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CH. 5
Regression
(124)defined ind. var.,dep. var. free to vary, predict Y from X.
Correlation
(125)have paired X and Y scores and want to see if variables are related and how strong
the association is, no obvious IV, no preselected values of X or Y so both free to vary.
Bivariate
representation of the joint freq. of 2 var.
.
Reversion toward the mean
(126)Galton.
Reversion Line
best fitting straight line.
Correlation coefficient
(127)# that describes the degree of ass. or strength of a relationship btw 2 variables.
Pearson product moment
correlation coefficient(r
XY
or
r)
(127)measure strength & direction of linear relationship btw two quantitative var.; most widely used.
Cross Product
(131)product of the 2 deviations
(X
i
Xbar)(Y
i
Ybar)
.
Covariance
(132)obtain strength of ass. that is ind. of the # of pairs of scores, mean of the
cross product sum
(133):
S
xy
= Σ(X
i
Xbar)(Y
i
Ybar)/ n;
CPS reflects
Coefficient of Determination (r
2
)
(135)variance explained or accounted for.
Coefficient of NONdetermination(k
2
)
k
2 =
2
1
r

; variance not explained.
(136)
S
X
2
and S
Y
2
sample variances(measure of the dispersion of scores).
Common Errors in Correlation
(138)
1)
R
is not a % of association b/w 2 variables but measure of strength; 1
to 1.
2)
Interpreting
r
in terms of arbitrary descriptive labels
3)
Inferring that b/c 2 variables are correlated, 1 causes the other.
Factors that affect the size of a correlation
coefficient
(140):
1)
Nature of the relationship between X and Y:
correlation ratio or eta squared(η
2
)
determines strength of assoc. btw nonlinearly related var.
Eyeball test
(141)

most
simple evidence of nonlinearity.
2)Truncated Range
(restricted)size of
r
will be reduced.
3)
Spurious effects due to subgroups w/ different means or standard deviations(142).
Discontinuous Dist.
(144)results when sample is restricted to sm. # of points along continuum or when sample contains outliers, i.e. extreme groups.
Heteroscedasticity
(145)unequal
Homoscedasticity
dispersions are uniform.
Spearman Rank Correlation
(r
S
)
(147)

paired data are in
ranks
; measure of the
monotonic relationship btw 2 sets of ranks
(149):
r
s
=1 (6Σ(Rx
i
Ry
i
)
2
)/ (n(n
2
1))
; where
Rx
i
Ry
i
=difference btw the
i
th person’s ranks on X and Y,
n
=# of pairs of ranks; coefficient=1
if each person’s X and Y ranks are equal.
CH. 6
Regression Analysis
(160)paired data(X
i
,Y
i
) where X is the ind. variable w/ values X
i
that are selected in advance and Y is the dep.
variable w/ values Y
i
.
Multiple regression
simultaneous use of 2 or more predictors in predicting a dep. var.
Predicting Y from X
(162)(usual method)best fitting line should minimize
some function of the error in predicting Y
i
from X
i
; vertical distances on Y axis.
Prediction Error or Residual
(
e
i
);
difference between the actual ith score(Y
i
) and the predicted
score
(
Y’
i)
: e
i
=Y
i
Y
i
’
.
Principal of least squaresline of best fit
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 Spring '08
 kirk
 Correlation

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