Analyze and Simulate the Old Faithful Geyser

Visualize the correlation between eruption duration and time between eruptions

Get data about the Old Faithful geyser, containing eruption durations (in seconds) and the time until the next eruption (in minutes):

In[1]:=

name={"Statistics","OldFaithful"};tab=Tabular[ExampleData[name],ExampleData[name,"ColumnHeadings"]]

Out[1]=

Visualize the waiting time versus the duration:

In[2]:=

ListPlottab//Normal,





Out[2]=

Compute the correlation between the columns:

In[3]:=

AggregateRows[tab,"corr"Function[Correlation[#Duration,#WaitingTime]]]

Out[3]=

Compute the means of the durations for waiting times shorter or longer than one hour:

In[4]:=

means=AggregateRows[tab,"MeanDuration"Function[Mean[#Duration]],"WT ≥ 60"Function[#WaitingTime≥60]]

Out[4]=

Color the points of each cluster:

In[5]:=

ListPlotFindClusters[FromTabular[tab,"Matrix"]],





Out[5]=

Find a distribution that models the data:

In[6]:=

distribution=KernelMixtureDistribution[FromTabular[tab,"Matrix"],{"Adaptive",Automatic,1}]

Out[6]=

Simulate 500 points of data:

In[7]:=

syntheticData=RandomVariate[distribution,500];

Compare the simulated data points with a density histogram of the real data:

In[8]:=

ShowSmoothDensityHistogramFromTabular[tab,"Matrix"],



,ListPlotFindClusters[syntheticData,2],





Out[8]=

Related Symbols