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456 CHAPTER 9 SIMPLE LINEAR REGRESSION AND CORRELATION
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Extrapolation
Extrapolation
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FIGURE 9.8.1
Sampled Interval
Example of extrapolation.
our sample by chance is drawn only from the interval where the relationship is linear,
we have only a limited representation of the population, and to project the
sample results beyond the interval represented by the sample may lead to false conclusions.
Figure 9.8.1 illustrates the possible pitfalls of extrapolation.
9.9 SUMMARY
In this chapter, two important tools of statistical analysis, simple linear regression and
correlation, are examined. The following outline for the application of these techniques
has been suggested.
1. Identify the model. Practitioners must know whether the regression model or the
correlation model is the appropriate one for answering their questions.
2. Review assumptions. It has been pointed out several times that the validity of the
conclusions depends on how well the analyzed data fit the chosen model.
3. Obtain the regression equation. We have seen how the regression equation is
obtained by the method of least squares. Although the computations, when done
by hand, are rather lengthy, involved, and subject to error, this is not the problem
today that it has been in the past. Computers are now in such widespread use that
the researcher or statistician without access to one is the exception rather than the
rule. No apology for lengthy computations is necessary to the researcher who has
a computer available.
4. Evaluate the equation. We have seen that the usefulness of the regression equation
for estimating and predicting purposes is determined by means of the analysis