1. The file RIMS.SYD contains three variables and 10 cases.  Each case represents ceramic vessel; the variable DIAMETER is the rim diameter in cm, VOLUME is the vessel volume in liters, and SIZE is the floor area in square meters of the house in which the vessel was found.

• Calculate the correlation matrix for these variables (using Pearson’s r), draw a scatterplot matrix, and interpret your results.
• Plot the values of VOLUME against DIAMETER (i.e., be sure that VOLUME is on the y-axis) and fit a line that describes the relationship between these two variables (you can fit a resistant line by hand or a least-squares line using the Statistics | Regression | Linear procedure in SYSTAT).  Show this line by superimposing it on the scatter diagram (you can display the least-squares line in SYSTAT by using the SMOOTH=LINEAR option with the PLOT command, or the “Linear” smoother in the scatterplot options dialog box).
• Now calculate the residuals from the above line and plot these residuals against house size.  (You can get the residuals in SYSTAT by checking “Save” in the linear regression dialog box and selecting “Residuals.”)

2. The dataset WARRIOR.SYD contains real data on Mississippian settlements in the Black Warrior valley.  SITE$ is the site name.  TYPE$ records whether a site is a "village" (without mounds) or a "center" (with at least one mound).  SIZE is the extent of the site's midden area in acres.  ACRES records the number of acres of arable land within a 0.6 mile walk of the site.  And BUSHELS is an estimate of the annual productivity of that farmland in thousands of bushels of corn.

• Plot SIZE against BUSHELS and calculate the correlation between these variables.
• Find the equation of the least-squares (regression) line that best fits this scatter of points.
• Now find the resistant line for the same set of points.
• Compare the two lines and discuss your results.
• Optionally, you may wish to repeat the above steps leaving Moundville out of the dataset.

3. Using the data in KNOLL.SYD, plot CONCHS against LEVEL and fit a lowess curve to the resulting scatter.  (You can do this by using the SMOOTH=LOWESS option of the PLOT command, or the “LOWESS” smoother in the scatterplot options dialog box.)  How does changing the F parameter (i.e., the TENSION option) affect the results?
 

4. Using the data in POINTS.SYD, compute the degree of association between the variables FACETS$ and CONTEXT$.  Compute phi, phi/phi_max (Cole's C7), and Yule's Q and compare the results (you can use the Statistics | Tables | Crosstabs | Two-way procedure to construct the contingency table and compute some of the coefficients; note the Statistics button in the lower right corner of the dialog box).   What do these results mean?

Datasets for this exercise (right-click to download):

• Rims.syd
• Warrior.syd
• Knoll.syd
• Points.syd

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