Regression
Lines
 y=mx+b


m = slope of the line; how steep it is
b = y-intercept of the line; where the line hits
the Y axis
Slope
 Slope
is the comparative rate of change
for Y and X.
 Steeper slope indicates a greater change
 Slope = m = ∆Y = (Y2-Y1) = rise
∆X (X2-X1) run
Compact and Augmented Model
 The
Compact Model says that your best guess
for any value in a sample is the mean.

C: Yi = β0 + εi
• Anyone’s Yi value (DV) is equal to the intercept (β0) plus
error
 The
Augmented Model makes your prediction
even better than the mean by adding a
predictor(s).

A: Yi = β0 + β1X1+ … + βnXn+εi
• With the average height of 5’5 we add other predictors
like shoe size or ring size.
Parameters and Degrees of
Freedom
A parameter is a numeric quantity, that
describes a certain population characteristic.
(i.e. population mean)
 The number of betas in your compact and
augmented model indicates how many
parameters you have in each model.
 df Regression = PA-PC
 df Residual = N-PA
 df Total = N-PC

Predicting Height From Mean
Height
 How
much error was there?
 C: Yi = β0 + εi; PC =1



Where β0 is your average height and εi is your
error in the compact mode
PC = 1
Ŷc = b0 = Ӯ.
Predicting Height from Shoe
Size and Mean Height
 How
much error was there now?
 A: Yi = β0 + β1X1+ εi ; PA = 2
β0 is the adjusted mean, β1 represents the
effect of shoe size, X1 is shoe size (a
predictor) and εi is the error
 ŶA = b0+b1X1
 b1= SSxy/SSx = slope
 b0 = Ӯ – b1(Xbar1)

Proportional Reduction in Error

PRE is the amount of error you have reduced
by using the augmented model to predict height
as opposed to the compact model
= R2 = ɳ2 = SSreg
SStotal
=
SSxy
√(SSx)(SSy)
 PRE

Creating the ANOVA Table
The Coefficients Table
Comparing Regression Printout
With ANOVA
Contrast Coding
 Contrast
codes are orthogonal codes meaning
that they are unrelated codes.
 Three rules to follow when using contrast
codes:



The sum of the weights for all groups must be zero
The sum of the products for each pair must be zero
The difference in the value of positive weights and
negative weights should be one for each code
variable
http://www.stat.sc.edu/~mclaina/psyc/1st%20lab%20notes%20710.pdf
Sums of Squares Everywhere!
 SSE(C)
=SSy = SSt
 SSE(A) = SSresid =SSw
 SSreg = SSb