Transcript Residuals - Fort Bend ISD

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.