PSY294 Statistics for Psychology

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PSY294 Statistics for Psychology
Multiple regression further topics
1) Calculation and analysis of residuals
RESIDUAL OBSERVATION-PREDICTION
Very important in multiple regression because we
cant draw simple scatter diagrams Examine
residuals for non-random patterns using
diagnostic plots (see L3 notes)
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PSY294 Statistics for Psychology
Multiple regression further topics
2) Role of R-SQ R-SQ is a key piece of
information which can be used to assess the
importance of each X-variable in the prediction
of Y In simple linear regression (one X-variable)
we have
R-SQ
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PSY294 Statistics for Psychology
Multiple regression further topics
2) Role of R-SQ (contd.) Can also use the
partial correlation coefficient to assess the
proportion of the remaining variability explained
by an X-variable after fitting others
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PSY294 Statistics for Psychology
Multiple regression further topics
3) Order of fitting The regression line, and
overall R-SQ are the same, whichever order the
variables are fitted. However, the contribution
of each predictor (X) variable will change if the
order of fitting is changed
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PSY294 Statistics for Psychology
Multiple regression further topics
3) Order of fitting (contd.) Some predictors may
contribute very little after others have been
fitted Such predictors may be unnecessary and can
be omitted. The change in R-SQ is a useful
indicator
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PSY294 Statistics for Psychology
Multiple regression further topics
4) Significance The overall significance of the
regression is given by the p-value shown in the
Analysis of Variance table The significance of
the contribution of individual predictors is
given in the coefficient table
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PSY294 Statistics for Psychology
Multiple regression further topics
5) Confidence/prediction intervals CI is a
confidence interval for the regression line (a
measure of uncertainty in the fitting
process) PI is a plausible range of values for
the response, i.e. for an observation taken at
specified X-values
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PSY294 Statistics for Psychology
Multiple regression further topics
6) Non-linear regression APPROACH A transform
the measurements using some kind of
mathematical process, e.g. square roots,
logarithms etc. APPROACH B fit a general curve,
polynomial regression
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PSY294 Statistics for Psychology
Learning Outcomes Weeks 1 5 By now you
should know how to Calculate a correlation
coefficient r Test the significance of
r Interpret r Calculate and test Spearmans rank
correlation,
Understand the simple linear regression
model Estimate the slope, b, and intercept,
a Predict responses Calculate a residual Use
residuals to check model validity Be able to
interpret various diagnostic plots
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PSY294 Statistics for Psychology
For multiple regression understand when it is
used and what it does Calculate a multiple
correlation coefficient (2 X-variables) Calculate
a partial correlation coefficient (2
X-variables) Choose a model when there are many
potential predictor variables Use Minitab for
simple and multiple regression Interpret the
output (Analysis of Variance deferred) Be aware
of commands (BREG, STEPWISE) used for model
selection. Be aware of methods to cope with
non-linearity.