How Faithful is Old Faithful?

Warm-up:

Did you know there is a relationship between the chirps per second of a ground cricket and the corresponding ground temperature?

The data is found at the website http://mathbits.com/Mathbits/TISection/Statistics2/linearREAL.htm

Read this data into R.  Call the variables chirps and temp.  Construct
a scatterplot of chirps (horizontal) against temp (vertical).  Find a 
least-squares fit and place the line on the plot.  Interpret the line.

1.  Look up Old Faithful Geyser on the internet.  Where is it located?
What are some things about this geyser that make it famous?  Have you
ever visited this geyser?

The dataset http://bayes.bgsu.edu/m400/data/oldfaith.txt contains
the following data collected about 107 eruptions:

Date
WaitNext - the waiting time in minutes
DurLast - the duration of the previous eruption
WaitLast - the waiting time for the next eruption

2.  Construct a graph of the waiting times.  Also compute some
descriptive statistics.  Based on the graph and stats, write a 
summary paragraph about the waiting times.

3.  Construct a graph and compute summaries of the geyser durations.
Write a summary paragraph about the durations.

4.  Construct a scatterplot of DurLast (horizontal) against
WaitNext (vertical).  Describe any patterns you see in this
scatterplot.

Suppose we are interested in predicting the waiting time of
Old Faithful from the duration of the previous eruption.

5.  Find the least-squares fit -- store the fit in the variable fit.  
Write down the equation of this best line.

6.  Put the best fitting line on the scatterplot.

7.  Suppose the eruption lasts 4 minutes.  Use the line
to predict the time you have to wait until the next eruption.

8.  Construct a 95% prediction interval for the time you will
have to wait until the next eruption (again if the eruption lasts
4 minutes).

9.  Explain what the 95% prediction interval means (see page 12-8).


One can look at the suitability of the best-line fit by looking at
residuals.

10.  Display the residuals.  Verify that the first residual has
been computed correctly.

11.  Construct a graph of DurLast (horizontal) against the residual
(vertical).

12.  Do you see any general pattern in the residual graph?

13.  Compare the variability of the residuals for small DurLast
against the variability of the residuals for large DurLast -- which
is larger or do they appear to be the same?

14.  Are the residuals normally distributed?  Answer this graph by
constructing two graphs:  a histogram of the residuals and a normal
probability plot of the residuals.