Glossary
Fitted value: The value of the response predicted by the fitted model at a value of the regressor in the data set. If the least squares estimates of intercept and slope are
and
, the fitted value for regressor value
is
.
Method of Least Squares: Method of model fitting that estimates parameters by minimizing the sum of squared errors (SSE). Assuming (1) the simple linear regression model,
, (2) n data values
i=1,...,n, and (3) estimates
of the intercept, and
of the slope, SSE is given by SSE
=
. The least squares estimators
and
are the values of
and
that make SSE(
) a minimum.
Residual: The vertical difference between a data point and the fitted line. Equivalently, the difference between the response and fitted value:
Residual plot: A plot of the residuals used to examine the model fit. Residuals may be plotted versus the regressor, the fitted values, or any other variables of interest (except the response).
SSE: Sum of Squared Errors. SSE
is a function that gives a measure of how far the line
is from the data (see the entry on Method of Least Squares for the formula). The least squares estimators of slope and intercept are those values of
and
that make SSE(
)a minimum.