Stat 226 - Section 2.4 - Describing Relationships Section...

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Section 2.4 Cautions About Correlation and Regression Section 2.4 1 Describing Relationships In chapter 2, we have found that the relationship between two quantitative variables can be described numerically with the variable means and standard deviations, along with the correlation between the two variables. In addition, the least-squares regression line is a mathematical description of the relationship between an explanatory variable and a response variable. Section 2.4 2 Describing Relationships Correlation and regression are among the most useful tools available in statistics and are used regularly in business applications. It is important to use these tools appropriately. It is important to understand the limitations and potential pitfalls associated with correlation and regression. Section 2.4 3 Cautions Some of the cautions related to correlation and regression include Statistical Limitations Extrapolation Correlations Based on Averaged Data Lurking Variables Correlation is Not Causation Section 2.4 4 Statistical Limitations Correlation and regression (in the context we have discussed) describe only linear relationships. If the relationship is not linear, correlation is not an appropriate measure of the strength and direction of the relationship. In fact, there may not be a preferred direction. How can one tell if the relationship is linear or not? Scatterplot Always plot your data! Section 2.4 5 Example - Nonlinear Relationship An Example of a Quadratic Relationship 1 2 3 4 5 -2 0 2 4 Quadratic Relationship x y The form of the relationship is quadratic.
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