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##load and inspect data

library(rstan)
## Loading required package: StanHeaders
## Loading required package: ggplot2
## rstan (Version 2.19.2, GitRev: 2e1f913d3ca3)
## For execution on a local, multicore CPU with excess RAM we recommend calling
## options(mc.cores = parallel::detectCores()).
## To avoid recompilation of unchanged Stan programs, we recommend calling
## rstan_options(auto_write = TRUE)
## For improved execution time, we recommend calling
## Sys.setenv(LOCAL_CPPFLAGS = '-march=native')
## although this causes Stan to throw an error on a few processors.
seaice <- read.csv("C:/Users/YIJIA001/Documents/HU Class/seaice.csv")
head(seaice)
##   ï..year extent_north extent_south
## 1    1979       12.328       11.700
## 2    1980       12.337       11.230
## 3    1981       12.127       11.435
## 4    1982       12.447       11.640
## 5    1983       12.332       11.389
## 6    1984       11.910       11.454

##plot the data

plot (extent_north ~ ï..year, pch = 20, data = seaice)

##Run a general linear model using lm()

lm1 <- lm (extent_north ~ ï..year, data = seaice)
lm1
## 
## Call:
## lm(formula = extent_north ~ ï..year, data = seaice)
## 
## Coefficients:
## (Intercept)      ï..year  
##   120.50304     -0.05457

##Prepare the data, re-run the lm() and extract summary statistics

summary(lm1)
## 
## Call:
## lm(formula = extent_north ~ ï..year, data = seaice)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.49925 -0.17713  0.04898  0.16923  0.32829 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 120.503036   6.267203   19.23   <2e-16 ***
## ï..year      -0.054574   0.003137  -17.40   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2205 on 37 degrees of freedom
## Multiple R-squared:  0.8911, Adjusted R-squared:  0.8881 
## F-statistic: 302.7 on 1 and 37 DF,  p-value: < 2.2e-16
plot(extent_north ~ ï..year, pch = 20, data = seaice)
abline(lm1, col = 3, lty = 2, lw = 1)

##Write the Stan model/Run the Stan model

summary(lm1)
## 
## Call:
## lm(formula = extent_north ~ ï..year, data = seaice)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.49925 -0.17713  0.04898  0.16923  0.32829 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 120.503036   6.267203   19.23   <2e-16 ***
## ï..year      -0.054574   0.003137  -17.40   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2205 on 37 degrees of freedom
## Multiple R-squared:  0.8911, Adjusted R-squared:  0.8881 
## F-statistic: 302.7 on 1 and 37 DF,  p-value: < 2.2e-16

##Compare your results to our results to “lm”

plot(extent_north ~ ï..year, pch = 20, data = seaice)
abline(lm1, col = 2, lty = 2, lw = 3)