cases <- c(465, 463, 866, 475, 1023, 917, 913, 1239, 1050, 1065, 1293, 1203, 912, 1431, 896, 1176, 1305)
plot(cases)
aveJUneTemp <- c(66.1, 69.1, 71.1, 68.2, 65.5, 73.4, 71, 72.7, 68.7, 67.7, 69.3, 69.5, 72.3, 68.9, 69.5, 69.7, 71.3)
aveJulyTemp <- c(72.4, 75.9, 77, 73.7, 72.2, 76.8, 79.7, 76, 75.6, 70, 76.3, 78.8, 80.2, 75, 71.5, 73.4, 75.5)
aveAugTemp <- c(72.2, 74.2, 70.9, 75.3, 66.3, 71.7, 72.1, 72.1, 72.5, 69.5, 77, 73.6, 72, 74.7, 73.3, 70.7, 73.4)
aveTotalTemp <- ((aveJUneTemp + aveJulyTemp + aveAugTemp)/3)
plot(aveTotalTemp)
totJuneRain <- c(4.56, 6.35, 8.3, 4.66, 3.06, 4.24, 2.81, 2.05, 2.7, 2.86, 6.25, 5.28, 2.59, 5.13, 11.36, 4.4, 4.49)
totJulyRain <- c(6.1, 2.12, 5.19, 2.05, 3.36, 2.94, 1.29, 3.29, 2.13, 2.17, 3.03, 5.23, 4.9, 3.51, 2.27, 7.32, 5.09)
totAugRain <- c(3.19, 2.31, 8.3, 1.12, 1.19, 5.22, 6.9, 9.32, 3.35, 6.43, 4.91, 3.03, 1.38, 2.07, 2.9, 2.99, 7.82)
totalRain <- (totJuneRain + totJulyRain + totAugRain)
plot(totalRain)
DIJune <- c(0, 3, 0, 1, 0, 2, 0, -3, 0, 0, 0, 3, 0, 2, 3, 0, 0)
DIJuly <- c(1, 2, 2, 1, 1, 2, -2, -3, 0, 0, 1, 3, -2, 0, 3, 0, 2)
DIAug <- c(2, 0, 3, 0, 1, 1, -2, -3, 0, 0, 2, 0, -3, 0, 3, 0, 3)
HDD <- c(6660, 8074, 6845, 7686, 7407, 6974, 6611, 7035, 7937, 7773, 7002, 7709, 5852, 7708, 8597, 7528, 6283)
TotalSnow <- c(36.2, 75.8, 66, 35, 66.3, 25.5, 44.4, 35.5, 44.9, 45, 40.7, 86.6, 22.3, 67.7, 69.8, 32.4, 36.7)
library(MASS)
mymod <- lm(cases ~ aveTotalTemp + totalRain + DIJune + DIJuly + DIAug + HDD + TotalSnow)
summary(mymod)
##
## Call:
## lm(formula = cases ~ aveTotalTemp + totalRain + DIJune + DIJuly +
## DIAug + HDD + TotalSnow)
##
## Residuals:
## Min 1Q Median 3Q Max
## -452.27 -197.82 7.38 179.15 361.94
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3.295e+03 5.479e+03 -0.601 0.562
## aveTotalTemp 4.969e+01 6.875e+01 0.723 0.488
## totalRain 3.713e+00 3.722e+01 0.100 0.923
## DIJune -5.295e+01 1.309e+02 -0.404 0.695
## DIJuly -8.627e+01 1.646e+02 -0.524 0.613
## DIAug 6.381e+01 1.259e+02 0.507 0.624
## HDD 6.351e-02 1.852e-01 0.343 0.739
## TotalSnow 4.723e+00 6.792e+00 0.695 0.504
##
## Residual standard error: 353.5 on 9 degrees of freedom
## Multiple R-squared: 0.1947, Adjusted R-squared: -0.4316
## F-statistic: 0.3109 on 7 and 9 DF, p-value: 0.9312
stepAIC(mymod, direction = "backward")
## Start: AIC=204.7
## cases ~ aveTotalTemp + totalRain + DIJune + DIJuly + DIAug +
## HDD + TotalSnow
##
## Df Sum of Sq RSS AIC
## - totalRain 1 1244 1126046 202.72
## - HDD 1 14701 1139503 202.92
## - DIJune 1 20448 1145250 203.00
## - DIAug 1 32101 1156902 203.18
## - DIJuly 1 34331 1159133 203.21
## - TotalSnow 1 60422 1185224 203.59
## - aveTotalTemp 1 65292 1190093 203.66
## <none> 1124802 204.70
##
## Step: AIC=202.72
## cases ~ aveTotalTemp + DIJune + DIJuly + DIAug + HDD + TotalSnow
##
## Df Sum of Sq RSS AIC
## - HDD 1 14701 1140747 200.94
## - DIJune 1 29867 1155913 201.16
## - DIJuly 1 34008 1160054 201.22
## - DIAug 1 47879 1173925 201.43
## - TotalSnow 1 75359 1201405 201.82
## - aveTotalTemp 1 105448 1231494 202.24
## <none> 1126046 202.72
##
## Step: AIC=200.94
## cases ~ aveTotalTemp + DIJune + DIJuly + DIAug + TotalSnow
##
## Df Sum of Sq RSS AIC
## - DIJune 1 20579 1161325 199.24
## - DIJuly 1 33855 1174602 199.44
## - DIAug 1 43095 1183842 199.57
## - aveTotalTemp 1 92536 1233283 200.26
## - TotalSnow 1 113805 1254552 200.55
## <none> 1140747 200.94
##
## Step: AIC=199.24
## cases ~ aveTotalTemp + DIJuly + DIAug + TotalSnow
##
## Df Sum of Sq RSS AIC
## - aveTotalTemp 1 80941 1242267 198.39
## - TotalSnow 1 98162 1259488 198.62
## - DIAug 1 122262 1283588 198.94
## <none> 1161325 199.24
## - DIJuly 1 193058 1354383 199.86
##
## Step: AIC=198.39
## cases ~ DIJuly + DIAug + TotalSnow
##
## Df Sum of Sq RSS AIC
## - TotalSnow 1 67902 1310169 197.29
## - DIAug 1 72272 1314539 197.35
## - DIJuly 1 146052 1388319 198.28
## <none> 1242267 198.39
##
## Step: AIC=197.29
## cases ~ DIJuly + DIAug
##
## Df Sum of Sq RSS AIC
## - DIAug 1 38850 1349018 195.79
## - DIJuly 1 82270 1392438 196.33
## <none> 1310169 197.29
##
## Step: AIC=195.79
## cases ~ DIJuly
##
## Df Sum of Sq RSS AIC
## - DIJuly 1 47790 1396808 194.38
## <none> 1349018 195.79
##
## Step: AIC=194.38
## cases ~ 1
##
## Call:
## lm(formula = cases ~ 1)
##
## Coefficients:
## (Intercept)
## 981.9
mymod2 <- lm(cases ~ aveJUneTemp + aveJulyTemp + aveAugTemp + totJuneRain + totJulyRain + totAugRain + DIJune + DIJuly + DIAug + HDD + TotalSnow)
summary(mymod2)
##
## Call:
## lm(formula = cases ~ aveJUneTemp + aveJulyTemp + aveAugTemp +
## totJuneRain + totJulyRain + totAugRain + DIJune + DIJuly +
## DIAug + HDD + TotalSnow)
##
## Residuals:
## 1 2 3 4 5 6 7 8 9
## -238.40 -363.96 -186.32 -117.71 92.81 -35.37 43.48 -81.55 -128.09
## 10 11 12 13 14 15 16 17
## 200.41 352.98 239.75 76.35 -34.15 128.24 65.20 -13.67
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.361e+04 7.042e+03 -1.932 0.1112
## aveJUneTemp 1.951e+02 1.096e+02 1.780 0.1351
## aveJulyTemp -4.360e+01 7.841e+01 -0.556 0.6022
## aveAugTemp 4.469e+01 4.706e+01 0.950 0.3859
## totJuneRain -1.735e+02 8.334e+01 -2.081 0.0919 .
## totJulyRain 5.590e+01 6.268e+01 0.892 0.4133
## totAugRain -5.890e+01 7.223e+01 -0.815 0.4519
## DIJune -2.630e+00 1.489e+02 -0.018 0.9866
## DIJuly -2.573e+02 1.730e+02 -1.487 0.1971
## DIAug 3.008e+02 1.604e+02 1.875 0.1196
## HDD 1.427e-01 2.833e-01 0.504 0.6359
## TotalSnow 1.888e+01 1.111e+01 1.699 0.1501
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 323.4 on 5 degrees of freedom
## Multiple R-squared: 0.6257, Adjusted R-squared: -0.1977
## F-statistic: 0.7599 on 11 and 5 DF, p-value: 0.6739
stepAIC(mymod2, direction = "backward")
## Start: AIC=199.67
## cases ~ aveJUneTemp + aveJulyTemp + aveAugTemp + totJuneRain +
## totJulyRain + totAugRain + DIJune + DIJuly + DIAug + HDD +
## TotalSnow
##
## Df Sum of Sq RSS AIC
## - DIJune 1 33 522835 197.68
## - HDD 1 26530 549332 198.51
## - aveJulyTemp 1 32327 555129 198.69
## <none> 522802 199.67
## - totAugRain 1 69527 592329 199.80
## - totJulyRain 1 83165 605967 200.18
## - aveAugTemp 1 94285 617087 200.49
## - DIJuly 1 231287 754089 203.90
## - TotalSnow 1 301739 824541 205.42
## - aveJUneTemp 1 331388 854190 206.02
## - DIAug 1 367663 890465 206.73
## - totJuneRain 1 452962 975764 208.28
##
## Step: AIC=197.67
## cases ~ aveJUneTemp + aveJulyTemp + aveAugTemp + totJuneRain +
## totJulyRain + totAugRain + DIJuly + DIAug + HDD + TotalSnow
##
## Df Sum of Sq RSS AIC
## - HDD 1 27034 549869 196.53
## - aveJulyTemp 1 32614 555449 196.70
## <none> 522835 197.68
## - aveAugTemp 1 97295 620130 198.58
## - totJulyRain 1 98898 621732 198.62
## - totAugRain 1 100241 623076 198.66
## - TotalSnow 1 329088 851923 203.97
## - DIJuly 1 367653 890488 204.73
## - aveJUneTemp 1 369607 892442 204.76
## - DIAug 1 392195 915030 205.19
## - totJuneRain 1 456266 979101 206.34
##
## Step: AIC=196.53
## cases ~ aveJUneTemp + aveJulyTemp + aveAugTemp + totJuneRain +
## totJulyRain + totAugRain + DIJuly + DIAug + TotalSnow
##
## Df Sum of Sq RSS AIC
## <none> 549869 196.53
## - totJulyRain 1 73186 623055 196.66
## - totAugRain 1 129142 679012 198.12
## - aveAugTemp 1 153126 702995 198.71
## - aveJulyTemp 1 205912 755782 199.94
## - DIJuly 1 340769 890638 202.73
## - DIAug 1 366514 916383 203.22
## - totJuneRain 1 447629 997498 204.66
## - aveJUneTemp 1 457061 1006930 204.82
## - TotalSnow 1 594298 1144167 206.99
##
## Call:
## lm(formula = cases ~ aveJUneTemp + aveJulyTemp + aveAugTemp +
## totJuneRain + totJulyRain + totAugRain + DIJuly + DIAug +
## TotalSnow)
##
## Coefficients:
## (Intercept) aveJUneTemp aveJulyTemp aveAugTemp totJuneRain
## -11939.13 208.49 -72.85 52.52 -171.76
## totJulyRain totAugRain DIJuly DIAug TotalSnow
## 44.02 -64.55 -241.50 276.32 21.62
anova(mymod, mymod2)
## Analysis of Variance Table
##
## Model 1: cases ~ aveTotalTemp + totalRain + DIJune + DIJuly + DIAug +
## HDD + TotalSnow
## Model 2: cases ~ aveJUneTemp + aveJulyTemp + aveAugTemp + totJuneRain +
## totJulyRain + totAugRain + DIJune + DIJuly + DIAug + HDD +
## TotalSnow
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 9 1124802
## 2 5 522802 4 602000 1.4394 0.3444
fishL <- c(1565443, 1565708, 1492913, 1461112, 1492913, 1461112, 1467677, 1458013, 1478193, 1478193, 1492087, 1481758, 1518357, 1492460, 1418995, 1487547, 1423502)
mymod3 <- lm(cases ~ aveTotalTemp + totalRain + DIJune + DIJuly + DIAug + HDD + TotalSnow + fishL)
anova(mymod, mymod3)
## Analysis of Variance Table
##
## Model 1: cases ~ aveTotalTemp + totalRain + DIJune + DIJuly + DIAug +
## HDD + TotalSnow
## Model 2: cases ~ aveTotalTemp + totalRain + DIJune + DIJuly + DIAug +
## HDD + TotalSnow + fishL
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 9 1124802
## 2 8 844216 1 280585 2.6589 0.1416
anova(mymod2, mymod3)
## Analysis of Variance Table
##
## Model 1: cases ~ aveJUneTemp + aveJulyTemp + aveAugTemp + totJuneRain +
## totJulyRain + totAugRain + DIJune + DIJuly + DIAug + HDD +
## TotalSnow
## Model 2: cases ~ aveTotalTemp + totalRain + DIJune + DIJuly + DIAug +
## HDD + TotalSnow + fishL
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 5 522802
## 2 8 844216 -3 -321414 1.0247 0.4561
cor(cases, fishL)
## [1] -0.4753386