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Regresyonda kavramlar:
Assumptions.
·
For each value of the independent variable, the
distribution of the dependent variable must be normal.
·
The variance of the distribution of the dependent
variable should be constant forall values of the independent variable.
·
The relationship between the dependent variable and
each independent variable should be linear, and all observations should be
independent.
Distances.
Measures to identify cases with
unusual combinations of values for the independent variables and cases that may
have a large impact on the regression model.
Mahalanobis.
A measure of how much a case’s
values on the independent variables differ from the average of all cases. A
large Mahalanobis distance identifies a case as having extreme values on one or
more of the independent variables.
Cook’s.
A measure of how much the residuals
of all cases would change if a particular case were excluded from the
calculation of the regression coefficients. A large Cook’s D indicates that
excluding a case from computation of the regression statistics changes the
coefficients substantially.
Leverage
values.
Measures the in fluence of a point
on the fit of the regression. The centered leverage ranges from 0 (no in
fluence on the fit) to (N-1)/N.
Prediction
Intervals.
The upper and lower bounds for both
mean and individual prediction intervals.
Mean.
Lower and upper bounds (two
variables) for the prediction interval of the mean
predicted response.
Individual.
Lower and upper bounds (two
variables) for the prediction interval of the dependent variable for a single
case.
Confidence
Interval.
Enter a value between 1 and 99.99 to
specify the confidence level for the two Prediction Intervals. Mean or
Individual must be selected before entering this value. Typical confidence
interval values are 90, 95, and 99.
Residuals.
The actual value of the dependent
variable minus the value predicted by the regression equation.
Unstandardized.
The difference between an observed
value and the value predicted by the
model.
Standardized.
The residual divided by an estimate
of its standard deviation. Standardized residuals, which are also known as
Pearson residuals, have a mean of 0 and a Standard deviation of 1.
Studentized.
The residual divided by an estimate
of its standard deviation that varies from case to case, depending on the
distance of each case’s values on the independent variables from the means of
the independent variables.
Deleted.
The residual for a case when that
case is excluded from the calculation of the regression coefficients. It is the
difference between the value of the dependent variable and the adjusted
predicted value.
Studentized
deleted.
The deleted residual for a case
divided by its standard error. The difference between a Studentized deleted
residual and its associated Studentized residual indicates how much difference
eliminating a case makes on its own prediction.
Influence
Statistics.
The change in the regression
coefficients (DfBeta[s]) and predicted values (DfFit) that results from the
exclusion of a particular case. Standardized DfBetas and DfFit values are also
available along with the covariance ratio.
DfBeta(s).
The difference in beta value is the
change in the regression coefficient that results from the exclusion of a
particular case. A value is computed for each term in the model, including the
constant.
Standardized DfBeta.
Standardized
difference in beta value. The change in the regression coefficient that results
from the exclusion of a particular case. You may want to examine cases
with absolute
values greater than 2 divided by the square root of N, where N is the number of
cases. A value is computed for each term in the model, including the constant.
DfFit.
The difference
in fit value is the change in the predicted value that results from the
exclusion of a particular case.
Standardized DfFit.
Standardized
difference in fit value. The change in the predicted value that results from
the exclusion of a particular case. You may want to examine standardized values
which in absolute value exceed 2 times the square root of p/N, where p is the
number of parameters in the model and N is the number of cases.
Covariance ratio.
The ratio of
the determinant of the covariance matrix with a particular case excluded from
the calculation of the regression coefficients to the determinant of the
covariance matrix with all cases included. If the ratio is close to 1, the case
does not significantly alter the covariance matrix.
Regression Coefficients.
Estimates
displays Regression coefficient B, standard error of B, standardized
coefficient beta, t value for B, and two-tailed significance level of t.
Confidence intervals
displays
confidence intervals with the specified level of confidence for each regression
coefficient or a covariance matrix.
Covariance matrix
displays a
variance-covariance matrix of regression coefficients with covariances off the
diagonal and variances on the diagonal. A correlation matrix is also displayed.
Model fit.
The variables
entered and removed from the model are listed, and the following
goodness-of-fit statistics are displayed: multiple R, R2 and adjusted R2,
standard error of the estimate, and an analysis-of-variance table.
R squared change.
The change in
the R2 statistic that is produced by adding or deleting an independent
variable. If the R2 change associated with a variable is large, that means that
the variable is a good predictor of the dependent variable.
Descriptives.
Provides the
number of valid cases, the mean, and the standard deviation for each variable
in the analysis. A correlation matrix with a one-tailed significance level and
the number of cases for each correlation are also displayed.
Partial Correlation.
The correlation
that remains between two variables after removing the correlation that is due
to their mutual association with the other variables. The correlation between
the dependent variable and an independen t variable when the linear effects of
the other independent variables in the model have been removed from both.
Part Correlation.
The correlation
between the dependent variable and an independent variable when the linear
effects of the other independent variables in the model have been removed from
the independent variable. It is related to the change in R-squared when a
variable is added to an equation. Sometimes called the semipartial correlation.
Collinearity diagnostics.
Collinearity
(or multicollinearity) is the undesirable situation when one independent
variable is a linear function of other independent variables. Eigenvalues of
the scaled and uncentered cross-products matrix, condition indices, and
variance-decomposition proportions are displayed along with variance inflation
factors (VIF) and tolerances for individual variables.
Residuals.
Displays the
Durbin-Watson test for serial correlation of the residuals and casewise
diagnostics for the cases meeting the selection criterion (outliers above n
standard deviations).
