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```Psychological Statistics Laboratory 10
Regression Analysis
Case 1. A neuroscientist suspects that low levels of the brain neurotransmitter serotonin may be causally related
to aggressive behavior. As a first step in investigating this hunch, she decides to do a correlative study involving
nine rhesus monkeys. The monkeys are observed daily for 6 months, and the number of aggressive acts is
recorded. Serotonin levels in the striatum (a brain region associated with aggressive behavior) are also measured
once per day for each animal. The resulting data are shown below. The number of aggressive acts for each
animal is the average for the 6 months, given on a per-day basis. Serotonin levels are also average values over
the 6-month period.
Serotonin Level
Number of Aggressive
(microgm/gm)
Acts/day
0.32
6.0
0.35
3.8
0.38
3.0
0.41
5.1
0.43
3.0
0.51
3.8
0.53
2.4
0.60
3.5
0.63
2.2
A. What is your predictor variable, what is the criterion variable?
B. What is the appropriate regression technique to use and why?
C. Make an APA table and write an interpretation for Regression and implication/inference.
Model Summary
Model
R
.637a
1
R Square
Square
.405
Std. Error of the
Estimate
.320
1.01817
a. Predictors: (Constant), Serotonin
ANOVAa
Model
1
Sum of Squares
Regression
Residual
Total
df
Mean Square
4.946
7.257
1
7
12.202
8
4.946
1.037
F
Sig.
4.771
.065b
a. Dependent Variable: Aggression
b. Predictors: (Constant), Serotonin
Coefficientsa
Model
Unstandardized Coefficients
B
1
(Constant)
Serotonin
Std. Error
6.939
-7.127
1.546
3.263
Standardized
Coefficients
Beta
-.637
t
4.488
-2.184
Sig.
.003
.065
a. Dependent Variable: Aggression
Case 2. A statistics professor conducts a study to investigate the relationship between the performance of his
students on exams and their anxiety. Ten students from his class are selected for the experiment. Just before
taking the final exam, the 10 students are given an anxiety questionnaire. Here are final exam and anxiety scores
for the 10 students.
A. What is your predictor variable, what is the criterion variable?
B. What is the appropriate regression technique to use and why?
C. Make an APA table and write an interpretation for Regression and implication/inference.
Model Summary
Model
R
.691a
1
R Square
Square
.477
Std. Error of the
Estimate
.412
10.86532
a. Predictors: (Constant), Anxiety
ANOVAa
Model
1
Sum of Squares
Regression
Residual
Total
df
Mean Square
861.959
944.441
1
8
1806.400
9
861.959
118.055
F
Sig.
7.301
.027b
a. Dependent Variable: Final exam score
b. Predictors: (Constant), Anxiety
Coefficientsa
Model
Unstandardized Coefficients
B
1
(Constant)
Anxiety
125.883
-1.429
a. Dependent Variable: Final exam score
Std. Error
21.111
.529
Standardized
Coefficients
Beta
-.691
t
5.963
-2.702
Sig.
.000
.027
APA SAMPLE ON REGRESSION (LINEAR)
A clinical psychologist is interested in the relationship between testosterone level in married males and the
quality of their marital relationship. A study is conducted in which the testosterone levels of eight married men
are measured. The eight men also fill out a standardized questionnaire assessing quality of marital relationship.
The questionnaire scale is 0 – 25, with higher numbers indicating better relationships. Testosterone scores are in
nanomoles/liters of serum. The data are shown below.
A. What is your X (predictor) variable, what is Y (criterion) variable?
Predictor=Testosterone, Criterion=Marital relationship quality/Quality of marital relationship
B. What is the appropriate regression technique to use and why? Simple linear regression
C. Make an APA table and write an interpretation for Regression (indicate if your X variable significantly
Model Summary
Model
R
R Square
.562a
1
Square
.316
Std. Error of the
Estimate
.202
4.24199
a. Predictors: (Constant), Testosterone
ANOVAa
Model
1
Sum of Squares
df
Mean Square
Regression
Residual
49.908
107.967
1
6
Total
157.875
7
F
49.908
17.995
Sig.
.147b
2.774
a. Dependent Variable: Relationship
b. Predictors: (Constant), Testosterone
Coefficientsa
Model
Unstandardized Coefficients
B
(Constant)
Testosterone
1
Std. Error
24.964
-.513
Standardized
Coefficients
Beta
5.227
.308
t
Sig.
4.776
-1.665
-.562
.003
.147
a. Dependent Variable: Relationship
Table 5
Predictor of marital relationship
Model
1
Predictor
Variable
Testosterone
R
R2
F
ß
p
.562
.316
2.774
-.513
.147
Verbal
Interpretation
Not Significant
***p<.001, **p<.01
Table 5 shows the predictor of marital relationship. The correlation indicates an inverse moderate relationship
and the regression describes the total variance of marital relationship by 31.6%. However, the model implied
that Testosterone did not significantly predict marital relationship quality, F (1, 6) = 2.774, ß= -0.513, p=.147.
The implication of this is that whatever level of testosterone the married man has does not affect their marital
relationship if they become happier or not.
```
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