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1. Exploratory Data Analysis
1.4. EDA Case Studies
1.4.2. Case Studies Beam Deflections

Work This Example Yourself

View Dataplot Macro for this Case Study This page allows you to repeat the analysis outlined in the case study description on the previous page using Dataplot . It is required that you have already downloaded and installed Dataplot and configured your browser. to run Dataplot. Output from each analysis step below will be displayed in one or more of the Dataplot windows. The four main windows are the Output window, the Graphics window, the Command History window, and the data sheet window. Across the top of the main windows there are menus for executing Dataplot commands. Across the bottom is a command entry window where commands can be typed in.
Data Analysis Steps Results and Conclusions

Click on the links below to start Dataplot and run this case study yourself. Each step may use results from previous steps, so please be patient. Wait until the software verifies that the current step is complete before clicking on the next step.

The links in this column will connect you with more detailed information about each analysis step from the case study description.

1. Invoke Dataplot and read data.
   1. Read in the data.

 1. You have read 1 column of numbers 
    into Dataplot, variable Y.
2. Validate assumptions.
   1. 4-plot of Y.

   2. Generate a run sequence plot.

   3. Generate a lag plot.

   4. Generate an autocorrelation plot.

   5. Generate a spectral plot.

   6. Generate a table of summary
   7. Generate a linear fit to detect
      drift in location.

   8. Detect drift in variation by
      dividing the data into quarters and
      computing Levene's test statistic for
      equal standard deviations.

   9. Check for randomness by generating
      a runs test.

 1. Based on the 4-plot, there are no
    obvious shifts in location and scale,
    but the data are not random.
 2. Based on the run sequence plot, there
    are no obvious shifts in location and
 3. Based on the lag plot, the data
    are not random.
 4. The autocorrelation plot shows
    significant autocorrelation at lag 1.
 5. The spectral plot shows a single dominant
    low frequency peak.
 6. The summary statistics table displays
    25+ statistics.
 7. The linear fit indicates no drift in
    location since the slope parameter
    is not statistically significant.
 8. Levene's test indicates no
    significant drift in variation.

 9. The runs test indicates significant

3. Fit
Yi = C + A*SIN(2*PI*omega*ti+phi).
   1. Generate a complex demodulation
      phase plot.

   2. Generate a complex demodulation
      amplitude plot.

   3. Fit the non-linear model.

 1. Complex demodulation phase plot
    indicates a starting frequency
    of 0.3025.

 2. Complex demodulation amplitude
    plot indicates an amplitude of 
    390 (but there is a short start-up

 3. Non-linear fit generates final
    parameter estimates.  The
    residual standard deviation from
    the fit is 155.85 (compared to the
    standard deviation of 277.73 from
    the original data).

4. Validate fit.

   1. Generate a 4-plot of the residuals
      from the fit.

   2. Generate a nonlinear fit with
      outliers removed.

   3. Generate a 4-plot of the residuals
      from the fit with the outliers

 1. The 4-plot indicates that the assumptions
    of constant location and scale are valid.
    The lag plot indicates that the data are
    random.  The histogram and normal
    probability plot indicate that the residuals
    that the normality assumption for the
    residuals are not seriously violated,
    although there is a bend on the probablity
    plot that warrants attention.

 2. The fit after removing 3 outliers shows
    some marginal improvement in the model
    (a 5% reduction in the residual standard

 3. The 4-plot of the model fit after
    3 outliers removed shows marginal
    improvement in satisfying model 

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