What's TRUE about the residual, \( e \), of a data point? It measures how far the observed value, \( Y \), is from the expected value, \( \widehat{Y} \). The residual is always negative. \( e=Y-\widehat{Y} \) The residual is always positive. All data points have equal residual. \( e=|Y-\widehat{Y}| \)
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The residual, \( e \), is indeed a measure of how far the observed value, \( Y \), is from the expected value, \( \widehat{Y} \), and is calculated as \( e = Y - \widehat{Y} \). This means that it can be positive, negative, or zero, depending on whether the observed value is above, below, or exactly equal to the expected value. A common mistake when working with residuals is assuming they are always positive or negative. In reality, they vary based on the fit of the model to the data, and interpreting them correctly is critical for understanding the accuracy of your predictions and the overall performance of your regression analysis!