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DUFS
Direction
Unusual
Form
Strength
Direction
+/-/none
Unusual
clusters, outliers
Form
linear/non-linear
Strength
strong/weak/moderate
Context
the relationship between variable 1 & 2
Interpreting r (correlation coefficient)
use DUFS except for U
strong (-1), moderate (-0.5), weak (0), moderate (0.5), strong (1)
nonresistant to outliers
has no units
as long as pattern of points stays same r is same
y=a+bx
prediction = y-int + slope x
extrapolation
predictions outside data set
residuals
actual - prediction (A-P)
interpret residuals
the actual context of y was residual higher/lower than predicted for x-value.
y-int
when context of x is 0, the predicted context of y is y-int
slope
a predicted slope in context for every context of x
residual plots
show how good a fit the LSRL is worth the data (better than r!)
we want to see a random scatter with no pattern or large clusters
r^2 (coefficient of determination)
measures the % reduction in Sigma(residual)^2 when using LSRL
interpret r^2
About (r^2)% of the variability in context of y is accounted for by the LSRL
standard deviation of the residuals (s)
= square root (sigma r^2)/(n-2)
n-2 because 2 points makes a line
no variation from LSRL
interpret s
The actual context of y is typically about s away from the number predicted by the LSRL.
why not just use residuals?
Any LSRL has sigma residuals about equal to 0, so r^2 tells us more!
r^2 = sigma (residuals)^2 = (correlation)^2
(slope) b =
r sy/sx
S.D. of y residuals
S.D. of x residuals
(y-int) a =
y-bar = b x-bar
mean y & x
To transform data, use inverses
function I graph
linear I x vs. y
exponent I x vs. logy
power I logx vs. logy
predictions/residuals
substitute into the transferred LSRL may need to use algebra to solve for y
inverses → log vs. 10^x ; lnx vs. e^x ; x^3 vs. cubic root x ; etc.
choosing the best regression
check transformed scatterplot for linear pattern
check residual plot for no leftover pattern
if deciding between several option
r close to +-1
r^2 close to 1
s small as possible
last two are better than r
Note 
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