Transcript 10/27/2015

Psychology 202a
Advanced Psychological
Statistics
October 27, 2015
The plan for today
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Continuing correlation and regression
The decomposition of the sum of squares
Regression inference
Assumptions
The problem of restriction of range
Another way to understand correlation
Decomposing the sum of squares
• Recall that the model can be broken down
into two components:
– the part we do understand
– the part we don’t understand
• The sum of squares can be broken down
into corresponding components.
• These components have the same
additive relationship as the model
components.
Decomposition (cont.)
• This decomposition of variability is the
basis for inference in regression.
• Mean squares
• The F ratio
• The ANOVA table
The ANOVA Table
Source
Model
Error
Total
SS
df
MS
F
The ANOVA Table
Source
SS
Model
 Yˆ  M 
Error
2
e

Total
df
2
Y
 Y
 MY

2
MS
F
The ANOVA Table
Source
SS
Model
 Yˆ  M 
1
Error
2
e

N-2
Total
df
2
Y
 Y
 MY

2
N-1
MS
F
The ANOVA Table
Source
SS
df
MS
Model
 Yˆ  M 
1
SSM / dfM
Error
2
e

N–2
SSE / dfE
Total
2
Y
 Y
 MY

2
N-1
F
The ANOVA Table
Source
SS
df
MS
F
Model
 Yˆ  M 
1
SSM / dfM
MSM / MSE
Error
2
e

N–2
SSE / dfE
Total
2
Y
 Y
 MY

2
N-1
Assumptions for inference
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Linear relationship
Independent errors
Homoscedastic errors
Normally distributed errors
(digression in R)