2.1-2.9

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

1) check transformed scatterplot for linear pattern

2) check residual plot for no leftover pattern

3) if deciding between several option

r close to +-1

r^2 close to 1

s small as possible

last two are better than r