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IPS6eCh02_4bb - Looking at Data Relationships IPS Chapter...

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    Looking at Data - Relationships Cautions about Correlation and  Regression IPS Chapter 2.4
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Objectives (IPS Chapter 2.4) Cautions about correlation and regression Residuals Outliers and influential points Lurking variables Correlation/regression using averages The restricted range problem
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Correlation/regression using averages Many regression or correlation studies use average data. While this is appropriate, you should know that correlations based on averages are usually quite higher than those made on the raw data. The correlation is a measure of spread (scatter) in a linear relationship. Using averages greatly reduces the scatter. Therefore, r and r 2 are typically greatly increased when averages are used.
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Each dot represents an average. The variation among boys per age class is not shown. Should parents be worried if their son does not match the point for his age? If the raw values were used in the correlation instead of the mean, there would be a lot of spread in the y -direction, and thus the correlation would be smaller. Boys These histograms illustrate that each mean represents a distribution of boys of a particular age. Boys
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That's why typically growth charts show a range of values (here from 5th to 95th percentiles). This is a more comprehensive way of displaying the same information.
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The distances from each point to the least-squares regression line give us potentially useful information about the contribution of individual data points to the overall pattern of scatter.
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