STAT W21 Chapter Notes - Chapter 10: Heteroscedasticity, Scatter Plot
Chapter 10: Regression Diagnostics
Residual Plots
● Residual: vertical difference between the Y value of an individual and the regression line
at the value of X corresponding to that individual for regressing Y on X
○ Suppose there are n pairs of measurements of X and Y: (x1,y1)...(xn,yn)
○ The equation of the regression line is: y = ax + b
○ Vertical residual e1 for the first datum
■ e1 = y1 - (ax1 + b)
○ Vertical residual for the second datum
■ E2 = y2 - (ax2 + b)
● Regular scatter plot
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● Residual Plot
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Reading Residual Plots
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Document Summary
Residual: vertical difference between the y value of an individual and the regression line at the value of x corresponding to that individual for regressing y on x. Suppose there are n pairs of measurements of x and y: (x1,y1)(xn,yn) The equation of the regression line is: y = ax + b. Vertical residual e1 for the first datum. E1 = y1 - (ax1 + b) E2 = y2 - (ax2 + b) Residual plots make some aspects of the data easier to see. Residuals have heteroskedasticity, nonlinear or outliers only if the original data do too. It is easier to see heteroscedasticity, nonlinearity, and outliers in a residual plot than in a scatter plot of the original data. Heteroscedasticity shows up in a residual plot as a difference in the scatter of the residuals for different range of values of the independent variable.
