Page 203 - DMGT404 RESEARCH_METHODOLOGY

Unit 9: Correlation and Regression

– 0.046 max(0, 234 – ibt) Notes
– 0.016 max(0, wind – 7) max(0, 200 – vis)

Figure 9.10

Variable Interaction in a MARS Model

This expression models air pollution (the ozone level) as a function of the temperature and a few
other variables. Note that the last term in the formula (on the last line) incorporates an interaction
between wind and vis.

The figure on the right plots the predicted ozone as wind and vis vary, with the other variables
fixed at their median values. The figure shows that wind does not affect the ozone level unless
visibility is low. We see that MARS can build quite flexible regression surfaces by combining
hinge functions.

Self Assessment

Fill in the blanks:

18. The regression equations are useful for predicting the value of ....................... variable for
given value of the ....................... variable.
19. …………………………….is a form of regression analysis introduced by Jerome Friedman.
20. The ……………regression is a non-parametric technique in statistics to estimate the
conditional expectation of a random variable.

9.5 Summary

 Researchers sometimes put all the data together, as if they were one sample.
 There are two simple ways to approach these types of data.
 We can use the technique of correlation to test the statistical significance of the association.
 In other cases we use regression analysis to describe the relationship precisely by means
of an equation that has predictive value.

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