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Residuals Residual = observed y – predicted y y yˆ The mean of the residuals is always zero Residuals • __A Residual______ is the vertical distance that a point on a scatterplot is from the LSRL. • The sum of the residuals is ALWAYS equal to ____zero_____. • Residuals = (given y value) – (predicted y value) Residuals • Residual Plots • A scatterplot of the residuals plotted against the x-values or the predicted or fitted values Residuals • The purpose of a residual plot is to determine if the model (equation) is an appropriate fit for the data. – The residual plot should look like a random scatter of points. Residuals • If no pattern exists between the points in the residual plot, then the model is appropriate. • If a pattern does exist, then the model is not appropriate for the data. Coefficient Of Determination • Coefficient of determination (r2) • gives the proportion of variation in y that can be attributed to an approximate linear relationship between x & y • remains the same no matter which variable is labeled x • R^2 • In a regression setting, an outlier is a data point with a large residual. • An influential point is a point that influences where the LSRL is located. If removed, it will significantly change the slope of the LSRL.
