Task 1

We will load the TSA library which contains all of the datasets needed to recreate the figures. The following plot is the rainfall amounts that were recorded in Los Angeles, California, over 100 years.

library(TSA)
data(larain)
plot(larain,ylab='Inches',xlab='Year',
     main = 'Time Series Plot of Los Angeles Annual Rainfall',type='o',
     pch=16)

In this TSA package there is a special function called zlag(). This function computes the lag of a time series.

plot(y=larain,x= zlag(larain),main="Scatterplotplot of
    LA Rainfall versus Last Year's LA
     Rainfall",ylab='Inches',xlab='Previous Year Inches', pch=16)

The scatterplot shows that there is little to no correlation between the previous years and the current.

data("color")
plot(color, ylab="Color Property",
     xlab= "Batch",main="Time Series 
     Plot of Color Property from a Chemical Process",
     col="aquamarine4",pch=16,type= 'o')

This data is from an industrial chemical process. The variable we are looking at is the color property from each batch of the process.

plot(y=color,x= zlag(color), main = "
     Scatterplot of Color Value verus Previous Color Value"
     ,ylab="Color Property",xlab="Previous Color Property",
     col="goldenrod",pch=16)

There is a trend in this time series but nothing significant.

data("hare")
plot(hare,ylab="Abundance",xlab="Year",main ="
     Abundance of Canadian Hare",
       type= "o",pch=16, col= "royalblue")

plot(y=hare,x=zlag(hare),main= "Hare Abundance versus
     Previous Year's Hare Abundance",
     ylab="Abundance", xlab= "Previous Abundance",
     pch=16)

The dataset above is of the Candian Hare. The points seem to be related to one another.

data("tempdub")
plot(tempdub,main="Average Monthly Temperature,Dubuque,Iowa",
     ylab="Temperature ",type = "o",pch=16)

This time series is of average monthly temperatures. It appears to have a property of seasonality.

data("oilfilters")
plot(oilfilters,main="
     Monthly Oil Filter Sales"
       ,ylab= "Sales", type='o',pch=16)

The data above is the monthly sales of dealers of specialty oil for special construction equipment. During the winter months the sales tend to be higher while during the warmer months sales tend to be lower.

plot(oilfilters,main ="Monthly Oil Filter Sales with
     Special Plotting Symbols", 
     type = 'l',ylab = "Sales",)
points(y= oilfilters,x= time(oilfilters),
       pch = as.vector(season(oilfilters)))

Task 2

data("LakeHuron")
plot(LakeHuron,ylab="Water Level",type="o",pch=16,
     main="Water Levels of Lake Huron 1875-1972")

The data gathered here is the water levels of Lake Huron from 1875 to 1972. The water levels are measured in feet. This dataset is a standard dataset that can be accessed through the dataset package in RStudio. The highest data point would be around 1880. The minimum data point would be past 1960s. There is no obvious trend for this dataset. However, due to the nature of the data one can speculate the low drops in feet could be attributed to weather conditions.