install.packages(“devtools”) library(“devtools”) install_github(“ndphillips/yarrr”) library(“yarrr”)

capture <- read.table("http://nathanieldphillips.com/wp-content/uploads/2015/12/capture.txt", 
                      sep = "\t", 
                      header = T)

??capture

# Q0

#C
names(capture)
##  [1] "size"          "cannons"       "style"         "warnshot"     
##  [5] "date"          "heardof"       "decorations"   "daysfromshore"
##  [9] "speed"         "treasure"
# D
head(capture)
##   size cannons   style warnshot date heardof decorations daysfromshore
## 1   48      54 classic        0  172       1           8            28
## 2   51      56  modern        0   15       0           3             6
## 3   50      44  modern        0   63       0           3            23
## 4   54      54  modern        0  362       1           2            23
## 5   50      56  modern        0  183       1           2            12
## 6   51      48  modern        0  279       0           1             3
##   speed treasure
## 1    16     2175
## 2    29     2465
## 3    18     1925
## 4    19     2200
## 5    21     2290
## 6    24     2195
# Q1
# A
plot(x = capture$size,
y = capture$treasure,
xlab = "Ship size",
ylab = "treasure in the ship",
main = "Relationship between size and treasure")

size.treasure.lm <- lm(treasure~ size,
data = capture)
abline(size.treasure.lm,
lty = 1,
lwd = 2,
col = "coral")

# B
plot(x = capture$cannons,
y = capture$treasure,
xlab = "cannons",
ylab = "treasure in the ship",
main = "Relationship between cannons and treasure")
cannons.treasure.lm <- lm(treasure~ cannons,
data = capture)
abline(cannons.treasure.lm,
lty = 1,
lwd = 2,
col = "blue")

# C
plot(x = capture$date,
y = capture$treasure,
xlab = "date",
ylab = "treasure in the ship",
main = "Relationship between date and treasure")
date.treasure.lm <- lm(treasure~ date,
data = capture)
abline(date.treasure.lm,
lty = 1,
lwd = 2,
col = "red")

# D
plot(x = capture$decorations,
y = capture$treasure,
xlab = "decorations",
ylab = "treasure in the ship",
main = "Relationship between decorations and treasure")
decorations.treasure.lm <- lm(treasure~ decorations,
data = capture)
abline(decorations.treasure.lm,
lty = 1,
lwd = 2,
col = "green")

# E
plot(x = capture$daysfromshore,
y = capture$treasure,
xlab = "daysfromshore",
ylab = "treasure in the ship",
main = "Relationship between daysfromshore and treasure")
daysfromshore.treasure.lm <- lm(treasure~ daysfromshore,
data = capture)
abline(daysfromshore.treasure.lm,
lty = 1,
lwd = 2,
col = "orange")

# F
plot(x = capture$speed,
y = capture$treasure,
xlab = "speed",
ylab = "treasure in the ship",
main = "Relationship between speed and treasure")
speed.treasure.lm <- lm(treasure~ speed,
data = capture)
abline(speed.treasure.lm,
lty = 1,
lwd = 2,
col = "violet")

# Q2
require(beanplot)
## Loading required package: beanplot
# A
beanplot(treasure ~ style,
        data = capture,
        col = "blue",
        ylab = "treasure",
        xlab = "style",
        main = "treasure by style"
        )
## log="y" selected
style.treasure.lm <- lm(treasure~ style,
data = capture)
abline(style.treasure.lm,
lty = 1,
lwd = 2,
col = "violet")

# B
beanplot(treasure ~ warnshot,
        data = capture,
        col = "blue",
        ylab = "treasure",
        xlab = "warnshot",
        main = "treasure by warnshot"
        )
## log="y" selected
warnshot.treasure.lm <- lm(treasure~ warnshot,
data = capture)
abline(warnshot.treasure.lm,
lty = 1,
lwd = 2,
col = "blue")

# C
beanplot(treasure ~ heardof,
        data = capture,
        col = "blue",
        ylab = "treasure",
        xlab = "heardof",
        main = "treasure by heardof"
        )
## log="y" selected
heardof.treasure.lm <- lm(treasure~ heardof,
data = capture)
abline(heardof.treasure.lm,
lty = 1,
lwd = 2,
col = "orange")

# Q3
# A
style.treasure.median <- aggregate(formula = treasure ~ style, 
FUN = median, 
na.rm = T, 
data = capture)
style.treasure.median
##     style treasure
## 1 classic     2000
## 2  modern     1895
# B
warnshot.treasure.median <- aggregate(formula = treasure ~ warnshot, 
FUN = median, 
na.rm = T, 
data = capture)
warnshot.treasure.median
##   warnshot treasure
## 1        0     1885
## 2        1     1945
# C
decorations.treasure.median <- aggregate(formula = treasure ~ decorations, 
FUN = median, 
na.rm = T, 
data = capture)
decorations.treasure.median
##    decorations treasure
## 1            1   2657.5
## 2            2   1780.0
## 3            3   1905.0
## 4            4   1797.5
## 5            5   1880.0
## 6            6   1855.0
## 7            7   1920.0
## 8            8   1935.0
## 9            9   1935.0
## 10          10   1955.0
# Q4
# A
cor.test(~ size + cannons, 
         data = capture)
## 
##  Pearson's product-moment correlation
## 
## data:  size and cannons
## t = 0.90501, df = 998, p-value = 0.3657
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.03341657  0.09046832
## sample estimates:
##        cor 
## 0.02863584

p-value = 0.3657

# B
size.cannons.lm <- lm(size ~ cannons,
data = capture)
size.cannons.lm
## 
## Call:
## lm(formula = size ~ cannons, data = capture)
## 
## Coefficients:
## (Intercept)      cannons  
##   49.859132     0.006266
summary(size.cannons.lm)
## 
## Call:
## lm(formula = size ~ cannons, data = capture)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -12.9844  -2.8873  -0.0596   2.9028  13.1409 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 49.859132   0.262458 189.970   <2e-16 ***
## cannons      0.006266   0.006923   0.905    0.366    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.14 on 998 degrees of freedom
## Multiple R-squared:  0.00082,    Adjusted R-squared:  -0.0001812 
## F-statistic: 0.819 on 1 and 998 DF,  p-value: 0.3657

p-value = 0.3657

# Q5
# A
treasure.model <- lm(treasure ~ .,
data = capture)
treasure.model
## 
## Call:
## lm(formula = treasure ~ ., data = capture)
## 
## Coefficients:
##   (Intercept)           size        cannons    stylemodern       warnshot  
##      749.8957        22.5203        19.3817      -165.0932        89.0164  
##          date        heardof    decorations  daysfromshore          speed  
##        0.1508        92.1270       -96.3998        -8.6119         9.2639
# B
summary(treasure.model)
## 
## Call:
## lm(formula = treasure ~ ., data = capture)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -880.96 -443.16 -211.02   66.08 2427.97 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    749.8957   351.0514   2.136 0.032913 *  
## size            22.5203     5.9602   3.778 0.000167 ***
## cannons         19.3817     1.2932  14.987  < 2e-16 ***
## stylemodern   -165.0932    84.6314  -1.951 0.051371 .  
## warnshot        89.0164    61.0610   1.458 0.145205    
## date             0.1508     0.2313   0.652 0.514511    
## heardof         92.1270    54.7238   1.683 0.092595 .  
## decorations    -96.3998    10.0249  -9.616  < 2e-16 ***
## daysfromshore   -8.6119     2.8180  -3.056 0.002303 ** 
## speed            9.2639     8.3892   1.104 0.269750    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 771.4 on 990 degrees of freedom
## Multiple R-squared:  0.2661, Adjusted R-squared:  0.2594 
## F-statistic: 39.88 on 9 and 990 DF,  p-value: < 2.2e-16

There is a significant correlation between decorations and treasure

The correlation is negative, also for daysfromshore variable.

D There is no significant correlation between treasure and stylemodern,warnshot, date, heardof and speed.