LARain <- read.csv(choose.files(), header = TRUE)
names(LARain)
## [1] "Year" "APMAM" "APSAB" "APSLAKE" "OPBPC" "OPRC" "OPSLAKE"
## [8] "BSAAM"
plot(LARain)
plot(LARain$BSAAM ~ LARain$APMAM)
lm(LARain$BSAAM ~ LARain$APMAM)
##
## Call:
## lm(formula = LARain$BSAAM ~ LARain$APMAM)
##
## Coefficients:
## (Intercept) LARain$APMAM
## 63363 1965
a <- lm(LARain$BSAAM ~ LARain$APMAM)
summary(a)
##
## Call:
## lm(formula = LARain$BSAAM ~ LARain$APMAM)
##
## Residuals:
## Min 1Q Median 3Q Max
## -37043 -16339 -5457 17158 72467
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 63364 9917 6.39 1.2e-07 ***
## LARain$APMAM 1965 1249 1.57 0.12
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 25100 on 41 degrees of freedom
## Multiple R-squared: 0.0569, Adjusted R-squared: 0.0339
## F-statistic: 2.47 on 1 and 41 DF, p-value: 0.123
b <- lm(LARain$BSAAM ~ LARain$OPBPC)
summary(b) #r2: .78 #pvalue: 2.996e-15
##
## Call:
## lm(formula = LARain$BSAAM ~ LARain$OPBPC)
##
## Residuals:
## Min 1Q Median 3Q Max
## -21183 -7298 -819 4731 38430
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 40017 3589 11.2 5.5e-14 ***
## LARain$OPBPC 2940 241 12.2 3.0e-15 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 12000 on 41 degrees of freedom
## Multiple R-squared: 0.785, Adjusted R-squared: 0.779
## F-statistic: 149 on 1 and 41 DF, p-value: 3e-15
c <- lm(LARain$BSAAM ~ LARain$OPRC)
summary(c) #r2: .84 #pvalue: <2.2e-16
##
## Call:
## lm(formula = LARain$BSAAM ~ LARain$OPRC)
##
## Residuals:
## Min 1Q Median 3Q Max
## -24356 -5514 -522 7448 24854
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 21741 4044 5.38 3.3e-06 ***
## LARain$OPRC 4667 311 14.99 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 10100 on 41 degrees of freedom
## Multiple R-squared: 0.846, Adjusted R-squared: 0.842
## F-statistic: 225 on 1 and 41 DF, p-value: <2e-16
d <- lm(LARain$BSAAM ~ LARain$OPSLAKE)
summary(d) #r2: .88 #pvalue: <2.2e-16
##
## Call:
## lm(formula = LARain$BSAAM ~ LARain$OPSLAKE)
##
## Residuals:
## Min 1Q Median 3Q Max
## -17604 -5338 332 3411 20876
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 27015 3219 8.39 1.9e-10 ***
## LARain$OPSLAKE 3752 216 17.39 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 8920 on 41 degrees of freedom
## Multiple R-squared: 0.881, Adjusted R-squared: 0.878
## F-statistic: 303 on 1 and 41 DF, p-value: <2e-16
confint(d) #calculating confidence interval
## 2.5 % 97.5 %
## (Intercept) 20514 33515
## LARain$OPSLAKE 3317 4188
anova(d) # the null hyp of no assoc btwn x's and y's is definitely rejected
## Analysis of Variance Table
##
## Response: LARain$BSAAM
## Df Sum Sq Mean Sq F value Pr(>F)
## LARain$OPSLAKE 1 2.41e+10 2.41e+10 303 <2e-16 ***
## Residuals 41 3.26e+09 7.96e+07
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
plot(d, which = 1:2) #looking at residuals
#It seems that the OPSLAKE weather station #is the best predictor of runoff due to its #rsquared and p values.
bc <- lm(LARain$BSAAM ~ LARain$OPBPC + LARain$OPRC)
summary(bc) #r2: .87 #pvalue: <2.2e-16
##
## Call:
## lm(formula = LARain$BSAAM ~ LARain$OPBPC + LARain$OPRC)
##
## Residuals:
## Min 1Q Median 3Q Max
## -17377 -6600 -10 6240 18771
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 25353 3802 6.67 5.4e-08 ***
## LARain$OPBPC 1191 365 3.27 0.0022 **
## LARain$OPRC 3092 558 5.55 2.1e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 9130 on 40 degrees of freedom
## Multiple R-squared: 0.878, Adjusted R-squared: 0.872
## F-statistic: 144 on 2 and 40 DF, p-value: <2e-16
cd <- lm(LARain$BSAAM ~ LARain$OPRC + LARain$OPSLAKE)
summary(cd) #r2: .90 #pvalue: <2.2e-16
##
## Call:
## lm(formula = LARain$BSAAM ~ LARain$OPRC + LARain$OPSLAKE)
##
## Residuals:
## Min 1Q Median 3Q Max
## -15991 -6485 -498 4700 19946
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 22891 3278 6.98 2.0e-08 ***
## LARain$OPRC 1866 639 2.92 0.0057 **
## LARain$OPSLAKE 2401 503 4.77 2.5e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 8200 on 40 degrees of freedom
## Multiple R-squared: 0.902, Adjusted R-squared: 0.897
## F-statistic: 183 on 2 and 40 DF, p-value: <2e-16
bd <- lm(LARain$BSAAM ~ LARain$OPBPC + LARain$OPSLAKE)
summary(bd) #r2: .87 #pvalue: <2.2e-16
##
## Call:
## lm(formula = LARain$BSAAM ~ LARain$OPBPC + LARain$OPSLAKE)
##
## Residuals:
## Min 1Q Median 3Q Max
## -17591 -5277 276 3381 20867
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 27051.0 3540.1 7.64 2.4e-09 ***
## LARain$OPBPC 14.4 546.4 0.03 0.98
## LARain$OPSLAKE 3736.2 658.2 5.68 1.3e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 9030 on 40 degrees of freedom
## Multiple R-squared: 0.881, Adjusted R-squared: 0.875
## F-statistic: 148 on 2 and 40 DF, p-value: <2e-16
#If only 2 stations open, keep OPRC & OPSLAKE