![]() ![]() It is important to note that by using this "greater than 2, smaller than -2 rule," approximately 5% of the measurements in a data set will be flagged even though they are perfectly fine. Therefore, any observations with a standardized residual greater than 2 or smaller than -2 might be flagged for further investigation. Note! that there are a number of alternative ways to standardize residuals, which we will consider in Lesson 11.) Recall that the empirical rule tells us that, for data that are normally distributed, 95% of the measurements fall within 2 standard deviations of the mean. In this way, we create what is called " standardized residuals." They tell us how many standard deviations above - if positive - or below - if negative - a data point is from the estimated regression line. We can make the residuals "unitless" by dividing them by their standard deviation. Therefore, there is no one "rule of thumb" that we can define to flag a residual as being exceptionally unusual. And, if your measurements are made in inches, then the units of the residuals are in inches. That is, if your measurements are made in pounds, then the units of the residuals are in pounds. The answer is not straightforward, since the magnitude of the residuals depends on the units of the response variable. Now, you might be wondering how large a residual has to be before a data point should be flagged as being an outlier. The \(r^2\) value has jumped from 5% ("no-relationship") to 61.5% (" moderate relationship")! Can one data point greatly affect the value of \(r^2\)? Clearly, it can!
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