Year", type = "b", cex = 0.6, col = "purple",
ylim = c(0.01, 0.08))
plot(TempGrad ~ Year, data = afz_clust[137:170, ], main = "AFZ Cluster 5 Temperature Gradients 1979 to 2012",
ylab = "Temp Gradient (K/km)", xlab = "Year", type = "b", cex = 0.6, col = "green",
ylim = c(0.01, 0.08))
plot(TempGrad ~ Year, data = afz_clust[171:204, ], main = "AFZ Cluster 6 Temperature Gradients 1979 to 2012",
ylab = "Temp Gradient (K/km)", xlab = "Year", type = "b", cex = 0.6, col = "orange",
ylim = c(0.01, 0.08))
# Plots for Indices: AO
plot(AO_Index ~ Year, data = afz_clust[1:34, ], main = "July AO Index 1979 to 2012",
ylab = "Index Value", xlab = "Year", type = "l", col = "blue")
plot(AO_11Lag12Avg ~ Year, data = afz_clust[1:34, ], main = "AO Index 1979 to 2012 \n 12-month (June through July)",
ylab = "Index Value", xlab = "Year", type = "l", col = "red")
plot(AO_5Lag6Avg ~ Year, data = afz_clust[1:34, ], main = "AO Index 1979 to 2012 \n 6-month (February through July)",
ylab = "Index Value", xlab = "Year", type = "l", col = "green")
plot(AO_2Lag3Avg ~ Year, data = afz_clust[1:34, ], main = "AO Index 1979 to 2012 \n 3-month (May through July)",
ylab = "Index Value", xlab = "Year", type = "l", col = "orange")
## NAO
plot(NAO_Index ~ Year, data = afz_clust[1:34, ], main = "July NAO Index 1979 to 2012",
ylab = "Index Value", xlab = "Year", type = "l", col = "blue")
plot(NAO_11Lag12Avg ~ Year, data = afz_clust[1:34, ], main = "NAO Index 1979 to 2012 \n 12-month (June through July)",
ylab = "Index Value", xlab = "Year", type = "l", col = "red")
plot(NAO_5Lag6Avg ~ Year, data = afz_clust[1:34, ], main = "NAO Index 1979 to 2012 \n 6-month (February through July)",
ylab = "Index Value", xlab = "Year", type = "l", col = "green")
plot(NAO_2Lag3Avg ~ Year, data = afz_clust[1:34, ], main = "NAO Index 1979 to 2012 \n 3-month (May through July)",
ylab = "Index Value", xlab = "Year", type = "l", col = "orange")
## PNA
plot(PNA_Index ~ Year, data = afz_clust[1:34, ], main = "July PNA Index 1979 to 2012",
ylab = "Index Value", xlab = "Year", type = "l", col = "blue")
plot(PNA_11Lag12Avg ~ Year, data = afz_clust[1:34, ], main = "PNA Index 1979 to 2012 \n 12-month (June through July)",
ylab = "Index Value", xlab = "Year", type = "l", col = "red")
plot(PNA_5Lag6Avg ~ Year, data = afz_clust[1:34, ], main = "PNA Index 1979 to 2012 \n 6-month (February through July)",
ylab = "Index Value", xlab = "Year", type = "l", col = "green")
plot(PNA_2Lag3Avg ~ Year, data = afz_clust[1:34, ], main = "PNA Index 1979 to 2012 \n 3-month (May through July)",
ylab = "Index Value", xlab = "Year", type = "l", col = "orange")
# Plots for Temperature:
plot(GlobalJulyTemp ~ Year, data = afz_clust[1:34, ], main = "Global July Temperature Index 1979 to 2012",
ylab = "Index Value", xlab = "Year", type = "l", col = "blue")
plot(GT_11Lag12Avg ~ Year, data = afz_clust[1:34, ], main = "Global Temperature Index 1979 to 2012 \n 12-month (June through July)",
ylab = "Index Value", xlab = "Year", type = "l", col = "red")
plot(GT_5Lag6Avg ~ Year, data = afz_clust[1:34, ], main = "Global Temperature Index 1979 to 2012 \n 6-month (February through July)",
ylab = "Index Value", xlab = "Year", type = "l", col = "green")
plot(GT_2Lag3Avg ~ Year, data = afz_clust[1:34, ], main = "Global Temperature Index 1979 to 2012 \n 3-month (May through July)",
ylab = "Index Value", xlab = "Year", type = "l", col = "orange")
## Create Temporal Regression Model Create Model:
lm1c1yr <- lm(TempGrad ~ Year, data = afz_clust1)
summary(lm1c1yr) # I actually have a negative adjusted R^2
##
## Call:
## lm(formula = TempGrad ~ Year, data = afz_clust1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.017602 -0.004906 0.000573 0.004477 0.022684
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.58e-02 2.67e-01 -0.10 0.92
## Year 3.58e-05 1.34e-04 0.27 0.79
##
## Residual standard error: 0.00765 on 32 degrees of freedom
## Multiple R-squared: 0.00223, Adjusted R-squared: -0.0289
## F-statistic: 0.0716 on 1 and 32 DF, p-value: 0.791
# Examine/Plot Residuals:
plot(lm1c1yr$residuals ~ lm1c1yr$fitted.values, main = "Residuals for Linear Time Model: Cluster 1",
xlab = "Fitted Values (K/km)", ylab = "Residuals")
abline(0, 0)
qqnorm(lm1c1yr$residuals)
qqline(lm1c1yr$residuals)
# Shapiro-Wilk Test:
shapiro.test(lm1c1yr$residuals) # Null not rejected; only 34 points, but the residuals are just about normally distributed. Time is not a big issue?
##
## Shapiro-Wilk normality test
##
## data: lm1c1yr$residuals
## W = 0.9681, p-value = 0.411
# Plot Results:
plot(TempGrad ~ Year, data = afz_clust1, main = "AFZ July Temperature Gradients: Cluster 1",
xlab = "Years", ylab = "Temperature Gradient (K/km)", cex = 0.6)
curve(predict(lm1c1yr, data.frame(Year = x), type = "resp"), add = TRUE, col = "blue",
lwd = 3)
## Run Durbin-Watson Test
library(lmtest)
# Null Hypothesis: rho = 0; there is only random error and no
# autocorrelation
dwtest(lm1c1yr) # DW = 1.6138, p-value = 0.09058
##
## Durbin-Watson test
##
## data: lm1c1yr
## DW = 1.614, p-value = 0.09058
## alternative hypothesis: true autocorrelation is greater than 0
# This tells us that at the 0.05 level, there is no autocorrelation; rho =
# 0. Data is stationary!
## Create Temporal Regression Model Create Model:
lm1c2yr <- lm(TempGrad ~ Year, data = afz_clust2)
summary(lm1c2yr) # Not a significant relationship.
##
## Call:
## lm(formula = TempGrad ~ Year, data = afz_clust2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.015255 -0.004528 -0.000521 0.003993 0.027860
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.425754 0.305492 -1.39 0.17
## Year 0.000233 0.000153 1.52 0.14
##
## Residual standard error: 0.00876 on 32 degrees of freedom
## Multiple R-squared: 0.0673, Adjusted R-squared: 0.0382
## F-statistic: 2.31 on 1 and 32 DF, p-value: 0.138
# Examine/Plot Residuals:
plot(lm1c2yr$residuals ~ lm1c2yr$fitted.values, main = "Residuals for Linear Time Model: Cluster 2",
xlab = "Fitted Values (K/km)", ylab = "Residuals")
abline(0, 0)
qqnorm(lm1c2yr$residuals)
qqline(lm1c2yr$residuals)
# Shapiro-Wilk Test:
shapiro.test(lm1c2yr$residuals) # Null not rejected; only 34 points, but the residuals are just about normally distributed. Time is not a big issue?
##
## Shapiro-Wilk normality test
##
## data: lm1c2yr$residuals
## W = 0.9538, p-value = 0.16
# Plot Results:
plot(TempGrad ~ Year, data = afz_clust2, main = "AFZ July Temperature Gradients: Cluster 2",
xlab = "Years", ylab = "Temperature Gradient (K/km)", cex = 0.6)
curve(predict(lm1c2yr, data.frame(Year = x), type = "resp"), add = TRUE, col = "red",
lwd = 3)
## Run Durbin-Watson Test
library(lmtest)
# Null Hypothesis: rho = 0; there is only random error and no
# autocorrelation
dwtest(lm1c2yr) # DW = 1.6244, p-value = 0.09593
##
## Durbin-Watson test
##
## data: lm1c2yr
## DW = 1.624, p-value = 0.09593
## alternative hypothesis: true autocorrelation is greater than 0
# This tells us that at the 0.05 level, there is no autocorrelation; rho =
# 0. Data is stationary!
## Create Temporal Regression Model Create Model:
lm1c3yr <- lm(TempGrad ~ Year, data = afz_clust3)
summary(lm1c3yr) # Not a significant relationship.
##
## Call:
## lm(formula = TempGrad ~ Year, data = afz_clust3)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.028834 -0.007343 0.000026 0.006540 0.025773
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.155893 0.407239 -0.38 0.70
## Year 0.000101 0.000204 0.50 0.62
##
## Residual standard error: 0.0117 on 32 degrees of freedom
## Multiple R-squared: 0.00766, Adjusted R-squared: -0.0234
## F-statistic: 0.247 on 1 and 32 DF, p-value: 0.623
# Examine/Plot Residuals:
plot(lm1c3yr$residuals ~ lm1c2yr$fitted.values, main = "Residuals for Linear Time Model: Cluster 3",
xlab = "Fitted Values (K/km)", ylab = "Residuals")
abline(0, 0)
qqnorm(lm1c3yr$residuals)
qqline(lm1c3yr$residuals)
# Shapiro-Wilk Test:
shapiro.test(lm1c3yr$residuals) # Null not rejected; only 34 points, but the residuals are just about normally distributed. Time is not a big issue?
##
## Shapiro-Wilk normality test
##
## data: lm1c3yr$residuals
## W = 0.9849, p-value = 0.9099
# Plot Results:
plot(TempGrad ~ Year, data = afz_clust3, main = "AFZ July Temperature Gradients: Cluster 3",
xlab = "Years", ylab = "Temperature Gradient (K/km)", cex = 0.6)
curve(predict(lm1c3yr, data.frame(Year = x), type = "resp"), add = TRUE, col = "pink",
lwd = 3)
## Run Durbin-Watson Test
library(lmtest)
# Null Hypothesis: rho = 0; there is only random error and no
# autocorrelation
dwtest(lm1c3yr) # DW = 1.427, p-value = 0.02774
##
## Durbin-Watson test
##
## data: lm1c3yr
## DW = 1.427, p-value = 0.02774
## alternative hypothesis: true autocorrelation is greater than 0
# This tells us that at the 0.05 level, there IS autocorrelation; rho > 0.
# Data is not stationary, but there's also no trend.
## Create Temporal Regression Model Create Model:
lm1c4yr <- lm(TempGrad ~ Year, data = afz_clust4)
summary(lm1c4yr) # Not a significant relationship. (But close...)
##
## Call:
## lm(formula = TempGrad ~ Year, data = afz_clust4)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.01416 -0.00322 -0.00169 0.00242 0.01862
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.423573 0.237979 -1.78 0.085 .
## Year 0.000231 0.000119 1.94 0.062 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.00682 on 32 degrees of freedom
## Multiple R-squared: 0.105, Adjusted R-squared: 0.077
## F-statistic: 3.75 on 1 and 32 DF, p-value: 0.0615
# Examine/Plot Residuals:
plot(lm1c4yr$residuals ~ lm1c4yr$fitted.values, main = "Residuals for Linear Time Model: Cluster 4",
xlab = "Fitted Values (K/km)", ylab = "Residuals")
abline(0, 0)
qqnorm(lm1c4yr$residuals) # This is the first one that looks aweful.
qqline(lm1c4yr$residuals)
# Shapiro-Wilk Test:
shapiro.test(lm1c4yr$residuals) # Null rejected; these residuals are NOT normally distributed.
##
## Shapiro-Wilk normality test
##
## data: lm1c4yr$residuals
## W = 0.9329, p-value = 0.03799
# Plot Results:
plot(TempGrad ~ Year, data = afz_clust4, main = "AFZ July Temperature Gradients: Cluster 4",
xlab = "Years", ylab = "Temperature Gradient (K/km)", cex = 0.6)
curve(predict(lm1c4yr, data.frame(Year = x), type = "resp"), add = TRUE, col = "purple",
lwd = 3) # It looks like a qudratic or logarithmic x-value may be decent.
## Run Durbin-Watson Test
library(lmtest)
# Null Hypothesis: rho = 0; there is only random error and no
# autocorrelation
dwtest(lm1c4yr) # DW = 1.9166, p-value = 0.3326
##
## Durbin-Watson test
##
## data: lm1c4yr
## DW = 1.917, p-value = 0.3326
## alternative hypothesis: true autocorrelation is greater than 0
# This tells us that at the 0.05 level, there is no autocorrelation; rho =
# 0. Data is stationary!
## Create Temporal Regression Model Create Model:
lm1c5yr <- lm(TempGrad ~ Year, data = afz_clust5)
summary(lm1c5yr) # p-value = 0.00395; Adj R^2 = 0.2077
##
## Call:
## lm(formula = TempGrad ~ Year, data = afz_clust5)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.024774 -0.006917 -0.000566 0.007315 0.025065
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.140146 0.383308 -2.97 0.0055 **
## Year 0.000597 0.000192 3.11 0.0039 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.011 on 32 degrees of freedom
## Multiple R-squared: 0.232, Adjusted R-squared: 0.208
## F-statistic: 9.65 on 1 and 32 DF, p-value: 0.00395
# Examine/Plot Residuals:
plot(lm1c5yr$residuals ~ lm1c2yr$fitted.values, main = "Residuals for Linear Time Model: Cluster 5",
xlab = "Fitted Values (K/km)", ylab = "Residuals")
abline(0, 0)
qqnorm(lm1c5yr$residuals)
qqline(lm1c5yr$residuals)
# Shapiro-Wilk Test:
shapiro.test(lm1c5yr$residuals) # p-value = 0.9955 Null not rejected; only 34 points, but the residuals are just about normally distributed. Time is not a big issue?
##
## Shapiro-Wilk normality test
##
## data: lm1c5yr$residuals
## W = 0.9918, p-value = 0.9955
# Plot Results:
plot(TempGrad ~ Year, data = afz_clust5, main = "AFZ July Temperature Gradients: Cluster 5",
xlab = "Years", ylab = "Temperature Gradient (K/km)", cex = 0.6)
curve(predict(lm1c5yr, data.frame(Year = x), type = "resp"), add = TRUE, col = "green",
lwd = 3)
## Run Durbin-Watson Test
library(lmtest)
# Null Hypothesis: rho = 0; there is only random error and no
# autocorrelation
dwtest(lm1c5yr) # DW = 1.9315, p-value = 0.3488
##
## Durbin-Watson test
##
## data: lm1c5yr
## DW = 1.931, p-value = 0.3488
## alternative hypothesis: true autocorrelation is greater than 0
# This tells us that at the 0.05 level, there is no autocorrelation; rho =
# 0. Data is stationary!
## Create Temporal Regression Model Create Model:
lm1c6yr <- lm(TempGrad ~ Year, data = afz_clust6)
summary(lm1c6yr) # Just barely a significant relationship. adj R^2 = 0.08946
##
## Call:
## lm(formula = TempGrad ~ Year, data = afz_clust6)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.01380 -0.00672 -0.00170 0.00711 0.01476
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.597509 0.313384 -1.91 0.066 .
## Year 0.000323 0.000157 2.06 0.048 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.00898 on 32 degrees of freedom
## Multiple R-squared: 0.117, Adjusted R-squared: 0.0895
## F-statistic: 4.24 on 1 and 32 DF, p-value: 0.0476
# Examine/Plot Residuals:
plot(lm1c6yr$residuals ~ lm1c6yr$fitted.values, main = "Residuals for Linear Time Model: Cluster 6",
xlab = "Fitted Values (K/km)", ylab = "Residuals")
abline(0, 0)
qqnorm(lm1c6yr$residuals) # Weirdly patterned residuals
qqline(lm1c6yr$residuals)
# Shapiro-Wilk Test:
shapiro.test(lm1c6yr$residuals) # Null not rejected, but they're still weird.
##
## Shapiro-Wilk normality test
##
## data: lm1c6yr$residuals
## W = 0.9402, p-value = 0.06232
# Plot Results:
plot(TempGrad ~ Year, data = afz_clust6, main = "AFZ July Temperature Gradients: Cluster 6",
xlab = "Years", ylab = "Temperature Gradient (K/km)", cex = 0.6)
curve(predict(lm1c6yr, data.frame(Year = x), type = "resp"), add = TRUE, col = "orange",
lwd = 3)
## Run Durbin-Watson Test
library(lmtest)
# Null Hypothesis: rho = 0; there is only random error and no
# autocorrelation
dwtest(lm1c6yr) # DW = 1.8462, p-value = 0.2608
##
## Durbin-Watson test
##
## data: lm1c6yr
## DW = 1.846, p-value = 0.2608
## alternative hypothesis: true autocorrelation is greater than 0
# This tells us that at the 0.05 level, there is no autocorrelation; rho =
# 0. Data is stationary!
## Create Temporal Regression Model Create Model:
lm1AOyr <- lm(AO_Index ~ Year, data = afz_clust2)
summary(lm1AOyr) # Not a significant relationship.
##
## Call:
## lm(formula = AO_Index ~ Year, data = afz_clust2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.1696 -0.2609 0.0022 0.2488 0.9143
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 14.48194 15.11112 0.96 0.35
## Year -0.00730 0.00757 -0.96 0.34
##
## Residual standard error: 0.433 on 32 degrees of freedom
## Multiple R-squared: 0.0282, Adjusted R-squared: -0.00212
## F-statistic: 0.93 on 1 and 32 DF, p-value: 0.342
# Examine/Plot Residuals:
plot(lm1AOyr$residuals ~ lm1AOyr$fitted.values, main = "Residuals for Linear Time Model: AO Index",
xlab = "Fitted Values (AO Index)", ylab = "Residuals")
abline(0, 0)
qqnorm(lm1AOyr$residuals)
qqline(lm1AOyr$residuals)
# Shapiro-Wilk Test:
shapiro.test(lm1AOyr$residuals) # Null not rejected; only 34 points, but the residuals are just about normally distributed. Time is not a big issue?
##
## Shapiro-Wilk normality test
##
## data: lm1AOyr$residuals
## W = 0.9844, p-value = 0.8961
# Plot Results:
plot(AO_Index ~ Year, data = afz_clust2, main = "July AO Index: 1979 - 2012",
xlab = "Years", ylab = "AO Index", cex = 0.6)
curve(predict(lm1AOyr, data.frame(Year = x), type = "resp"), add = TRUE, col = "red",
lwd = 3)
## Run Durbin-Watson Test
library(lmtest)
# Null Hypothesis: rho = 0; there is only random error and no
# autocorrelation
dwtest(lm1AOyr) # DW = 2.6305, p-value = 0.9572
##
## Durbin-Watson test
##
## data: lm1AOyr
## DW = 2.631, p-value = 0.9572
## alternative hypothesis: true autocorrelation is greater than 0
# This tells us that at the 0.05 level, there is no autocorrelation; rho =
# 0. Data is stationary!
## Create Temporal Regression Model Create Model:
lm12AOyr <- lm(AO_11Lag12Avg ~ Year, data = afz_clust2)
summary(lm12AOyr) # Not a significant relationship.
##
## Call:
## lm(formula = AO_11Lag12Avg ~ Year, data = afz_clust2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.971 -0.263 -0.121 0.262 1.080
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.016507 14.755141 -0.07 0.95
## Year 0.000501 0.007394 0.07 0.95
##
## Residual standard error: 0.423 on 32 degrees of freedom
## Multiple R-squared: 0.000144, Adjusted R-squared: -0.0311
## F-statistic: 0.00459 on 1 and 32 DF, p-value: 0.946
# Examine/Plot Residuals:
plot(lm1AOyr$residuals ~ lm1AOyr$fitted.values, main = "Residuals for Linear Time Model: \n Annual (Aug - Jul) AO Index",
xlab = "Fitted Values (AO Index)", ylab = "Residuals")
abline(0, 0)
qqnorm(lm12AOyr$residuals)
qqline(lm12AOyr$residuals)
# Shapiro-Wilk Test:
shapiro.test(lm12AOyr$residuals) # Null not rejected; only 34 points, but the residuals are just about normally distributed. Time is not a big issue?
##
## Shapiro-Wilk normality test
##
## data: lm12AOyr$residuals
## W = 0.9522, p-value = 0.1429
# Plot Results:
plot(AO_11Lag12Avg ~ Year, data = afz_clust2, main = "Annual AO Index (Aug-Jul): 1979 - 2012",
xlab = "Years", ylab = "AO Index", cex = 0.6)
curve(predict(lm12AOyr, data.frame(Year = x), type = "resp"), add = TRUE, col = "red",
lwd = 3)
## Run Durbin-Watson Test
library(lmtest)
# Null Hypothesis: rho = 0; there is only random error and no
# autocorrelation
dwtest(lm12AOyr) # DW = 1.5088, p-value = 0.04853
##
## Durbin-Watson test
##
## data: lm12AOyr
## DW = 1.509, p-value = 0.04853
## alternative hypothesis: true autocorrelation is greater than 0
# This tells us that at the 0.05 level, there IS autocorrelation; rho > 0.
# Data is non-stationary!
## Create Temporal Regression Model Create Model:
lm1NAOyr <- lm(NAO_Index ~ Year, data = afz_clust2)
summary(lm1NAOyr) # Significant! adj. R^2 = 0.1668
##
## Call:
## lm(formula = NAO_Index ~ Year, data = afz_clust2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.196 -0.571 0.066 0.620 1.611
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 90.0736 32.6969 2.75 0.0096 **
## Year -0.0452 0.0164 -2.76 0.0095 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.937 on 32 degrees of freedom
## Multiple R-squared: 0.192, Adjusted R-squared: 0.167
## F-statistic: 7.61 on 1 and 32 DF, p-value: 0.00954
# Examine/Plot Residuals:
plot(lm1NAOyr$residuals ~ lm1NAOyr$fitted.values, main = "Residuals for Linear Time Model: NAO Index",
xlab = "Fitted Values (NAO Index)", ylab = "Residuals")
abline(0, 0)
qqnorm(lm1NAOyr$residuals)
qqline(lm1NAOyr$residuals)
# Shapiro-Wilk Test:
shapiro.test(lm1NAOyr$residuals) # Null rejected; residuals are not noramlly distributed.
##
## Shapiro-Wilk normality test
##
## data: lm1NAOyr$residuals
## W = 0.9307, p-value = 0.0327
# Plot Results:
plot(NAO_Index ~ Year, data = afz_clust2, main = "July NAO Index: 1979 - 2012",
xlab = "Years", ylab = "NAO Index", cex = 0.6)
curve(predict(lm1NAOyr, data.frame(Year = x), type = "resp"), add = TRUE, col = "red",
lwd = 3) # A quadratic or 1/log may be better
## Run Durbin-Watson Test
library(lmtest)
# Null Hypothesis: rho = 0; there is only random error and no
# autocorrelation
dwtest(lm1NAOyr) # DW = 2.2056, p-value = 0.6631
##
## Durbin-Watson test
##
## data: lm1NAOyr
## DW = 2.206, p-value = 0.6631
## alternative hypothesis: true autocorrelation is greater than 0
# This tells us that at the 0.05 level, there is no autocorrelation; rho =
# 0. Data is stationary!
## Create Temporal Regression Model Create Model:
lm12NAOyr <- lm(NAO_11Lag12Avg ~ Year, data = afz_clust2)
summary(lm12NAOyr) # Significant! adj R^2 = 0.1432
##
## Call:
## lm(formula = NAO_11Lag12Avg ~ Year, data = afz_clust2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.6024 -0.1917 -0.0314 0.2390 0.6817
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 29.47494 11.52394 2.56 0.015 *
## Year -0.01474 0.00577 -2.55 0.016 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.33 on 32 degrees of freedom
## Multiple R-squared: 0.169, Adjusted R-squared: 0.143
## F-statistic: 6.52 on 1 and 32 DF, p-value: 0.0157
# Examine/Plot Residuals:
plot(lm1NAOyr$residuals ~ lm1NAOyr$fitted.values, main = "Residuals for Linear Time Model: \n Annual (Aug - Jul) NAO Index",
xlab = "Fitted Values (NAO Index)", ylab = "Residuals")
abline(0, 0)
qqnorm(lm12NAOyr$residuals)
qqline(lm12NAOyr$residuals)
# Shapiro-Wilk Test:
shapiro.test(lm12NAOyr$residuals) # Null not rejected; only 34 points, but the residuals are just about normally distributed. Time is not a big issue?
##
## Shapiro-Wilk normality test
##
## data: lm12NAOyr$residuals
## W = 0.972, p-value = 0.519
# Plot Results:
plot(NAO_11Lag12Avg ~ Year, data = afz_clust2, main = "Annual NAO Index (Aug-Jul): 1979 - 2012",
xlab = "Years", ylab = "NAO Index", cex = 0.6)
curve(predict(lm12NAOyr, data.frame(Year = x), type = "resp"), add = TRUE, col = "red",
lwd = 3) # Again, quadratic may be superior
## Run Durbin-Watson Test
library(lmtest)
# Null Hypothesis: rho = 0; there is only random error and no
# autocorrelation
dwtest(lm12NAOyr) # DW = 1.8871, p-value = 0.3016
##
## Durbin-Watson test
##
## data: lm12NAOyr
## DW = 1.887, p-value = 0.3016
## alternative hypothesis: true autocorrelation is greater than 0
# This tells us that at the 0.05 level, there is not autocorrelation; rho
# = 0. Data is stationary!
## Create Temporal Regression Model Create Model:
lm1PNAyr <- lm(PNA_Index ~ Year, data = afz_clust2)
summary(lm1PNAyr) # Not a significant relationship.
##
## Call:
## lm(formula = PNA_Index ~ Year, data = afz_clust2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.7557 -0.5256 -0.0609 0.6732 1.8940
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -34.4640 36.6423 -0.94 0.35
## Year 0.0175 0.0184 0.95 0.35
##
## Residual standard error: 1.05 on 32 degrees of freedom
## Multiple R-squared: 0.0275, Adjusted R-squared: -0.00288
## F-statistic: 0.905 on 1 and 32 DF, p-value: 0.349
# Examine/Plot Residuals:
plot(lm1PNAyr$residuals ~ lm1PNAyr$fitted.values, main = "Residuals for Linear Time Model: PNA Index",
xlab = "Fitted Values (PNA Index)", ylab = "Residuals")
abline(0, 0)
qqnorm(lm1PNAyr$residuals)
qqline(lm1PNAyr$residuals)
# Shapiro-Wilk Test:
shapiro.test(lm1PNAyr$residuals) # Null not rejected; only 34 points, but the residuals are just about normally distributed. Time is not a big issue?
##
## Shapiro-Wilk normality test
##
## data: lm1PNAyr$residuals
## W = 0.9558, p-value = 0.1829
# Plot Results:
plot(PNA_Index ~ Year, data = afz_clust2, main = "July PNA Index: 1979 - 2012",
xlab = "Years", ylab = "PNA Index", cex = 0.6)
curve(predict(lm1PNAyr, data.frame(Year = x), type = "resp"), add = TRUE, col = "red",
lwd = 3)
## Run Durbin-Watson Test
library(lmtest)
# Null Hypothesis: rho = 0; there is only random error and no
# autocorrelation
dwtest(lm1PNAyr) # DW = 2.0189, p-value = 0.4479
##
## Durbin-Watson test
##
## data: lm1PNAyr
## DW = 2.019, p-value = 0.4479
## alternative hypothesis: true autocorrelation is greater than 0
# This tells us that at the 0.05 level, there is no autocorrelation; rho =
# 0. Data is stationary!
## Create Temporal Regression Model Create Model:
lm12PNAyr <- lm(PNA_11Lag12Avg ~ Year, data = afz_clust2)
summary(lm12PNAyr) # Not a significant relationship.
##
## Call:
## lm(formula = PNA_11Lag12Avg ~ Year, data = afz_clust2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.5235 -0.2814 -0.0343 0.2079 0.7182
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -7.07882 11.19903 -0.63 0.53
## Year 0.00362 0.00561 0.65 0.52
##
## Residual standard error: 0.321 on 32 degrees of freedom
## Multiple R-squared: 0.0128, Adjusted R-squared: -0.018
## F-statistic: 0.416 on 1 and 32 DF, p-value: 0.523
# Examine/Plot Residuals:
plot(lm1PNAyr$residuals ~ lm1PNAyr$fitted.values, main = "Residuals for Linear Time Model: \n Annual (Aug - Jul) PNA Index",
xlab = "Fitted Values (PNA Index)", ylab = "Residuals")
abline(0, 0)
qqnorm(lm12PNAyr$residuals)
qqline(lm12PNAyr$residuals)
# Shapiro-Wilk Test:
shapiro.test(lm12PNAyr$residuals) # Null not rejected; only 34 points, but the residuals are just about normally distributed. Time is not a big issue?
##
## Shapiro-Wilk normality test
##
## data: lm12PNAyr$residuals
## W = 0.9732, p-value = 0.5549
# Plot Results:
plot(PNA_11Lag12Avg ~ Year, data = afz_clust2, main = "Annual PNA Index (Aug-Jul): 1979 - 2012",
xlab = "Years", ylab = "PNA Index", cex = 0.6)
curve(predict(lm12PNAyr, data.frame(Year = x), type = "resp"), add = TRUE, col = "red",
lwd = 3)
## Run Durbin-Watson Test
library(lmtest)
# Null Hypothesis: rho = 0; there is only random error and no
# autocorrelation
dwtest(lm12PNAyr) # DW = 2.1675, p-value = 0.6209
##
## Durbin-Watson test
##
## data: lm12PNAyr
## DW = 2.167, p-value = 0.6209
## alternative hypothesis: true autocorrelation is greater than 0
# This tells us that at the 0.05 level, there is not autocorrelation; rho
# = 0. Data is stationary!
## Create Temporal Regression Model Create Model:
lm1GTyr <- lm(GlobalJulyTemp ~ Year, data = afz_clust2)
summary(lm1GTyr) # Significant! adj. R^2 = 0.7306
##
## Call:
## lm(formula = GlobalJulyTemp ~ Year, data = afz_clust2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.3810 -0.0788 0.0159 0.0850 0.3381
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -46.49129 4.92628 -9.44 9.2e-11 ***
## Year 0.02349 0.00247 9.51 7.6e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.141 on 32 degrees of freedom
## Multiple R-squared: 0.739, Adjusted R-squared: 0.731
## F-statistic: 90.5 on 1 and 32 DF, p-value: 7.58e-11
# Examine/Plot Residuals:
plot(lm1GTyr$residuals ~ lm1GTyr$fitted.values, main = "Residuals for Linear Time Model: Global Temperature Index",
xlab = "Fitted Values (GT Index)", ylab = "Residuals")
abline(0, 0)
qqnorm(lm1GTyr$residuals)
qqline(lm1GTyr$residuals)
# Shapiro-Wilk Test:
shapiro.test(lm1GTyr$residuals) # Null not rejected; only 34 points, but the residuals are just about normally distributed. Time is not a big issue?
##
## Shapiro-Wilk normality test
##
## data: lm1GTyr$residuals
## W = 0.9768, p-value = 0.668
# Plot Results:
plot(GlobalJulyTemp ~ Year, data = afz_clust2, main = "July Global Temperature Index: 1979 - 2012",
xlab = "Years", ylab = "GT Index", cex = 0.6)
curve(predict(lm1GTyr, data.frame(Year = x), type = "resp"), add = TRUE, col = "red",
lwd = 3)
## Run Durbin-Watson Test
library(lmtest)
# Null Hypothesis: rho = 0; there is only random error and no
# autocorrelation
dwtest(lm1GTyr) # DW = 1.7507, p-value = 0.1775
##
## Durbin-Watson test
##
## data: lm1GTyr
## DW = 1.751, p-value = 0.1775
## alternative hypothesis: true autocorrelation is greater than 0
# This tells us that at the 0.05 level, there is no autocorrelation; rho =
# 0. Data is stationary!
## Create Temporal Regression Model Create Model:
lm12GTyr <- lm(GT_11Lag12Avg ~ Year, data = afz_clust2)
summary(lm12GTyr) # Significant! adj. R^2 = 0.7906
##
## Call:
## lm(formula = GT_11Lag12Avg ~ Year, data = afz_clust2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.26138 -0.09002 0.00935 0.09598 0.19898
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -47.09771 4.24157 -11.1 1.6e-12 ***
## Year 0.02382 0.00213 11.2 1.3e-12 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.122 on 32 degrees of freedom
## Multiple R-squared: 0.797, Adjusted R-squared: 0.791
## F-statistic: 126 on 1 and 32 DF, p-value: 1.3e-12
# Examine/Plot Residuals:
plot(lm1GTyr$residuals ~ lm1GTyr$fitted.values, main = "Residuals for Linear Time Model: \n Annual (Aug - Jul) GT Index",
xlab = "Fitted Values (GT Index)", ylab = "Residuals")
abline(0, 0)
qqnorm(lm12GTyr$residuals)
qqline(lm12GTyr$residuals)
# Shapiro-Wilk Test:
shapiro.test(lm12GTyr$residuals) # Null not rejected; only 34 points, but the residuals are just about normally distributed. Time is not a big issue?
##
## Shapiro-Wilk normality test
##
## data: lm12GTyr$residuals
## W = 0.9687, p-value = 0.4255
# Plot Results:
plot(GT_11Lag12Avg ~ Year, data = afz_clust2, main = "Annual GT Index (Aug-Jul): 1979 - 2012",
xlab = "Years", ylab = "GT Index", cex = 0.6)
curve(predict(lm12GTyr, data.frame(Year = x), type = "resp"), add = TRUE, col = "red",
lwd = 3)
## Run Durbin-Watson Test
library(lmtest)
# Null Hypothesis: rho = 0; there is only random error and no
# autocorrelation
dwtest(lm12GTyr) # DW = 1.5574, p-value = 0.06559
##
## Durbin-Watson test
##
## data: lm12GTyr
## DW = 1.557, p-value = 0.06559
## alternative hypothesis: true autocorrelation is greater than 0
# This tells us that at the 0.05 level, there is not autocorrelation; rho
# = 0. Data is stationary!
After trying some regressions, I realized that my variables are complicated and not entirely intuitive. Results are just straight up weird. So correlation (which is simpler) is probably the better starting point.
## AO -- no significant relationships
cor.test(afz_clust1$TempGrad, afz_clust1$AO_Index) # -0.087
##
## Pearson's product-moment correlation
##
## data: afz_clust1$TempGrad and afz_clust1$AO_Index
## t = -0.4927, df = 32, p-value = 0.6256
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.4128 0.2590
## sample estimates:
## cor
## -0.08676
cor.test(afz_clust1$TempGrad, afz_clust1$AO_3LagAvg) # -0.012
##
## Pearson's product-moment correlation
##
## data: afz_clust1$TempGrad and afz_clust1$AO_3LagAvg
## t = -0.0664, df = 32, p-value = 0.9475
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.3485 0.3277
## sample estimates:
## cor
## -0.01173
cor.test(afz_clust1$TempGrad, afz_clust1$AO_6LagAvg) # -0.115
##
## Pearson's product-moment correlation
##
## data: afz_clust1$TempGrad and afz_clust1$AO_6LagAvg
## t = -0.6566, df = 32, p-value = 0.5161
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.4364 0.2319
## sample estimates:
## cor
## -0.1153
cor.test(afz_clust1$TempGrad, afz_clust1$AO_12LagAvg) # -0.091
##
## Pearson's product-moment correlation
##
## data: afz_clust1$TempGrad and afz_clust1$AO_12LagAvg
## t = -0.515, df = 32, p-value = 0.6101
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.4161 0.2553
## sample estimates:
## cor
## -0.09067
cor.test(afz_clust1$TempGrad, afz_clust1$AO_6Lag3Avg) # -0.131
##
## Pearson's product-moment correlation
##
## data: afz_clust1$TempGrad and afz_clust1$AO_6Lag3Avg
## t = -0.7469, df = 32, p-value = 0.4606
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.4492 0.2169
## sample estimates:
## cor
## -0.1309
cor.test(afz_clust1$TempGrad, afz_clust1$AO_2Lag3Avg) # -0.025
##
## Pearson's product-moment correlation
##
## data: afz_clust1$TempGrad and afz_clust1$AO_2Lag3Avg
## t = -0.1387, df = 32, p-value = 0.8906
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.3597 0.3163
## sample estimates:
## cor
## -0.02451
cor.test(afz_clust1$TempGrad, afz_clust1$AO_5Lag6Avg) # -0.128
##
## Pearson's product-moment correlation
##
## data: afz_clust1$TempGrad and afz_clust1$AO_5Lag6Avg
## t = -0.7291, df = 32, p-value = 0.4713
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.4467 0.2198
## sample estimates:
## cor
## -0.1278
cor.test(afz_clust1$TempGrad, afz_clust1$AO_11Lag12Avg) # -0.100
##
## Pearson's product-moment correlation
##
## data: afz_clust1$TempGrad and afz_clust1$AO_11Lag12Avg
## t = -0.5705, df = 32, p-value = 0.5723
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.4241 0.2462
## sample estimates:
## cor
## -0.1003
## NAO -- No Significant Values
cor.test(afz_clust1$TempGrad, afz_clust1$NAO_Index) # 0.326 -- p=0.0597
##
## Pearson's product-moment correlation
##
## data: afz_clust1$TempGrad and afz_clust1$NAO_Index
## t = 1.952, df = 32, p-value = 0.0597
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.01341 0.59839
## sample estimates:
## cor
## 0.3262
cor.test(afz_clust1$TempGrad, afz_clust1$NAO_3LagAvg) # -0.012
##
## Pearson's product-moment correlation
##
## data: afz_clust1$TempGrad and afz_clust1$NAO_3LagAvg
## t = -0.066, df = 32, p-value = 0.9478
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.3485 0.3278
## sample estimates:
## cor
## -0.01167
cor.test(afz_clust1$TempGrad, afz_clust1$NAO_6LagAvg) # -0.051
##
## Pearson's product-moment correlation
##
## data: afz_clust1$TempGrad and afz_clust1$NAO_6LagAvg
## t = -0.2902, df = 32, p-value = 0.7735
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.3828 0.2920
## sample estimates:
## cor
## -0.05124
cor.test(afz_clust1$TempGrad, afz_clust1$NAO_12LagAvg) # -0.057
##
## Pearson's product-moment correlation
##
## data: afz_clust1$TempGrad and afz_clust1$NAO_12LagAvg
## t = -0.3252, df = 32, p-value = 0.7471
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.3880 0.2863
## sample estimates:
## cor
## -0.0574
cor.test(afz_clust1$TempGrad, afz_clust1$NAO_6Lag3Avg) # -0.067
##
## Pearson's product-moment correlation
##
## data: afz_clust1$TempGrad and afz_clust1$NAO_6Lag3Avg
## t = -0.3804, df = 32, p-value = 0.7062
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.3963 0.2774
## sample estimates:
## cor
## -0.06709
cor.test(afz_clust1$TempGrad, afz_clust1$NAO_2Lag3Avg) # 0.208
##
## Pearson's product-moment correlation
##
## data: afz_clust1$TempGrad and afz_clust1$NAO_2Lag3Avg
## t = 1.201, df = 32, p-value = 0.2385
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.1403 0.5101
## sample estimates:
## cor
## 0.2077
cor.test(afz_clust1$TempGrad, afz_clust1$NAO_5Lag6Avg) # 0.071
##
## Pearson's product-moment correlation
##
## data: afz_clust1$TempGrad and afz_clust1$NAO_5Lag6Avg
## t = 0.4047, df = 32, p-value = 0.6884
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.2734 0.3999
## sample estimates:
## cor
## 0.07136
cor.test(afz_clust1$TempGrad, afz_clust1$NAO_11Lag12Avg) # -0.002
##
## Pearson's product-moment correlation
##
## data: afz_clust1$TempGrad and afz_clust1$NAO_11Lag12Avg
## t = -0.0133, df = 32, p-value = 0.9895
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.3402 0.3361
## sample estimates:
## cor
## -0.002347
## PNA -- Index is significant
cor.test(afz_clust1$TempGrad, afz_clust1$PNA_Index) # 0.359*
##
## Pearson's product-moment correlation
##
## data: afz_clust1$TempGrad and afz_clust1$PNA_Index
## t = 2.173, df = 32, p-value = 0.03731
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.02321 0.62138
## sample estimates:
## cor
## 0.3586
cor.test(afz_clust1$TempGrad, afz_clust1$PNA_3LagAvg) # -0.111
##
## Pearson's product-moment correlation
##
## data: afz_clust1$TempGrad and afz_clust1$PNA_3LagAvg
## t = -0.6296, df = 32, p-value = 0.5334
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.4326 0.2364
## sample estimates:
## cor
## -0.1106
cor.test(afz_clust1$TempGrad, afz_clust1$PNA_6LagAvg) # -0.059
##
## Pearson's product-moment correlation
##
## data: afz_clust1$TempGrad and afz_clust1$PNA_6LagAvg
## t = -0.332, df = 32, p-value = 0.7421
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.3890 0.2852
## sample estimates:
## cor
## -0.05859
cor.test(afz_clust1$TempGrad, afz_clust1$PNA_12LagAvg) # -0.055
##
## Pearson's product-moment correlation
##
## data: afz_clust1$TempGrad and afz_clust1$PNA_12LagAvg
## t = -0.3129, df = 32, p-value = 0.7564
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.3862 0.2883
## sample estimates:
## cor
## -0.05524
cor.test(afz_clust1$TempGrad, afz_clust1$PNA_6Lag3Avg) # 0.008
##
## Pearson's product-moment correlation
##
## data: afz_clust1$TempGrad and afz_clust1$PNA_6Lag3Avg
## t = 0.0466, df = 32, p-value = 0.9632
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.3309 0.3454
## sample estimates:
## cor
## 0.008231
cor.test(afz_clust1$TempGrad, afz_clust1$PNA_2Lag3Avg) # 0.086
##
## Pearson's product-moment correlation
##
## data: afz_clust1$TempGrad and afz_clust1$PNA_2Lag3Avg
## t = 0.4862, df = 32, p-value = 0.6301
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.2601 0.4119
## sample estimates:
## cor
## 0.08563
cor.test(afz_clust1$TempGrad, afz_clust1$PNA_5Lag6Avg) # 0.083
##
## Pearson's product-moment correlation
##
## data: afz_clust1$TempGrad and afz_clust1$PNA_5Lag6Avg
## t = 0.4726, df = 32, p-value = 0.6397
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.2623 0.4099
## sample estimates:
## cor
## 0.08325
cor.test(afz_clust1$TempGrad, afz_clust1$PNA_11Lag12Avg) # -0.004
##
## Pearson's product-moment correlation
##
## data: afz_clust1$TempGrad and afz_clust1$PNA_11Lag12Avg
## t = -0.0218, df = 32, p-value = 0.9827
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.3416 0.3347
## sample estimates:
## cor
## -0.003862
## GT -- no significant values
cor.test(afz_clust1$TempGrad, afz_clust1$GlobalJulyTemp) # 0.104
##
## Pearson's product-moment correlation
##
## data: afz_clust1$TempGrad and afz_clust1$GlobalJulyTemp
## t = 0.5894, df = 32, p-value = 0.5597
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.2431 0.4268
## sample estimates:
## cor
## 0.1036
cor.test(afz_clust1$TempGrad, afz_clust1$GT_3LagAvg) # 0.035
##
## Pearson's product-moment correlation
##
## data: afz_clust1$TempGrad and afz_clust1$GT_3LagAvg
## t = 0.1956, df = 32, p-value = 0.8462
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.3072 0.3684
## sample estimates:
## cor
## 0.03455
cor.test(afz_clust1$TempGrad, afz_clust1$GT_6LagAvg) # 0.123
##
## Pearson's product-moment correlation
##
## data: afz_clust1$TempGrad and afz_clust1$GT_6LagAvg
## t = 0.7039, df = 32, p-value = 0.4866
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.2240 0.4431
## sample estimates:
## cor
## 0.1235
cor.test(afz_clust1$TempGrad, afz_clust1$GT_12LagAvg) # 0.133
##
## Pearson's product-moment correlation
##
## data: afz_clust1$TempGrad and afz_clust1$GT_12LagAvg
## t = 0.7609, df = 32, p-value = 0.4523
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.2145 0.4511
## sample estimates:
## cor
## 0.1333
cor.test(afz_clust1$TempGrad, afz_clust1$GT_6Lag3Avg) # 0.188
##
## Pearson's product-moment correlation
##
## data: afz_clust1$TempGrad and afz_clust1$GT_6Lag3Avg
## t = 1.082, df = 32, p-value = 0.2872
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.1604 0.4947
## sample estimates:
## cor
## 0.1879
cor.test(afz_clust1$TempGrad, afz_clust1$GT_2Lag3Avg) # 0.050
##
## Pearson's product-moment correlation
##
## data: afz_clust1$TempGrad and afz_clust1$GT_2Lag3Avg
## t = 0.283, df = 32, p-value = 0.779
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.2932 0.3817
## sample estimates:
## cor
## 0.04996
cor.test(afz_clust1$TempGrad, afz_clust1$GT_5Lag6Avg) # 0.093
##
## Pearson's product-moment correlation
##
## data: afz_clust1$TempGrad and afz_clust1$GT_5Lag6Avg
## t = 0.529, df = 32, p-value = 0.6005
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.2530 0.4181
## sample estimates:
## cor
## 0.09311
cor.test(afz_clust1$TempGrad, afz_clust1$GT_11Lag12Avg) # 0.142
##
## Pearson's product-moment correlation
##
## data: afz_clust1$TempGrad and afz_clust1$GT_11Lag12Avg
## t = 0.8135, df = 32, p-value = 0.422
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.2057 0.4584
## sample estimates:
## cor
## 0.1423
## AO -- No significant relationships
cor.test(afz_clust2$TempGrad, afz_clust2$AO_Index) # 0.013
##
## Pearson's product-moment correlation
##
## data: afz_clust2$TempGrad and afz_clust2$AO_Index
## t = 0.076, df = 32, p-value = 0.9399
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.3262 0.3500
## sample estimates:
## cor
## 0.01343
cor.test(afz_clust2$TempGrad, afz_clust2$AO_3LagAvg) # 0.157
##
## Pearson's product-moment correlation
##
## data: afz_clust2$TempGrad and afz_clust2$AO_3LagAvg
## t = 0.9011, df = 32, p-value = 0.3743
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.1910 0.4704
## sample estimates:
## cor
## 0.1573
cor.test(afz_clust2$TempGrad, afz_clust2$AO_6LagAvg) # 0.177
##
## Pearson's product-moment correlation
##
## data: afz_clust2$TempGrad and afz_clust2$AO_6LagAvg
## t = 1.017, df = 32, p-value = 0.317
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.1715 0.4860
## sample estimates:
## cor
## 0.1769
cor.test(afz_clust2$TempGrad, afz_clust2$AO_12LagAvg) # 0.145
##
## Pearson's product-moment correlation
##
## data: afz_clust2$TempGrad and afz_clust2$AO_12LagAvg
## t = 0.8271, df = 32, p-value = 0.4143
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.2034 0.4603
## sample estimates:
## cor
## 0.1447
cor.test(afz_clust2$TempGrad, afz_clust2$AO_6Lag3Avg) # 0.146
##
## Pearson's product-moment correlation
##
## data: afz_clust2$TempGrad and afz_clust2$AO_6Lag3Avg
## t = 0.8332, df = 32, p-value = 0.4109
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.2024 0.4612
## sample estimates:
## cor
## 0.1457
cor.test(afz_clust2$TempGrad, afz_clust2$AO_2Lag3Avg) # 0.099
##
## Pearson's product-moment correlation
##
## data: afz_clust2$TempGrad and afz_clust2$AO_2Lag3Avg
## t = 0.5603, df = 32, p-value = 0.5792
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.2479 0.4226
## sample estimates:
## cor
## 0.09857
cor.test(afz_clust2$TempGrad, afz_clust2$AO_5Lag6Avg) # 0.153
##
## Pearson's product-moment correlation
##
## data: afz_clust2$TempGrad and afz_clust2$AO_5Lag6Avg
## t = 0.8743, df = 32, p-value = 0.3885
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.1955 0.4668
## sample estimates:
## cor
## 0.1527
cor.test(afz_clust2$TempGrad, afz_clust2$AO_11Lag12Avg) # 0.149
##
## Pearson's product-moment correlation
##
## data: afz_clust2$TempGrad and afz_clust2$AO_11Lag12Avg
## t = 0.852, df = 32, p-value = 0.4006
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.1993 0.4637
## sample estimates:
## cor
## 0.1489
## NAO -- No Significant Values
cor.test(afz_clust2$TempGrad, afz_clust2$NAO_Index) # 0.107
##
## Pearson's product-moment correlation
##
## data: afz_clust2$TempGrad and afz_clust2$NAO_Index
## t = 0.608, df = 32, p-value = 0.5475
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.2400 0.4295
## sample estimates:
## cor
## 0.1069
cor.test(afz_clust2$TempGrad, afz_clust2$NAO_3LagAvg) # 0.038
##
## Pearson's product-moment correlation
##
## data: afz_clust2$TempGrad and afz_clust2$NAO_3LagAvg
## t = 0.2132, df = 32, p-value = 0.8325
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.3044 0.3711
## sample estimates:
## cor
## 0.03766
cor.test(afz_clust2$TempGrad, afz_clust2$NAO_6LagAvg) # 0.092
##
## Pearson's product-moment correlation
##
## data: afz_clust2$TempGrad and afz_clust2$NAO_6LagAvg
## t = 0.524, df = 32, p-value = 0.6039
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.2538 0.4174
## sample estimates:
## cor
## 0.09224
cor.test(afz_clust2$TempGrad, afz_clust2$NAO_12LagAvg) # -0.023
##
## Pearson's product-moment correlation
##
## data: afz_clust2$TempGrad and afz_clust2$NAO_12LagAvg
## t = -0.1294, df = 32, p-value = 0.8978
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.3583 0.3178
## sample estimates:
## cor
## -0.02287
cor.test(afz_clust2$TempGrad, afz_clust2$NAO_6Lag3Avg) # 0.106
##
## Pearson's product-moment correlation
##
## data: afz_clust2$TempGrad and afz_clust2$NAO_6Lag3Avg
## t = 0.6004, df = 32, p-value = 0.5525
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.2412 0.4284
## sample estimates:
## cor
## 0.1055
cor.test(afz_clust2$TempGrad, afz_clust2$NAO_2Lag3Avg) # 0.012
##
## Pearson's product-moment correlation
##
## data: afz_clust2$TempGrad and afz_clust2$NAO_2Lag3Avg
## t = 0.0675, df = 32, p-value = 0.9466
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.3276 0.3487
## sample estimates:
## cor
## 0.01193
cor.test(afz_clust2$TempGrad, afz_clust2$NAO_5Lag6Avg) # 0.106
##
## Pearson's product-moment correlation
##
## data: afz_clust2$TempGrad and afz_clust2$NAO_5Lag6Avg
## t = 0.6056, df = 32, p-value = 0.549
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.2404 0.4292
## sample estimates:
## cor
## 0.1065
cor.test(afz_clust2$TempGrad, afz_clust2$NAO_11Lag12Avg) # -0.009
##
## Pearson's product-moment correlation
##
## data: afz_clust2$TempGrad and afz_clust2$NAO_11Lag12Avg
## t = -0.0509, df = 32, p-value = 0.9597
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.3461 0.3302
## sample estimates:
## cor
## -0.008994
## PNA -- No significant values
cor.test(afz_clust2$TempGrad, afz_clust2$PNA_Index) # 0.328 -- p=0.05786
##
## Pearson's product-moment correlation
##
## data: afz_clust2$TempGrad and afz_clust2$PNA_Index
## t = 1.967, df = 32, p-value = 0.05786
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.01089 0.60000
## sample estimates:
## cor
## 0.3285
cor.test(afz_clust2$TempGrad, afz_clust2$PNA_3LagAvg) # -0.247
##
## Pearson's product-moment correlation
##
## data: afz_clust2$TempGrad and afz_clust2$PNA_3LagAvg
## t = -1.444, df = 32, p-value = 0.1586
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.5403 0.0992
## sample estimates:
## cor
## -0.2473
cor.test(afz_clust2$TempGrad, afz_clust2$PNA_6LagAvg) # -0.133
##
## Pearson's product-moment correlation
##
## data: afz_clust2$TempGrad and afz_clust2$PNA_6LagAvg
## t = -0.7572, df = 32, p-value = 0.4545
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.4506 0.2151
## sample estimates:
## cor
## -0.1327
cor.test(afz_clust2$TempGrad, afz_clust2$PNA_12LagAvg) # -0.014
##
## Pearson's product-moment correlation
##
## data: afz_clust2$TempGrad and afz_clust2$PNA_12LagAvg
## t = -0.0774, df = 32, p-value = 0.9388
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.3502 0.3260
## sample estimates:
## cor
## -0.01368
cor.test(afz_clust2$TempGrad, afz_clust2$PNA_6Lag3Avg) # 0.016
##
## Pearson's product-moment correlation
##
## data: afz_clust2$TempGrad and afz_clust2$PNA_6Lag3Avg
## t = 0.091, df = 32, p-value = 0.9281
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.3238 0.3523
## sample estimates:
## cor
## 0.01609
cor.test(afz_clust2$TempGrad, afz_clust2$PNA_2Lag3Avg) # 0.038
##
## Pearson's product-moment correlation
##
## data: afz_clust2$TempGrad and afz_clust2$PNA_2Lag3Avg
## t = 0.2165, df = 32, p-value = 0.83
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.3039 0.3716
## sample estimates:
## cor
## 0.03824
cor.test(afz_clust2$TempGrad, afz_clust2$PNA_5Lag6Avg) # -0.019
##
## Pearson's product-moment correlation
##
## data: afz_clust2$TempGrad and afz_clust2$PNA_5Lag6Avg
## t = -0.1069, df = 32, p-value = 0.9155
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.3548 0.3213
## sample estimates:
## cor
## -0.01889
cor.test(afz_clust2$TempGrad, afz_clust2$PNA_11Lag12Avg) # 0.033
##
## Pearson's product-moment correlation
##
## data: afz_clust2$TempGrad and afz_clust2$PNA_11Lag12Avg
## t = 0.1873, df = 32, p-value = 0.8526
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.3085 0.3671
## sample estimates:
## cor
## 0.03308
## GT -- 6LagAvg, 12LagAvg, 6Lag3Avg, 11Lag12Avg
cor.test(afz_clust2$TempGrad, afz_clust2$GlobalJulyTemp) # 0.212
##
## Pearson's product-moment correlation
##
## data: afz_clust2$TempGrad and afz_clust2$GlobalJulyTemp
## t = 1.227, df = 32, p-value = 0.2287
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.1359 0.5134
## sample estimates:
## cor
## 0.212
cor.test(afz_clust2$TempGrad, afz_clust2$GT_3LagAvg) # 0.238
##
## Pearson's product-moment correlation
##
## data: afz_clust2$TempGrad and afz_clust2$GT_3LagAvg
## t = 1.384, df = 32, p-value = 0.1759
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.1093 0.5330
## sample estimates:
## cor
## 0.2377
cor.test(afz_clust2$TempGrad, afz_clust2$GT_6LagAvg) # 0.343*
##
## Pearson's product-moment correlation
##
## data: afz_clust2$TempGrad and afz_clust2$GT_6LagAvg
## t = 2.069, df = 32, p-value = 0.04673
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.005987 0.610694
## sample estimates:
## cor
## 0.3435
cor.test(afz_clust2$TempGrad, afz_clust2$GT_12LagAvg) # 0.363*
##
## Pearson's product-moment correlation
##
## data: afz_clust2$TempGrad and afz_clust2$GT_12LagAvg
## t = 2.202, df = 32, p-value = 0.03501
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.02799 0.62431
## sample estimates:
## cor
## 0.3627
cor.test(afz_clust2$TempGrad, afz_clust2$GT_6Lag3Avg) # 0.401*
##
## Pearson's product-moment correlation
##
## data: afz_clust2$TempGrad and afz_clust2$GT_6Lag3Avg
## t = 2.474, df = 32, p-value = 0.01883
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.07241 0.65074
## sample estimates:
## cor
## 0.4008
cor.test(afz_clust2$TempGrad, afz_clust2$GT_2Lag3Avg) # 0.213
##
## Pearson's product-moment correlation
##
## data: afz_clust2$TempGrad and afz_clust2$GT_2Lag3Avg
## t = 1.231, df = 32, p-value = 0.2272
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.1352 0.5139
## sample estimates:
## cor
## 0.2127
cor.test(afz_clust2$TempGrad, afz_clust2$GT_5Lag6Avg) # 0.294
##
## Pearson's product-moment correlation
##
## data: afz_clust2$TempGrad and afz_clust2$GT_5Lag6Avg
## t = 1.741, df = 32, p-value = 0.09123
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.04882 0.57515
## sample estimates:
## cor
## 0.2942
cor.test(afz_clust2$TempGrad, afz_clust2$GT_11Lag12Avg) # 0.358*
##
## Pearson's product-moment correlation
##
## data: afz_clust2$TempGrad and afz_clust2$GT_11Lag12Avg
## t = 2.167, df = 32, p-value = 0.03776
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.0223 0.6208
## sample estimates:
## cor
## 0.3578
## AO -- no significant relationships
cor.test(afz_clust3$TempGrad, afz_clust3$AO_Index) # 0.007
##
## Pearson's product-moment correlation
##
## data: afz_clust3$TempGrad and afz_clust3$AO_Index
## t = 0.0379, df = 32, p-value = 0.97
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.3322 0.3441
## sample estimates:
## cor
## 0.006691
cor.test(afz_clust3$TempGrad, afz_clust3$AO_3LagAvg) # 0.065
##
## Pearson's product-moment correlation
##
## data: afz_clust3$TempGrad and afz_clust3$AO_3LagAvg
## t = 0.3703, df = 32, p-value = 0.7136
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.2790 0.3948
## sample estimates:
## cor
## 0.06532
cor.test(afz_clust3$TempGrad, afz_clust3$AO_6LagAvg) # -0.012
##
## Pearson's product-moment correlation
##
## data: afz_clust3$TempGrad and afz_clust3$AO_6LagAvg
## t = -0.0665, df = 32, p-value = 0.9474
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.3485 0.3277
## sample estimates:
## cor
## -0.01176
cor.test(afz_clust3$TempGrad, afz_clust3$AO_12LagAvg) # 0.135
##
## Pearson's product-moment correlation
##
## data: afz_clust3$TempGrad and afz_clust3$AO_12LagAvg
## t = 0.7704, df = 32, p-value = 0.4467
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.2129 0.4525
## sample estimates:
## cor
## 0.1349
cor.test(afz_clust3$TempGrad, afz_clust3$AO_6Lag3Avg) # -0.041
##
## Pearson's product-moment correlation
##
## data: afz_clust3$TempGrad and afz_clust3$AO_6Lag3Avg
## t = -0.2333, df = 32, p-value = 0.817
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.3742 0.3012
## sample estimates:
## cor
## -0.0412
cor.test(afz_clust3$TempGrad, afz_clust3$AO_2Lag3Avg) # 0.225
##
## Pearson's product-moment correlation
##
## data: afz_clust3$TempGrad and afz_clust3$AO_2Lag3Avg
## t = 1.307, df = 32, p-value = 0.2006
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.1224 0.5234
## sample estimates:
## cor
## 0.2251
cor.test(afz_clust3$TempGrad, afz_clust3$AO_5Lag6Avg) # -0.066
##
## Pearson's product-moment correlation
##
## data: afz_clust3$TempGrad and afz_clust3$AO_5Lag6Avg
## t = -0.3734, df = 32, p-value = 0.7113
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.3952 0.2785
## sample estimates:
## cor
## -0.06587
cor.test(afz_clust3$TempGrad, afz_clust3$AO_11Lag12Avg) # 0.138
##
## Pearson's product-moment correlation
##
## data: afz_clust3$TempGrad and afz_clust3$AO_11Lag12Avg
## t = 0.7899, df = 32, p-value = 0.4354
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.2097 0.4552
## sample estimates:
## cor
## 0.1383
## NAO -- No Significant Values
cor.test(afz_clust3$TempGrad, afz_clust3$NAO_Index) # 0.267
##
## Pearson's product-moment correlation
##
## data: afz_clust3$TempGrad and afz_clust3$NAO_Index
## t = 1.565, df = 32, p-value = 0.1273
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.07855 0.55482
## sample estimates:
## cor
## 0.2667
cor.test(afz_clust3$TempGrad, afz_clust3$NAO_3LagAvg) # 0.011
##
## Pearson's product-moment correlation
##
## data: afz_clust3$TempGrad and afz_clust3$NAO_3LagAvg
## t = 0.06, df = 32, p-value = 0.9526
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.3287 0.3475
## sample estimates:
## cor
## 0.0106
cor.test(afz_clust3$TempGrad, afz_clust3$NAO_6LagAvg) # 0.007
##
## Pearson's product-moment correlation
##
## data: afz_clust3$TempGrad and afz_clust3$NAO_6LagAvg
## t = 0.0412, df = 32, p-value = 0.9674
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.3317 0.3446
## sample estimates:
## cor
## 0.007288
cor.test(afz_clust3$TempGrad, afz_clust3$NAO_12LagAvg) # 0.162
##
## Pearson's product-moment correlation
##
## data: afz_clust3$TempGrad and afz_clust3$NAO_12LagAvg
## t = 0.9286, df = 32, p-value = 0.36
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.1864 0.4742
## sample estimates:
## cor
## 0.162
cor.test(afz_clust3$TempGrad, afz_clust3$NAO_6Lag3Avg) # 0.001
##
## Pearson's product-moment correlation
##
## data: afz_clust3$TempGrad and afz_clust3$NAO_6Lag3Avg
## t = 0.0074, df = 32, p-value = 0.9941
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.3370 0.3393
## sample estimates:
## cor
## 0.001312
cor.test(afz_clust3$TempGrad, afz_clust3$NAO_2Lag3Avg) # 0.145
##
## Pearson's product-moment correlation
##
## data: afz_clust3$TempGrad and afz_clust3$NAO_2Lag3Avg
## t = 0.8279, df = 32, p-value = 0.4138
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.2033 0.4604
## sample estimates:
## cor
## 0.1448
cor.test(afz_clust3$TempGrad, afz_clust3$NAO_5Lag6Avg) # 0.035
##
## Pearson's product-moment correlation
##
## data: afz_clust3$TempGrad and afz_clust3$NAO_5Lag6Avg
## t = 0.1992, df = 32, p-value = 0.8434
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.3066 0.3690
## sample estimates:
## cor
## 0.0352
cor.test(afz_clust3$TempGrad, afz_clust3$NAO_11Lag12Avg) # 0.190
##
## Pearson's product-moment correlation
##
## data: afz_clust3$TempGrad and afz_clust3$NAO_11Lag12Avg
## t = 1.094, df = 32, p-value = 0.2822
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.1585 0.4962
## sample estimates:
## cor
## 0.1898
## PNA -- No significant values
cor.test(afz_clust3$TempGrad, afz_clust3$PNA_Index) # 0.257
##
## Pearson's product-moment correlation
##
## data: afz_clust3$TempGrad and afz_clust3$PNA_Index
## t = 1.504, df = 32, p-value = 0.1423
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.08889 0.54758
## sample estimates:
## cor
## 0.257
cor.test(afz_clust3$TempGrad, afz_clust3$PNA_3LagAvg) # -0.154
##
## Pearson's product-moment correlation
##
## data: afz_clust3$TempGrad and afz_clust3$PNA_3LagAvg
## t = -0.8807, df = 32, p-value = 0.3851
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.4677 0.1945
## sample estimates:
## cor
## -0.1538
cor.test(afz_clust3$TempGrad, afz_clust3$PNA_6LagAvg) # -0.214
##
## Pearson's product-moment correlation
##
## data: afz_clust3$TempGrad and afz_clust3$PNA_6LagAvg
## t = -1.237, df = 32, p-value = 0.225
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.5147 0.1342
## sample estimates:
## cor
## -0.2137
cor.test(afz_clust3$TempGrad, afz_clust3$PNA_12LagAvg) # -0.093
##
## Pearson's product-moment correlation
##
## data: afz_clust3$TempGrad and afz_clust3$PNA_12LagAvg
## t = -0.527, df = 32, p-value = 0.6019
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.4178 0.2534
## sample estimates:
## cor
## -0.09275
cor.test(afz_clust3$TempGrad, afz_clust3$PNA_6Lag3Avg) # -0.201
##
## Pearson's product-moment correlation
##
## data: afz_clust3$TempGrad and afz_clust3$PNA_6Lag3Avg
## t = -1.163, df = 32, p-value = 0.2535
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.5051 0.1468
## sample estimates:
## cor
## -0.2014
cor.test(afz_clust3$TempGrad, afz_clust3$PNA_2Lag3Avg) # -0.107
##
## Pearson's product-moment correlation
##
## data: afz_clust3$TempGrad and afz_clust3$PNA_2Lag3Avg
## t = -0.6071, df = 32, p-value = 0.5481
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.4294 0.2401
## sample estimates:
## cor
## -0.1067
cor.test(afz_clust3$TempGrad, afz_clust3$PNA_5Lag6Avg) # -0.048
##
## Pearson's product-moment correlation
##
## data: afz_clust3$TempGrad and afz_clust3$PNA_5Lag6Avg
## t = -0.2714, df = 32, p-value = 0.7878
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.3799 0.2950
## sample estimates:
## cor
## -0.04793
cor.test(afz_clust3$TempGrad, afz_clust3$PNA_11Lag12Avg) # -0.048
##
## Pearson's product-moment correlation
##
## data: afz_clust3$TempGrad and afz_clust3$PNA_11Lag12Avg
## t = -0.272, df = 32, p-value = 0.7874
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.3800 0.2949
## sample estimates:
## cor
## -0.04803
## GT -- no significant values
cor.test(afz_clust3$TempGrad, afz_clust3$GlobalJulyTemp) # 0.084
##
## Pearson's product-moment correlation
##
## data: afz_clust3$TempGrad and afz_clust3$GlobalJulyTemp
## t = 0.4741, df = 32, p-value = 0.6386
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.2620 0.4101
## sample estimates:
## cor
## 0.08352
cor.test(afz_clust3$TempGrad, afz_clust3$GT_3LagAvg) # 0.038
##
## Pearson's product-moment correlation
##
## data: afz_clust3$TempGrad and afz_clust3$GT_3LagAvg
## t = 0.2125, df = 32, p-value = 0.8331
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.3045 0.3710
## sample estimates:
## cor
## 0.03753
cor.test(afz_clust3$TempGrad, afz_clust3$GT_6LagAvg) # 0.101
##
## Pearson's product-moment correlation
##
## data: afz_clust3$TempGrad and afz_clust3$GT_6LagAvg
## t = 0.5761, df = 32, p-value = 0.5686
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.2453 0.4249
## sample estimates:
## cor
## 0.1013
cor.test(afz_clust3$TempGrad, afz_clust3$GT_12LagAvg) # 0.181
##
## Pearson's product-moment correlation
##
## data: afz_clust3$TempGrad and afz_clust3$GT_12LagAvg
## t = 1.043, df = 32, p-value = 0.3048
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.1671 0.4895
## sample estimates:
## cor
## 0.1813
cor.test(afz_clust3$TempGrad, afz_clust3$GT_6Lag3Avg) # 0.145
##
## Pearson's product-moment correlation
##
## data: afz_clust3$TempGrad and afz_clust3$GT_6Lag3Avg
## t = 0.8317, df = 32, p-value = 0.4117
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.2027 0.4610
## sample estimates:
## cor
## 0.1455
cor.test(afz_clust3$TempGrad, afz_clust3$GT_2Lag3Avg) # 0.078
##
## Pearson's product-moment correlation
##
## data: afz_clust3$TempGrad and afz_clust3$GT_2Lag3Avg
## t = 0.4402, df = 32, p-value = 0.6628
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.2676 0.4051
## sample estimates:
## cor
## 0.07758
cor.test(afz_clust3$TempGrad, afz_clust3$GT_5Lag6Avg) # 0.091
##
## Pearson's product-moment correlation
##
## data: afz_clust3$TempGrad and afz_clust3$GT_5Lag6Avg
## t = 0.5157, df = 32, p-value = 0.6096
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.2552 0.4162
## sample estimates:
## cor
## 0.09079
cor.test(afz_clust3$TempGrad, afz_clust3$GT_11Lag12Avg) # 0.180
##
## Pearson's product-moment correlation
##
## data: afz_clust3$TempGrad and afz_clust3$GT_11Lag12Avg
## t = 1.034, df = 32, p-value = 0.3087
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.1685 0.4883
## sample estimates:
## cor
## 0.1799
## AO -- no significant relationships
cor.test(afz_clust4$TempGrad, afz_clust4$AO_Index) # 0.038
##
## Pearson's product-moment correlation
##
## data: afz_clust4$TempGrad and afz_clust4$AO_Index
## t = 0.2175, df = 32, p-value = 0.8292
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.3037 0.3718
## sample estimates:
## cor
## 0.03841
cor.test(afz_clust4$TempGrad, afz_clust4$AO_3LagAvg) # 0.263
##
## Pearson's product-moment correlation
##
## data: afz_clust4$TempGrad and afz_clust4$AO_3LagAvg
## t = 1.539, df = 32, p-value = 0.1335
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.08296 0.55175
## sample estimates:
## cor
## 0.2626
cor.test(afz_clust4$TempGrad, afz_clust4$AO_6LagAvg) # -0.129
##
## Pearson's product-moment correlation
##
## data: afz_clust4$TempGrad and afz_clust4$AO_6LagAvg
## t = -0.7362, df = 32, p-value = 0.4669
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.4477 0.2186
## sample estimates:
## cor
## -0.1291
cor.test(afz_clust4$TempGrad, afz_clust4$AO_12LagAvg) # -0.119
##
## Pearson's product-moment correlation
##
## data: afz_clust4$TempGrad and afz_clust4$AO_12LagAvg
## t = -0.6805, df = 32, p-value = 0.5011
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.4398 0.2279
## sample estimates:
## cor
## -0.1194
cor.test(afz_clust4$TempGrad, afz_clust4$AO_6Lag3Avg) # -0.255
##
## Pearson's product-moment correlation
##
## data: afz_clust4$TempGrad and afz_clust4$AO_6Lag3Avg
## t = -1.49, df = 32, p-value = 0.1459
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.54590 0.09126
## sample estimates:
## cor
## -0.2548
cor.test(afz_clust4$TempGrad, afz_clust4$AO_2Lag3Avg) # 0.228
##
## Pearson's product-moment correlation
##
## data: afz_clust4$TempGrad and afz_clust4$AO_2Lag3Avg
## t = 1.323, df = 32, p-value = 0.1953
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.1197 0.5254
## sample estimates:
## cor
## 0.2277
cor.test(afz_clust4$TempGrad, afz_clust4$AO_5Lag6Avg) # -0.109
##
## Pearson's product-moment correlation
##
## data: afz_clust4$TempGrad and afz_clust4$AO_5Lag6Avg
## t = -0.6193, df = 32, p-value = 0.5401
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.4311 0.2381
## sample estimates:
## cor
## -0.1088
cor.test(afz_clust4$TempGrad, afz_clust4$AO_11Lag12Avg) # -0.113
##
## Pearson's product-moment correlation
##
## data: afz_clust4$TempGrad and afz_clust4$AO_11Lag12Avg
## t = -0.6413, df = 32, p-value = 0.5259
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.4343 0.2345
## sample estimates:
## cor
## -0.1126
## NAO -- No Significant Values
cor.test(afz_clust4$TempGrad, afz_clust4$NAO_Index) # 0.142
##
## Pearson's product-moment correlation
##
## data: afz_clust4$TempGrad and afz_clust4$NAO_Index
## t = 0.8144, df = 32, p-value = 0.4214
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.2056 0.4586
## sample estimates:
## cor
## 0.1425
cor.test(afz_clust4$TempGrad, afz_clust4$NAO_3LagAvg) # -0.055
##
## Pearson's product-moment correlation
##
## data: afz_clust4$TempGrad and afz_clust4$NAO_3LagAvg
## t = -0.3107, df = 32, p-value = 0.7581
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.3858 0.2887
## sample estimates:
## cor
## -0.05484
cor.test(afz_clust4$TempGrad, afz_clust4$NAO_6LagAvg) # -0.126
##
## Pearson's product-moment correlation
##
## data: afz_clust4$TempGrad and afz_clust4$NAO_6LagAvg
## t = -0.7196, df = 32, p-value = 0.477
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.4454 0.2214
## sample estimates:
## cor
## -0.1262
cor.test(afz_clust4$TempGrad, afz_clust4$NAO_12LagAvg) # -0.110
##
## Pearson's product-moment correlation
##
## data: afz_clust4$TempGrad and afz_clust4$NAO_12LagAvg
## t = -0.624, df = 32, p-value = 0.537
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.4318 0.2373
## sample estimates:
## cor
## -0.1096
cor.test(afz_clust4$TempGrad, afz_clust4$NAO_6Lag3Avg) # -0.139
##
## Pearson's product-moment correlation
##
## data: afz_clust4$TempGrad and afz_clust4$NAO_6Lag3Avg
## t = -0.7925, df = 32, p-value = 0.4339
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.4555 0.2092
## sample estimates:
## cor
## -0.1387
cor.test(afz_clust4$TempGrad, afz_clust4$NAO_2Lag3Avg) # 0.068
##
## Pearson's product-moment correlation
##
## data: afz_clust4$TempGrad and afz_clust4$NAO_2Lag3Avg
## t = 0.3832, df = 32, p-value = 0.7041
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.2769 0.3967
## sample estimates:
## cor
## 0.06758
cor.test(afz_clust4$TempGrad, afz_clust4$NAO_5Lag6Avg) # -0.141
##
## Pearson's product-moment correlation
##
## data: afz_clust4$TempGrad and afz_clust4$NAO_5Lag6Avg
## t = -0.8057, df = 32, p-value = 0.4263
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.4574 0.2070
## sample estimates:
## cor
## -0.141
cor.test(afz_clust4$TempGrad, afz_clust4$NAO_11Lag12Avg) # -0.082
##
## Pearson's product-moment correlation
##
## data: afz_clust4$TempGrad and afz_clust4$NAO_11Lag12Avg
## t = -0.4645, df = 32, p-value = 0.6454
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.4087 0.2636
## sample estimates:
## cor
## -0.08184
## PNA -- Nothing sigificant
cor.test(afz_clust4$TempGrad, afz_clust4$PNA_Index) # 0.046
##
## Pearson's product-moment correlation
##
## data: afz_clust4$TempGrad and afz_clust4$PNA_Index
## t = 0.2595, df = 32, p-value = 0.7969
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.2969 0.3781
## sample estimates:
## cor
## 0.04582
cor.test(afz_clust4$TempGrad, afz_clust4$PNA_3LagAvg) # -0.265
##
## Pearson's product-moment correlation
##
## data: afz_clust4$TempGrad and afz_clust4$PNA_3LagAvg
## t = -1.552, df = 32, p-value = 0.1305
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.55325 0.08081
## sample estimates:
## cor
## -0.2646
cor.test(afz_clust4$TempGrad, afz_clust4$PNA_6LagAvg) # -0.101
##
## Pearson's product-moment correlation
##
## data: afz_clust4$TempGrad and afz_clust4$PNA_6LagAvg
## t = -0.5744, df = 32, p-value = 0.5697
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.4247 0.2455
## sample estimates:
## cor
## -0.101
cor.test(afz_clust4$TempGrad, afz_clust4$PNA_12LagAvg) # -0.112
##
## Pearson's product-moment correlation
##
## data: afz_clust4$TempGrad and afz_clust4$PNA_12LagAvg
## t = -0.6392, df = 32, p-value = 0.5272
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.4340 0.2348
## sample estimates:
## cor
## -0.1123
cor.test(afz_clust4$TempGrad, afz_clust4$PNA_6Lag3Avg) # 0.083
##
## Pearson's product-moment correlation
##
## data: afz_clust4$TempGrad and afz_clust4$PNA_6Lag3Avg
## t = 0.4683, df = 32, p-value = 0.6427
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.2630 0.4093
## sample estimates:
## cor
## 0.08251
cor.test(afz_clust4$TempGrad, afz_clust4$PNA_2Lag3Avg) # -0.305 -- p=0.079
##
## Pearson's product-moment correlation
##
## data: afz_clust4$TempGrad and afz_clust4$PNA_2Lag3Avg
## t = -1.813, df = 32, p-value = 0.07914
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.58324 0.03667
## sample estimates:
## cor
## -0.3053
cor.test(afz_clust4$TempGrad, afz_clust4$PNA_5Lag6Avg) # -0.145
##
## Pearson's product-moment correlation
##
## data: afz_clust4$TempGrad and afz_clust4$PNA_5Lag6Avg
## t = -0.8298, df = 32, p-value = 0.4128
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.4607 0.2030
## sample estimates:
## cor
## -0.1451
cor.test(afz_clust4$TempGrad, afz_clust4$PNA_11Lag12Avg) # -0.081
##
## Pearson's product-moment correlation
##
## data: afz_clust4$TempGrad and afz_clust4$PNA_11Lag12Avg
## t = -0.4609, df = 32, p-value = 0.648
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.4082 0.2642
## sample estimates:
## cor
## -0.0812
## GT -- All significant except the 6LagAvg
cor.test(afz_clust4$TempGrad, afz_clust4$GlobalJulyTemp) # 0.408*
##
## Pearson's product-moment correlation
##
## data: afz_clust4$TempGrad and afz_clust4$GlobalJulyTemp
## t = 2.527, df = 32, p-value = 0.01664
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.08085 0.65561
## sample estimates:
## cor
## 0.4079
cor.test(afz_clust4$TempGrad, afz_clust4$GT_3LagAvg) # 0.347*
##
## Pearson's product-moment correlation
##
## data: afz_clust4$TempGrad and afz_clust4$GT_3LagAvg
## t = 2.096, df = 32, p-value = 0.0441
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.01048 0.61350
## sample estimates:
## cor
## 0.3474
cor.test(afz_clust4$TempGrad, afz_clust4$GT_6LagAvg) # 0.333 -- p=0.054
##
## Pearson's product-moment correlation
##
## data: afz_clust4$TempGrad and afz_clust4$GT_6LagAvg
## t = 2, df = 32, p-value = 0.05401
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.005387 0.603512
## sample estimates:
## cor
## 0.3334
cor.test(afz_clust4$TempGrad, afz_clust4$GT_12LagAvg) # 0.378*
##
## Pearson's product-moment correlation
##
## data: afz_clust4$TempGrad and afz_clust4$GT_12LagAvg
## t = 2.308, df = 32, p-value = 0.02758
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.04549 0.63489
## sample estimates:
## cor
## 0.3778
cor.test(afz_clust4$TempGrad, afz_clust4$GT_6Lag3Avg) # 0.290
##
## Pearson's product-moment correlation
##
## data: afz_clust4$TempGrad and afz_clust4$GT_6Lag3Avg
## t = 1.716, df = 32, p-value = 0.09584
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.0531 0.5723
## sample estimates:
## cor
## 0.2903
cor.test(afz_clust4$TempGrad, afz_clust4$GT_2Lag3Avg) # 0.415*
##
## Pearson's product-moment correlation
##
## data: afz_clust4$TempGrad and afz_clust4$GT_2Lag3Avg
## t = 2.58, df = 32, p-value = 0.01467
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.08935 0.66046
## sample estimates:
## cor
## 0.415
cor.test(afz_clust4$TempGrad, afz_clust4$GT_5Lag6Avg) # 0.342*
##
## Pearson's product-moment correlation
##
## data: afz_clust4$TempGrad and afz_clust4$GT_5Lag6Avg
## t = 2.061, df = 32, p-value = 0.04751
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.004692 0.609881
## sample estimates:
## cor
## 0.3423
cor.test(afz_clust4$TempGrad, afz_clust4$GT_11Lag12Avg) # 0.383*
##
## Pearson's product-moment correlation
##
## data: afz_clust4$TempGrad and afz_clust4$GT_11Lag12Avg
## t = 2.349, df = 32, p-value = 0.02517
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.05205 0.63880
## sample estimates:
## cor
## 0.3835
## AO -- no significant relationships
cor.test(afz_clust5$TempGrad, afz_clust5$AO_Index) # -0.038
##
## Pearson's product-moment correlation
##
## data: afz_clust5$TempGrad and afz_clust5$AO_Index
## t = -0.2159, df = 32, p-value = 0.8305
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.3715 0.3040
## sample estimates:
## cor
## -0.03813
cor.test(afz_clust5$TempGrad, afz_clust5$AO_3LagAvg) # 0.022
##
## Pearson's product-moment correlation
##
## data: afz_clust5$TempGrad and afz_clust5$AO_3LagAvg
## t = 0.1256, df = 32, p-value = 0.9008
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.3184 0.3577
## sample estimates:
## cor
## 0.02219
cor.test(afz_clust5$TempGrad, afz_clust5$AO_6LagAvg) # 0.007
##
## Pearson's product-moment correlation
##
## data: afz_clust5$TempGrad and afz_clust5$AO_6LagAvg
## t = 0.0413, df = 32, p-value = 0.9673
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.3317 0.3446
## sample estimates:
## cor
## 0.007293
cor.test(afz_clust5$TempGrad, afz_clust5$AO_12LagAvg) # -0.140
##
## Pearson's product-moment correlation
##
## data: afz_clust5$TempGrad and afz_clust5$AO_12LagAvg
## t = -0.8026, df = 32, p-value = 0.4281
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.4569 0.2075
## sample estimates:
## cor
## -0.1405
cor.test(afz_clust5$TempGrad, afz_clust5$AO_6Lag3Avg) # 0.000
##
## Pearson's product-moment correlation
##
## data: afz_clust5$TempGrad and afz_clust5$AO_6Lag3Avg
## t = 0.0019, df = 32, p-value = 0.9985
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.3379 0.3385
## sample estimates:
## cor
## 0.0003282
cor.test(afz_clust5$TempGrad, afz_clust5$AO_2Lag3Avg) # -0.203
##
## Pearson's product-moment correlation
##
## data: afz_clust5$TempGrad and afz_clust5$AO_2Lag3Avg
## t = -1.174, df = 32, p-value = 0.249
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.5066 0.1449
## sample estimates:
## cor
## -0.2032
cor.test(afz_clust5$TempGrad, afz_clust5$AO_5Lag6Avg) # -0.0286
##
## Pearson's product-moment correlation
##
## data: afz_clust5$TempGrad and afz_clust5$AO_5Lag6Avg
## t = -0.162, df = 32, p-value = 0.8723
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.3633 0.3126
## sample estimates:
## cor
## -0.02863
cor.test(afz_clust5$TempGrad, afz_clust5$AO_11Lag12Avg) # -0.144
##
## Pearson's product-moment correlation
##
## data: afz_clust5$TempGrad and afz_clust5$AO_11Lag12Avg
## t = -0.8224, df = 32, p-value = 0.4169
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.4597 0.2042
## sample estimates:
## cor
## -0.1439
## NAO -- No Significant Values
cor.test(afz_clust5$TempGrad, afz_clust5$NAO_Index) # -0.146
##
## Pearson's product-moment correlation
##
## data: afz_clust5$TempGrad and afz_clust5$NAO_Index
## t = -0.8331, df = 32, p-value = 0.4109
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.4612 0.2024
## sample estimates:
## cor
## -0.1457
cor.test(afz_clust5$TempGrad, afz_clust5$NAO_3LagAvg) # -0.134
##
## Pearson's product-moment correlation
##
## data: afz_clust5$TempGrad and afz_clust5$NAO_3LagAvg
## t = -0.7655, df = 32, p-value = 0.4496
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.4518 0.2138
## sample estimates:
## cor
## -0.1341
cor.test(afz_clust5$TempGrad, afz_clust5$NAO_6LagAvg) # -0.105
##
## Pearson's product-moment correlation
##
## data: afz_clust5$TempGrad and afz_clust5$NAO_6LagAvg
## t = -0.5997, df = 32, p-value = 0.5529
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.4283 0.2413
## sample estimates:
## cor
## -0.1054
cor.test(afz_clust5$TempGrad, afz_clust5$NAO_12LagAvg) # -0.313
##
## Pearson's product-moment correlation
##
## data: afz_clust5$TempGrad and afz_clust5$NAO_12LagAvg
## t = -1.863, df = 32, p-value = 0.07163
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.58873 0.02831
## sample estimates:
## cor
## -0.3128
cor.test(afz_clust5$TempGrad, afz_clust5$NAO_6Lag3Avg) # -0.026
##
## Pearson's product-moment correlation
##
## data: afz_clust5$TempGrad and afz_clust5$NAO_6Lag3Avg
## t = -0.1479, df = 32, p-value = 0.8833
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.3611 0.3148
## sample estimates:
## cor
## -0.02615
cor.test(afz_clust5$TempGrad, afz_clust5$NAO_2Lag3Avg) # -0.177
##
## Pearson's product-moment correlation
##
## data: afz_clust5$TempGrad and afz_clust5$NAO_2Lag3Avg
## t = -1.02, df = 32, p-value = 0.3154
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.4864 0.1710
## sample estimates:
## cor
## -0.1774
cor.test(afz_clust5$TempGrad, afz_clust5$NAO_5Lag6Avg) # -0.181
##
## Pearson's product-moment correlation
##
## data: afz_clust5$TempGrad and afz_clust5$NAO_5Lag6Avg
## t = -1.039, df = 32, p-value = 0.3066
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.4889 0.1678
## sample estimates:
## cor
## -0.1807
cor.test(afz_clust5$TempGrad, afz_clust5$NAO_11Lag12Avg) # -0.327 - p=0.05911
##
## Pearson's product-moment correlation
##
## data: afz_clust5$TempGrad and afz_clust5$NAO_11Lag12Avg
## t = -1.957, df = 32, p-value = 0.05911
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.59890 0.01261
## sample estimates:
## cor
## -0.327
## PNA -- Nothing is significant
cor.test(afz_clust5$TempGrad, afz_clust5$PNA_Index) # 0.294
##
## Pearson's product-moment correlation
##
## data: afz_clust5$TempGrad and afz_clust5$PNA_Index
## t = 1.742, df = 32, p-value = 0.09104
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.04864 0.57527
## sample estimates:
## cor
## 0.2944
cor.test(afz_clust5$TempGrad, afz_clust5$PNA_3LagAvg) # -0.032
##
## Pearson's product-moment correlation
##
## data: afz_clust5$TempGrad and afz_clust5$PNA_3LagAvg
## t = -0.182, df = 32, p-value = 0.8568
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.3663 0.3094
## sample estimates:
## cor
## -0.03215
cor.test(afz_clust5$TempGrad, afz_clust5$PNA_6LagAvg) # 0.126
##
## Pearson's product-moment correlation
##
## data: afz_clust5$TempGrad and afz_clust5$PNA_6LagAvg
## t = 0.7181, df = 32, p-value = 0.4779
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.2217 0.4451
## sample estimates:
## cor
## 0.1259
cor.test(afz_clust5$TempGrad, afz_clust5$PNA_12LagAvg) # 0.006
##
## Pearson's product-moment correlation
##
## data: afz_clust5$TempGrad and afz_clust5$PNA_12LagAvg
## t = 0.0337, df = 32, p-value = 0.9733
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.3329 0.3434
## sample estimates:
## cor
## 0.005963
cor.test(afz_clust5$TempGrad, afz_clust5$PNA_6Lag3Avg) # 0.232
##
## Pearson's product-moment correlation
##
## data: afz_clust5$TempGrad and afz_clust5$PNA_6Lag3Avg
## t = 1.351, df = 32, p-value = 0.1861
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.1149 0.5289
## sample estimates:
## cor
## 0.2323
cor.test(afz_clust5$TempGrad, afz_clust5$PNA_2Lag3Avg) # 0.171
##
## Pearson's product-moment correlation
##
## data: afz_clust5$TempGrad and afz_clust5$PNA_2Lag3Avg
## t = 0.9841, df = 32, p-value = 0.3325
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.1770 0.4816
## sample estimates:
## cor
## 0.1714
cor.test(afz_clust5$TempGrad, afz_clust5$PNA_5Lag6Avg) # 0.137
##
## Pearson's product-moment correlation
##
## data: afz_clust5$TempGrad and afz_clust5$PNA_5Lag6Avg
## t = 0.7819, df = 32, p-value = 0.44
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.2110 0.4541
## sample estimates:
## cor
## 0.1369
cor.test(afz_clust5$TempGrad, afz_clust5$PNA_11Lag12Avg) # 0.070
##
## Pearson's product-moment correlation
##
## data: afz_clust5$TempGrad and afz_clust5$PNA_11Lag12Avg
## t = 0.3964, df = 32, p-value = 0.6944
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.2748 0.3986
## sample estimates:
## cor
## 0.06991
## GT -- All significant
cor.test(afz_clust5$TempGrad, afz_clust5$GlobalJulyTemp) # 0.552*
##
## Pearson's product-moment correlation
##
## data: afz_clust5$TempGrad and afz_clust5$GlobalJulyTemp
## t = 3.744, df = 32, p-value = 0.0007158
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.2627 0.7501
## sample estimates:
## cor
## 0.5519
cor.test(afz_clust5$TempGrad, afz_clust5$GT_3LagAvg) # 0.520*
##
## Pearson's product-moment correlation
##
## data: afz_clust5$TempGrad and afz_clust5$GT_3LagAvg
## t = 3.446, df = 32, p-value = 0.001611
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.221 0.730
## sample estimates:
## cor
## 0.5202
cor.test(afz_clust5$TempGrad, afz_clust5$GT_6LagAvg) # 0.504*
##
## Pearson's product-moment correlation
##
## data: afz_clust5$TempGrad and afz_clust5$GT_6LagAvg
## t = 3.302, df = 32, p-value = 0.002365
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.2001 0.7196
## sample estimates:
## cor
## 0.5041
cor.test(afz_clust5$TempGrad, afz_clust5$GT_12LagAvg) # 0.433*
##
## Pearson's product-moment correlation
##
## data: afz_clust5$TempGrad and afz_clust5$GT_12LagAvg
## t = 2.718, df = 32, p-value = 0.01052
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.1111 0.6727
## sample estimates:
## cor
## 0.433
cor.test(afz_clust5$TempGrad, afz_clust5$GT_6Lag3Avg) # 0.445*
##
## Pearson's product-moment correlation
##
## data: afz_clust5$TempGrad and afz_clust5$GT_6Lag3Avg
## t = 2.81, df = 32, p-value = 0.008373
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.1257 0.6807
## sample estimates:
## cor
## 0.4449
cor.test(afz_clust5$TempGrad, afz_clust5$GT_2Lag3Avg) # 0.525*
##
## Pearson's product-moment correlation
##
## data: afz_clust5$TempGrad and afz_clust5$GT_2Lag3Avg
## t = 3.485, df = 32, p-value = 0.00145
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.2266 0.7327
## sample estimates:
## cor
## 0.5245
cor.test(afz_clust5$TempGrad, afz_clust5$GT_5Lag6Avg) # 0.509*
##
## Pearson's product-moment correlation
##
## data: afz_clust5$TempGrad and afz_clust5$GT_5Lag6Avg
## t = 3.349, df = 32, p-value = 0.002092
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.2069 0.7230
## sample estimates:
## cor
## 0.5094
cor.test(afz_clust5$TempGrad, afz_clust5$GT_11Lag12Avg) # 0.448*
##
## Pearson's product-moment correlation
##
## data: afz_clust5$TempGrad and afz_clust5$GT_11Lag12Avg
## t = 2.835, df = 32, p-value = 0.007884
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.1294 0.6827
## sample estimates:
## cor
## 0.448
## AO -- no significant relationships
cor.test(afz_clust6$TempGrad, afz_clust6$AO_Index) # -0.075
##
## Pearson's product-moment correlation
##
## data: afz_clust6$TempGrad and afz_clust6$AO_Index
## t = -0.4269, df = 32, p-value = 0.6723
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.4032 0.2698
## sample estimates:
## cor
## -0.07525
cor.test(afz_clust6$TempGrad, afz_clust6$AO_3LagAvg) # -0.019
##
## Pearson's product-moment correlation
##
## data: afz_clust6$TempGrad and afz_clust6$AO_3LagAvg
## t = -0.1065, df = 32, p-value = 0.9158
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.3547 0.3214
## sample estimates:
## cor
## -0.01882
cor.test(afz_clust6$TempGrad, afz_clust6$AO_6LagAvg) # -0.161
##
## Pearson's product-moment correlation
##
## data: afz_clust6$TempGrad and afz_clust6$AO_6LagAvg
## t = -0.9249, df = 32, p-value = 0.3619
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.4737 0.1870
## sample estimates:
## cor
## -0.1614
cor.test(afz_clust6$TempGrad, afz_clust6$AO_12LagAvg) # -0.246
##
## Pearson's product-moment correlation
##
## data: afz_clust6$TempGrad and afz_clust6$AO_12LagAvg
## t = -1.435, df = 32, p-value = 0.161
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.5392 0.1007
## sample estimates:
## cor
## -0.2459
cor.test(afz_clust6$TempGrad, afz_clust6$AO_6Lag3Avg) # -0.179
##
## Pearson's product-moment correlation
##
## data: afz_clust6$TempGrad and afz_clust6$AO_6Lag3Avg
## t = -1.032, df = 32, p-value = 0.3099
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.488 0.169
## sample estimates:
## cor
## -0.1794
cor.test(afz_clust6$TempGrad, afz_clust6$AO_2Lag3Avg) # -0.216
##
## Pearson's product-moment correlation
##
## data: afz_clust6$TempGrad and afz_clust6$AO_2Lag3Avg
## t = -1.252, df = 32, p-value = 0.2196
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.5165 0.1317
## sample estimates:
## cor
## -0.2161
cor.test(afz_clust6$TempGrad, afz_clust6$AO_5Lag6Avg) # -0.159
##
## Pearson's product-moment correlation
##
## data: afz_clust6$TempGrad and afz_clust6$AO_5Lag6Avg
## t = -0.9112, df = 32, p-value = 0.369
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.4718 0.1893
## sample estimates:
## cor
## -0.159
cor.test(afz_clust6$TempGrad, afz_clust6$AO_11Lag12Avg) # -0.263
##
## Pearson's product-moment correlation
##
## data: afz_clust6$TempGrad and afz_clust6$AO_11Lag12Avg
## t = -1.541, df = 32, p-value = 0.1332
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.5519 0.0827
## sample estimates:
## cor
## -0.2628
## NAO -- No Significant Values
cor.test(afz_clust6$TempGrad, afz_clust6$NAO_Index) # 0.056
##
## Pearson's product-moment correlation
##
## data: afz_clust6$TempGrad and afz_clust6$NAO_Index
## t = 0.3163, df = 32, p-value = 0.7538
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.2878 0.3867
## sample estimates:
## cor
## 0.05583
cor.test(afz_clust6$TempGrad, afz_clust6$NAO_3LagAvg) # -0.019
##
## Pearson's product-moment correlation
##
## data: afz_clust6$TempGrad and afz_clust6$NAO_3LagAvg
## t = -0.1048, df = 32, p-value = 0.9172
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.3545 0.3217
## sample estimates:
## cor
## -0.01851
cor.test(afz_clust6$TempGrad, afz_clust6$NAO_6LagAvg) # -0.220
##
## Pearson's product-moment correlation
##
## data: afz_clust6$TempGrad and afz_clust6$NAO_6LagAvg
## t = -1.274, df = 32, p-value = 0.2119
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.5193 0.1280
## sample estimates:
## cor
## -0.2197
cor.test(afz_clust6$TempGrad, afz_clust6$NAO_12LagAvg) # -0.290
##
## Pearson's product-moment correlation
##
## data: afz_clust6$TempGrad and afz_clust6$NAO_12LagAvg
## t = -1.712, df = 32, p-value = 0.09657
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.57182 0.05377
## sample estimates:
## cor
## -0.2897
cor.test(afz_clust6$TempGrad, afz_clust6$NAO_6Lag3Avg) # -0.320 - p=0.0648
##
## Pearson's product-moment correlation
##
## data: afz_clust6$TempGrad and afz_clust6$NAO_6Lag3Avg
## t = -1.913, df = 32, p-value = 0.0648
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.59410 0.02006
## sample estimates:
## cor
## -0.3203
cor.test(afz_clust6$TempGrad, afz_clust6$NAO_2Lag3Avg) # -0.050
##
## Pearson's product-moment correlation
##
## data: afz_clust6$TempGrad and afz_clust6$NAO_2Lag3Avg
## t = -0.2859, df = 32, p-value = 0.7768
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.3821 0.2927
## sample estimates:
## cor
## -0.05048
cor.test(afz_clust6$TempGrad, afz_clust6$NAO_5Lag6Avg) # -0.145
##
## Pearson's product-moment correlation
##
## data: afz_clust6$TempGrad and afz_clust6$NAO_5Lag6Avg
## t = -0.8311, df = 32, p-value = 0.4121
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.4609 0.2028
## sample estimates:
## cor
## -0.1454
cor.test(afz_clust6$TempGrad, afz_clust6$NAO_11Lag12Avg) # -0.290
##
## Pearson's product-moment correlation
##
## data: afz_clust6$TempGrad and afz_clust6$NAO_11Lag12Avg
## t = -1.715, df = 32, p-value = 0.09597
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.57219 0.05322
## sample estimates:
## cor
## -0.2902
## PNA -- Nothing significant
cor.test(afz_clust6$TempGrad, afz_clust6$PNA_Index) # 0.302
##
## Pearson's product-moment correlation
##
## data: afz_clust6$TempGrad and afz_clust6$PNA_Index
## t = 1.794, df = 32, p-value = 0.08223
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.03991 0.58109
## sample estimates:
## cor
## 0.3023
cor.test(afz_clust6$TempGrad, afz_clust6$PNA_3LagAvg) # 0.056
##
## Pearson's product-moment correlation
##
## data: afz_clust6$TempGrad and afz_clust6$PNA_3LagAvg
## t = 0.3146, df = 32, p-value = 0.7551
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.2880 0.3864
## sample estimates:
## cor
## 0.05553
cor.test(afz_clust6$TempGrad, afz_clust6$PNA_6LagAvg) # 0.229
##
## Pearson's product-moment correlation
##
## data: afz_clust6$TempGrad and afz_clust6$PNA_6LagAvg
## t = 1.332, df = 32, p-value = 0.1922
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.1181 0.5266
## sample estimates:
## cor
## 0.2292
cor.test(afz_clust6$TempGrad, afz_clust6$PNA_12LagAvg) # 0.159
##
## Pearson's product-moment correlation
##
## data: afz_clust6$TempGrad and afz_clust6$PNA_12LagAvg
## t = 0.9108, df = 32, p-value = 0.3692
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.1894 0.4718
## sample estimates:
## cor
## 0.159
cor.test(afz_clust6$TempGrad, afz_clust6$PNA_6Lag3Avg) # 0.318 - p=0.06704
##
## Pearson's product-moment correlation
##
## data: afz_clust6$TempGrad and afz_clust6$PNA_6Lag3Avg
## t = 1.896, df = 32, p-value = 0.06704
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.02285 0.59229
## sample estimates:
## cor
## 0.3178
cor.test(afz_clust6$TempGrad, afz_clust6$PNA_2Lag3Avg) # 0.210
##
## Pearson's product-moment correlation
##
## data: afz_clust6$TempGrad and afz_clust6$PNA_2Lag3Avg
## t = 1.217, df = 32, p-value = 0.2325
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.1376 0.5121
## sample estimates:
## cor
## 0.2103
cor.test(afz_clust6$TempGrad, afz_clust6$PNA_5Lag6Avg) # 0.246
##
## Pearson's product-moment correlation
##
## data: afz_clust6$TempGrad and afz_clust6$PNA_5Lag6Avg
## t = 1.436, df = 32, p-value = 0.1607
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.1004 0.5394
## sample estimates:
## cor
## 0.2461
cor.test(afz_clust6$TempGrad, afz_clust6$PNA_11Lag12Avg) # 0.270
##
## Pearson's product-moment correlation
##
## data: afz_clust6$TempGrad and afz_clust6$PNA_11Lag12Avg
## t = 1.584, df = 32, p-value = 0.123
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.07538 0.55703
## sample estimates:
## cor
## 0.2697
## GT -- All significant except 12LagAvg
cor.test(afz_clust6$TempGrad, afz_clust6$GlobalJulyTemp) # 0.405*
##
## Pearson's product-moment correlation
##
## data: afz_clust6$TempGrad and afz_clust6$GlobalJulyTemp
## t = 2.507, df = 32, p-value = 0.01743
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.07771 0.65380
## sample estimates:
## cor
## 0.4052
cor.test(afz_clust6$TempGrad, afz_clust6$GT_3LagAvg) # 0.359*
##
## Pearson's product-moment correlation
##
## data: afz_clust6$TempGrad and afz_clust6$GT_3LagAvg
## t = 2.173, df = 32, p-value = 0.03731
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.02321 0.62138
## sample estimates:
## cor
## 0.3586
cor.test(afz_clust6$TempGrad, afz_clust6$GT_6LagAvg) # 0.378*
##
## Pearson's product-moment correlation
##
## data: afz_clust6$TempGrad and afz_clust6$GT_6LagAvg
## t = 2.307, df = 32, p-value = 0.02765
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.04531 0.63478
## sample estimates:
## cor
## 0.3777
cor.test(afz_clust6$TempGrad, afz_clust6$GT_12LagAvg) # 0.331 - p=0.05603
##
## Pearson's product-moment correlation
##
## data: afz_clust6$TempGrad and afz_clust6$GT_12LagAvg
## t = 1.983, df = 32, p-value = 0.05603
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.008319 0.601644
## sample estimates:
## cor
## 0.3308
cor.test(afz_clust6$TempGrad, afz_clust6$GT_6Lag3Avg) # 0.364*
##
## Pearson's product-moment correlation
##
## data: afz_clust6$TempGrad and afz_clust6$GT_6Lag3Avg
## t = 2.21, df = 32, p-value = 0.03437
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.02936 0.62515
## sample estimates:
## cor
## 0.3639
cor.test(afz_clust6$TempGrad, afz_clust6$GT_2Lag3Avg) # 0.377*
##
## Pearson's product-moment correlation
##
## data: afz_clust6$TempGrad and afz_clust6$GT_2Lag3Avg
## t = 2.305, df = 32, p-value = 0.02779
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.04495 0.63457
## sample estimates:
## cor
## 0.3774
cor.test(afz_clust6$TempGrad, afz_clust6$GT_5Lag6Avg) # 0.364*
##
## Pearson's product-moment correlation
##
## data: afz_clust6$TempGrad and afz_clust6$GT_5Lag6Avg
## t = 2.211, df = 32, p-value = 0.03428
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.02955 0.62526
## sample estimates:
## cor
## 0.3641
cor.test(afz_clust6$TempGrad, afz_clust6$GT_11Lag12Avg) # 0.341*
##
## Pearson's product-moment correlation
##
## data: afz_clust6$TempGrad and afz_clust6$GT_11Lag12Avg
## t = 2.054, df = 32, p-value = 0.04818
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.0036 0.6092
## sample estimates:
## cor
## 0.3414
Global temperature actually seems to be the strongest corrleating variable with temperature gradients despite the lack of autocorrelation in the data. I'm especially surprised by the inclusion of GT in the cluster 2 and 4 correlations, since they showed no trend either. AO is not significant anywhere. Neither is NAO, but NAO and PNA are over 0.300 frequently.
Why I'm not using ar or arima: ar() finds the best autroregressive model for a time series (made using ts) – problem: need something with a seasonal frequency of 2 or greater) – same goes for arima(). I do not have seasonal effects.
Basic Method: Use regsubsets to identify the best of 8 possible oscillation index lags for each index (including the global temperature index – total of 32). Past research has identified global warming as the force behind any temporal trend, and my brief modelling suggests that this works fairly well, especially for an annual average. Note that variation from that trend may be related to oscillations… which in turn may be influenced by the global trend. The effects may be impossible to extract from each other.
library(leaps)
reg1 <- regsubsets(TempGrad ~ AO_Index + AO_3LagAvg + AO_6LagAvg + AO_12LagAvg +
AO_6Lag3Avg + AO_2Lag3Avg + AO_5Lag6Avg + AO_11Lag12Avg + NAO_Index + NAO_3LagAvg +
NAO_6LagAvg + NAO_12LagAvg + NAO_6Lag3Avg + NAO_2Lag3Avg + NAO_5Lag6Avg +
NAO_11Lag12Avg + PNA_Index + PNA_3LagAvg + PNA_6LagAvg + PNA_12LagAvg +
PNA_6Lag3Avg + PNA_2Lag3Avg + PNA_5Lag6Avg + PNA_11Lag12Avg + GlobalJulyTemp +
GT_3LagAvg + GT_6LagAvg + GT_12LagAvg + GT_6Lag3Avg + GT_2Lag3Avg + GT_5Lag6Avg +
GT_11Lag12Avg, data = afz_clust1, nvmax = 12)
reg1sum <- summary(reg1)
par(mfrow = c(1, 2))
plot(1:12, y = reg1sum$adjr2, type = "o", xlab = "Number of Parameters", ylab = "Adj. r^2",
main = "Adj. r^2 by Model Size")
plot(1:12, y = reg1sum$bic, type = "o", xlab = "Number of Parameters", ylab = "BIC",
main = "BIC by Model Size")
par(mfrow = c(1, 1))
plot(reg1, main = "Variable Selection based on Regsubsets \n Cluster 1 Temperature Gradients")
# Make Best Model:
lmc18a <- lm(TempGrad ~ AO_Index + NAO_Index + PNA_2Lag3Avg + GT_3LagAvg + GT_6LagAvg +
GT_12LagAvg + GT_6Lag3Avg + GT_11Lag12Avg, data = afz_clust1)
summary(lmc18a)
##
## Call:
## lm(formula = TempGrad ~ AO_Index + NAO_Index + PNA_2Lag3Avg +
## GT_3LagAvg + GT_6LagAvg + GT_12LagAvg + GT_6Lag3Avg + GT_11Lag12Avg,
## data = afz_clust1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.009027 -0.003273 0.000311 0.003588 0.007455
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.04071 0.00197 20.63 < 2e-16 ***
## AO_Index -0.00807 0.00246 -3.28 0.00303 **
## NAO_Index 0.00503 0.00113 4.45 0.00016 ***
## PNA_2Lag3Avg 0.00384 0.00170 2.26 0.03313 *
## GT_3LagAvg -0.58910 0.14261 -4.13 0.00035 ***
## GT_6LagAvg 1.11289 0.28354 3.93 0.00060 ***
## GT_12LagAvg -0.20138 0.07543 -2.67 0.01314 *
## GT_6Lag3Avg -0.56422 0.14335 -3.94 0.00058 ***
## GT_11Lag12Avg 0.25232 0.08626 2.93 0.00722 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.005 on 25 degrees of freedom
## Multiple R-squared: 0.667, Adjusted R-squared: 0.56
## F-statistic: 6.25 on 8 and 25 DF, p-value: 0.000183
# Do I need all variables?
library(lmSupport)
## Loading required package: car
## Loading required package: MASS
## Loading required package: nnet
## Loading required package: psych
## Attaching package: 'psych'
## The following object(s) are masked from 'package:car':
##
## logit
## Loading required package: gplots
## Loading required package: gtools
## Attaching package: 'gtools'
## The following object(s) are masked from 'package:psych':
##
## logit
## The following object(s) are masked from 'package:car':
##
## logit
## Loading required package: gdata
## gdata: read.xls support for 'XLS' (Excel 97-2004) files ENABLED.
## ```
```r
lm.sumSquares(lmc18a) # Everything seems valuable
## SS dR-sqr pEta-sqr df F p-value
## (Intercept) 0.0106505 5.6740 0.9445 1 425.432 0.0000
## AO_Index 0.0002698 0.1438 0.3013 1 10.779 0.0030
## NAO_Index 0.0004947 0.2635 0.4415 1 19.760 0.0002
## PNA_2Lag3Avg 0.0001273 0.0678 0.1690 1 5.086 0.0331
## GT_3LagAvg 0.0004272 0.2276 0.4057 1 17.064 0.0004
## GT_6LagAvg 0.0003857 0.2055 0.3813 1 15.406 0.0006
## GT_12LagAvg 0.0001784 0.0951 0.2219 1 7.128 0.0131
## GT_6Lag3Avg 0.0003879 0.2066 0.3826 1 15.493 0.0006
## GT_11Lag12Avg 0.0002142 0.1141 0.2550 1 8.556 0.0072
## Error (SSE) 0.0006259 NA NA 25 NA NA
## Total (SST) 0.0018771 NA NA NA NA NA
anova(lmc18a)
## Analysis of Variance Table
##
## Response: TempGrad
## Df Sum Sq Mean Sq F value Pr(>F)
## AO_Index 1 0.000014 0.000014 0.56 0.45950
## NAO_Index 1 0.000358 0.000358 14.32 0.00086 ***
## PNA_2Lag3Avg 1 0.000041 0.000041 1.65 0.21025
## GT_3LagAvg 1 0.000126 0.000126 5.05 0.03365 *
## GT_6LagAvg 1 0.000123 0.000123 4.90 0.03619 *
## GT_12LagAvg 1 0.000018 0.000018 0.71 0.40604
## GT_6Lag3Avg 1 0.000356 0.000356 14.22 0.00089 ***
## GT_11Lag12Avg 1 0.000214 0.000214 8.56 0.00722 **
## Residuals 25 0.000626 0.000025
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
drop1(lmc18a, test = "F")
## Single term deletions
##
## Model:
## TempGrad ~ AO_Index + NAO_Index + PNA_2Lag3Avg + GT_3LagAvg +
## GT_6LagAvg + GT_12LagAvg + GT_6Lag3Avg + GT_11Lag12Avg
## Df Sum of Sq RSS AIC F value Pr(>F)
## <none> 0.000626 -353
## AO_Index 1 0.000270 0.000896 -343 10.78 0.00303 **
## NAO_Index 1 0.000495 0.001121 -335 19.76 0.00016 ***
## PNA_2Lag3Avg 1 0.000127 0.000753 -348 5.09 0.03313 *
## GT_3LagAvg 1 0.000427 0.001053 -337 17.06 0.00035 ***
## GT_6LagAvg 1 0.000386 0.001012 -338 15.41 0.00060 ***
## GT_12LagAvg 1 0.000178 0.000804 -346 7.13 0.01314 *
## GT_6Lag3Avg 1 0.000388 0.001014 -338 15.49 0.00058 ***
## GT_11Lag12Avg 1 0.000214 0.000840 -345 8.56 0.00722 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# Plot Results:
lmc18a_pred <- predict(lmc18a)
plot(TempGrad ~ Year, data = afz_clust1, main = "AFZ July Temperature Gradients: Cluster 1",
xlab = "Years", ylab = "Temperature Gradient (K/km)", cex = 0.6)
curve(predict(lm1c1yr, data.frame(Year = x), type = "resp"), add = TRUE, col = "blue",
lwd = 3)
lines(lmc18a_pred ~ afz_clust1$Year, add = TRUE, col = "aquamarine", lwd = 3,
lty = 2)
## Warning: "add" is not a graphical parameter
legend("topleft", c("trend in time", "8-var model"), lty = c(1, 2), col = c("blue",
"aquamarine"), lwd = 3)
