Operation Manual

Chapter 12: Statistics 189
The new function y=.192x
.522
appears to fit the data well. To get more information, examine a residual
plot.
The new residual plot shows that the residuals are random in sign, with the residuals increasing in
magnitude as the string length increases.
To see the magnitudes of the residuals, continue with these steps.
Now that you have a good model for the relationship between length and period, you can use the
model to predict the period for a given string length. To predict the periods for a pendulum with string
lengths of 20 cm and 50 cm, continue with these steps.
28. Press o to display the Y= editor.
Press | Í to deselect
Y1.
Press } Í to turn off Plot 1. Press ~Í to turn
on Plot 2.
Note: Step 19 defined Plot 2 to plot residuals (RESID)
versus string length (
L1).
29. Press q
9 to select 9:ZoomStat from the ZOOM
menu. The window variables are adjusted
automatically, and Plot 2 is displayed. This is a scatter
plot of the residuals.
30. Press r.
Press ~ and | to trace the data. Observe the values
for Y at each point.
With this model, the largest positive residual is about
0.041 and the smallest negative residual is about
L0.027. All other residuals are less than 0.02 in
magnitude.
31. Press  ~
1 to display the VARS Y-VARS
FUNCTION
secondary menu, and then press 1 to
select
1:Y1. Y1 is pasted to the home screen.
Note: You can also use the
YVARS (ta)
shortcut menu to select
Y1.
32. Press £
20 ¤ to enter a string length of 20 cm.
Press Í to calculate the predicted time of about
0.92 seconds.
Based on the residual analysis, we would expect the
prediction of about 0.92 seconds to be within about
0.02 seconds of the actual value.