WPA7
Ulrike
December 16, 2015
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download the data
capture <-read.table("http://nathanieldphillips.com/wp-content/uploads/2015/12/capture.txt")```
What are the names of the columns in the capture dataframe?
names(capture)## [1] "size" "cannons" "style" "warnshot"
## [5] "date" "heardof" "decorations" "daysfromshore"
## [9] "speed" "treasure"What are the first few rows of the dataframe?
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 2195Plot the relationship between the following continuous independent variable and treasure. For each plot, add axis and plot labels and a regression line showing the relationship between the independent and dependent variables.
A size
size.treasure <- lm( formula = treasure ~ size, data = capture)
plot(x = capture$size,
y = capture$treasure,
xlab = "size",
ylab = "treasure",
main = "Relationship between treasure and size")
abline(size.treasure)
B cannons
cannons.treasure <- lm(treasure ~ cannons, data = capture)
plot(x = capture$cannons,
y = capture$treasure,
xlab = "cannons",
ylab = "treasure",
main = "Relationship between treasure and cannons")
abline(cannons.treasure)
C date
date.treasure <- lm(treasure ~ date, data = capture)
plot(x = capture$date,
y = capture$treasure,
xlab = "date",
ylab = "treasure",
main = "Relationship between treasure and date")
abline(date.treasure)
D decoration
decorations.treasure <- lm(treasure ~ decorations, data = capture)
plot(x = capture$decorations,
y = capture$treasure,
xlab = "decorations",
ylab = "treasure",
main = "Relationship between treasure and decorations")
abline(decorations.treasure)
E daysfromshore
daysfromshore.treasure <- lm(treasure ~ daysfromshore, data = capture)
plot(x = capture$daysfromshore,
y = capture$treasure,
xlab = "daysfromshore",
ylab = "treasure",
main = "Relationship between treasure and days from shore")
abline(daysfromshore.treasure)
F speed
speed.treasure <- lm(treasure ~ speed, data = capture)
plot(x = capture$speed,
y = capture$treasure,
xlab = "speed",
ylab = "treasure",
main = "Relationship between treasure and speed")
abline(speed.treasure)
Q2 Now do the same for the following categorical independent variables and treasure (hint: try using the new pirateplot() function in the yarrr package! Look at how it works by running ?pirateplot). Again, add appropriate labels and a regression line in each plot.
A style:
capture\(style[capture\)style == “modern”] <- 0
capture\(style[capture\)style == “classic”] <- 1
treasure.style.glm <- glm(style ~ treasure, data = capture, family = “binomial”)
I really don’t know whats wron it doesn’t convert my style avriable into a binomial one and i don’t have an idea what to do. as I am missing class today I can’t ask you personally so I wrote my ideas in the comments
warnshot
treasure.warnshot.glm <- glm(warnshot ~ treasure,
data = capture,
family = "binomial")
capture.warnshot <- capture$warnshot == "1"
capture$treasure.cut <- cut(capture$treasure,
breaks = seq(1000, 5000, 1000))
probs <- aggregate(capture.warnshot ~ treasure.cut,
data = capture, FUN = mean)
plot(probs, xlab = "treasure (grouped)",
ylab = "p(ship fired a warnshot)",
main = "Probabiliy that a ship fired a warnshot given its amount of treasure")
heardof
treasure.heardof.glm <- glm(heardof ~ treasure,
data = capture,
family = "binomial")
capture.heardof <- capture$heardof == "1"
capture$treasure.cut <- cut(capture$treasure,
breaks = seq(1000, 5000, 1000))
probs <- aggregate(capture.heardof ~ treasure.cut,
data = capture, FUN = mean)
plot(probs, xlab = "treasure grouped", ylab = "p ship was heard of",
main = "Amount of treasure in relation to the probability that you have heard of that ship")
``` ###Q3 For each of the following variables (separately), calculate the median amount of treasure earned for each level of the IV: style, warnshot, decorations (hint: use aggregate or dplyr!)
aggregate (treasure ~ capture.heardof, data = capture, FUN = median)## capture.heardof treasure
## 1 FALSE 1875
## 2 TRUE 1940aggregate (treasure ~ capture.warnshot, data = capture, FUN = median)## capture.warnshot treasure
## 1 FALSE 1885
## 2 TRUE 1945aggregate (treasure ~ decorations, data = capture, FUN = 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 1955.0The formula notation for conducting a correlation test with cor.test() is a bit different from regular formula notation. Instead of dv ~ iv, you use ~ dv + iv. For example, the following code will test the correlation between chickens’ age and weight using the ChickWeight dataset.
cor.test(~ Time + weight,
data = ChickWeight)##
## Pearson's product-moment correlation
##
## data: Time and weight
## t = 36.725, df = 576, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.8109073 0.8599481
## sample estimates:
## cor
## 0.8371017Using the formula notation above, conduct a correlation test between the number of cannons a ship has and its size. What is the p-value?
cor.test(~cannons + size, data = capture)##
## Pearson's product-moment correlation
##
## data: cannons and size
## 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
## 0.02863584The p-Value is 0.3657.
Now do the same with linear regression. What is the p-value?
cannon.lm <- lm(cannons ~ size, data = capture)
summary(cannon.lm)##
## Call:
## lm(formula = cannons ~ size, data = capture)
##
## Residuals:
## Min 1Q Median 3Q Max
## -34.549 -14.324 -0.324 12.498 63.414
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 26.3039 7.2645 3.621 0.000308 ***
## size 0.1309 0.1446 0.905 0.365679
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 18.92 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: 0.3657The p-Value is the same (0.3657).
Q5 Conduct a linear regression with treasure as the dependent variable, and with all other variables as independent variables. Save the object as treasure.model
treasure.model<-lm (treasure ~ size + cannons + warnshot + date + heardof+ decorations + daysfromshore + speed, data = capture)Using the summary() function, print the coefficients and main statistics of the regression
summary(treasure.model)##
## Call:
## lm(formula = treasure ~ size + cannons + warnshot + date + heardof +
## decorations + daysfromshore + speed, data = capture)
##
## Residuals:
## Min 1Q Median 3Q Max
## -760.81 -451.21 -211.49 58.56 2423.42
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 604.0837 343.4865 1.759 0.078940 .
## size 22.5769 5.9685 3.783 0.000164 ***
## cannons 19.3464 1.2949 14.940 < 2e-16 ***
## warnshot 82.4122 61.0533 1.350 0.177375
## date 0.1328 0.2315 0.574 0.566326
## heardof 98.4881 54.7038 1.800 0.072104 .
## decorations -95.0941 10.0166 -9.494 < 2e-16 ***
## daysfromshore -8.4173 2.8202 -2.985 0.002909 **
## speed 8.7189 8.3965 1.038 0.299338
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 772.5 on 991 degrees of freedom
## Multiple R-squared: 0.2633, Adjusted R-squared: 0.2573
## F-statistic: 44.27 on 8 and 991 DF, p-value: < 2.2e-16as you can see from the results the more cannons a ship has the more treasure it is likely to carry, but the more decorations it has or the more days it is from shore, the less treasure it is likely to carry.
Not significantly realted to treasure are warnshots, date, heardof, and speed.
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