Many single samples are actually collected over time. The
precipitation data set used above is an example of this kind of data.
In some cases it is reasonable to assume that the observations are
independent of one another, but in other cases it is not. One way to
check the data for some form of serial correlation or trend is to plot
the observations against time, or against the order in which they were
obtained. I will use the ` plot-points` function to produce a
scatterplot of the precipitation data versus time. The
` plot-points` function is called as

(plot-points x-variable y-variable)Our

(iseq start end).To generate the sequence we need we use

(iseq 1 30).Thus to generate the scatter plot we type

> (plot-points (iseq 1 30) precipitation) #<Object: 3423466, prototype = SCATTERPLOT-PROTO> >and the result will look like Figure 4.

**Figure 4:** Scatterplot of precipitation levels against
time.

There does not appear to be much of a pattern to the data; an independence assumption may be reasonable.

Sometimes it is easier to see temporal patterns in a plot if the
points are connected by lines. Try the above command with
` plot-points` replaced by
` plot-lines`.

The ` plot-lines` function can also be used to
construct graphs of functions. Suppose you would like a plot of
from to . The constant is predefined as
the variable ` pi` . You can construct a list of **n**
equally spaced real numbers between **a** and **b** using the expression

(rseq a b n).Thus to draw the plot of using 50 equally spaced points type

> (plot-lines (rseq (- pi) pi 50) (sin (rseq (- pi) pi 50))) #<Object: 3423466, prototype = SCATTERPLOT-PROTO> >The plot should look like Figure 5.

Scatterplots are of course particularly useful for examining the
relationship between two numerical observations taken on the same
subject. Devore and Peck [11, Exercise 2.33,] give data
for HC and CO emission recorded for 46 automobiles. The results can be
placed in two variables, ` hc` and ` co`, and these variable
can then be plotted against one another with the ` plot-points`
function:

> (def hc (list .5 .46 .41 .44 .72 .83 .38 .60 .83 .34 .37 .87 .65 .48 .51 .47 .56 .51 .57 .36 .52 .58 .47 .65 .41 .39 .55 .64 .38 .50 .73 .57 .41 1.02 1.10 .43 .41 .41 .52 .70 .52 .51 .49 .61 .46 .55)) HC > (def co (list 5.01 8.60 4.95 7.51 14.59 11.53 5.21 9.62 15.13 3.95 4.12 19.00 11.20 3.45 4.10 4.74 5.36 5.69 6.02 2.03 6.78 6.02 5.22 14.67 4.42 7.24 12.30 7.98 4.10 12.10 14.97 5.04 3.38 23.53 22.92 3.81 1.85 2.26 4.29 14.93 6.35 5.79 4.62 8.43 3.99 7.47)) CO > (plot-points hc co) #<Object: 3423466, prototype = SCATTERPLOT-PROTO> >The resulting plot is shown in Figure 6.

**Figure 6:** Plot of HC against CO.

Tue Jan 21 15:04:48 CST 1997