#Exercise 2 
##A
gibbons<- c(1,2.3,4.5,6.7,8.9,9,9.9,8.7,6.5,4.4,3,5,7,12,2,3,4,5,7,8,5.5,7.7,8.6,7.5,6.5,7,8,6,4,2)
length(gibbons)
## [1] 30
##B
str(gibbons)
##  num [1:30] 1 2.3 4.5 6.7 8.9 9 9.9 8.7 6.5 4.4 ...

Gibbons is numerical data

##C
figs<- rnorm(30, mean=8*gibbons, sd=0.5*mean(gibbons))

##D
sort(gibbons)
##  [1]  1.0  2.0  2.0  2.3  3.0  3.0  4.0  4.0  4.4  4.5  5.0  5.0  5.5  6.0  6.5
## [16]  6.5  6.7  7.0  7.0  7.0  7.5  7.7  8.0  8.0  8.6  8.7  8.9  9.0  9.9 12.0
sort(gibbons, decreasing=TRUE)
##  [1] 12.0  9.9  9.0  8.9  8.7  8.6  8.0  8.0  7.7  7.5  7.0  7.0  7.0  6.7  6.5
## [16]  6.5  6.0  5.5  5.0  5.0  4.5  4.4  4.0  4.0  3.0  3.0  2.3  2.0  2.0  1.0

The sort() function reported the data by increasing order with the smallest value first. The sort(x,decreasing) command sorted the data by decreasing order with the highest number first.

##E 
greater.than.mean<-gibbons[gibbons>mean(gibbons)]
str(greater.than.mean)
##  num [1:16] 6.7 8.9 9 9.9 8.7 6.5 7 12 7 8 ...
##F
hist(gibbons, xlab = "Gibbon density", 
     main = "Distribution of Gibbon densities", 
     col = "orange")

hist(gibbons, xlab = "Gibbon density", 
     main = "Distribution of Gibbon densities", 
     col = "orange", breaks=7 )
hist(gibbons, xlab = "Gibbon density", 
     main = "Distribution of Gibbon densities", 
     col = "orange", breaks=8 )

This changes the number of bins in the histogram and spreads the data out

##G
hist(gibbons, xlab = "Gibbon density",
     main = "Distribution of Gibbon densities", 
     col = "orange", breaks=10, prob=TRUE)
     
     curve(dnorm(x, sd=0.5*(mean(gibbons))) , from=0, to=12, col="red", add=TRUE)

##H
plot(gibbons~figs,  xlab = "Fig density",ylab="Gibbon Density" )

plot(gibbons~figs,  xlab = "Fig density",ylab="Gibbon Density", pch=24, col="blue", cex= 3, bg="blue")
     
     
     abline(h=mean(gibbons))

##I
gf1<-lm(gibbons~figs)
summary(gf1)
## 
## Call:
## lm(formula = gibbons ~ figs)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.07598 -0.34411  0.08961  0.26260  0.87062 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 0.363441   0.218076   1.667    0.107    
## figs        0.118593   0.004163  28.487   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4924 on 28 degrees of freedom
## Multiple R-squared:  0.9666, Adjusted R-squared:  0.9655 
## F-statistic: 811.5 on 1 and 28 DF,  p-value: < 2.2e-16

The output of the linear model shoes that figs density is highly correlated to gibbon density as shown by the p-value of <2e-16.

##J
plot(gibbons,figs,xlab = "Fig density",ylab="Gibbon Density", pch=21, col="purple", cex= 2, bg="lavender" )
abline(gf1)

#Exercise 3
##A
mean(gibbons)
## [1] 6.023333

The issue with the original code is that it was incorrectly capitalized.

##B

plot(gibbons ~ figs, 
     xlab = "Fig density", 
     ylab = "Gibbon density",
     main = "Gibbon density vs. fig stem density", 
     col = "darkgreen")

The issue here was that darkgreen was not in quotation marks.

##B
hist(figs)
abline(h = mean(figs))

This code runs correctly

##D
plot(gibbons ~ figs, 
     xlab = "Fig density", 
     ylab = "Gibbon density",
     main = "Gibbon density vs. fig stem density")

The issue is that there was not a comma after ylab=“Gibbon density”.

##D
seq(from= 9, to= 10, by= 0.1)
##  [1]  9.0  9.1  9.2  9.3  9.4  9.5  9.6  9.7  9.8  9.9 10.0

The code needed to have the indications of “from”, “to” and “by”