Transcript The SAT Scores tell a story of the U.S. Demographic

THE SAT SCORES TELL A STORY
OF THE U.S. DEMOGRAPHIC
ECON 240A
TEAM MEMBERS
Tore Stautland Bjøndal
 Chungkai Gao
 Eric Howard
 Dan Helling
 Chien-Ju Lin
 Matt Mullens

CHOICE OF STUDY: SAT SCORES
Everyone can relate to the SATs
 No ambiguity in the numbers


Source: Moore, The Basic Practice of Statistics,
2nd Edition
WHY ARE SAT SCORES INTERESTING?



Can check dependencies on other variables
Standardized test, highly valued as a college
admission criteria
Locate differences throughout the U.S.
ANGLE OF ATTACK

Scatterplots

Bar-Charts

Regressions

Wald Test

Test for equality of
means
WHAT ARE WE LOOKING AT?




How does teacher salary affect the SAT Scores of
a particular state or region?
How does region play in to SAT Scores?
How does population without a high school
education affect the SAT Scores?
Does percentage of population taking the test
matter?
DEPENDENT VARIABLE: SAT SCORES

Independents:

Teacher average salary




Region ( 9 different )

Percentage of population
taking SAT






Percentage of population
with no high school
diploma


Regions:
ENC (East North Central) - Illinois,
Indiana, Michigan, Ohio, Wisconsin
ESC (East South Central) – Alabama,
Kentucky, Mississippi, Tennessee
MA (Mid-Atlantic) – New Jersey, New
York, Pennsylvania
MTN (Mountain) – Arizona, Colorado,
Idaho, Montana Nevada, New Mexico, Utah,
Wyoming
NE (New England) – Connecticut, Maine,
Mssachusetts, New Hampshire, Rhode
Island, Vermont
PAC (Pacific) – Alaska, California, Hawaii,
Oregon, Washington
SA (South Atlantic) – Delaware, Florida,
Georgia, Maryland, North Carolina, South
Carolina, Virginia, West Virginia, District of
Columbia
WNC (West North Central) – Iowa,
Kansas, Minnesota, Missouri, Nebraska,
North Dakota, and South Dakota
WSC (West South Central) – Arkansas,
Louisiana, Oklahoma, and Texas
1200
50
A
v
45 e
r
a
40
g
e
A
v 1150
e
r
a
g
e 1100
35
T
e
30 a
c
h
25 e
r
T
o
t
a 1050
l
20 S
a
l
15 a
r
y
10
S
A
T 1000
950
(
S
c
o
r
e
5
'
0
0
0
)
900
0
ENC
ESC
MA
MTN
NE
PAC
SA
WNC
Region
Average Total SAT
Average Teacher Salary
WSC
EXPLORATORY DATA ANALYSIS
Avg. SAT Score and Teacher Salary by
region
EXPLORATORY DATA ANALYSIS
Percent of State Population Taking
Exam vs. Score
1250
1200
1150
SAT Score 1100
1050
1000
950
0
10
20
30
40
50
60
70
Percent of state population taken the SAT
80
90
DESCRIPTIVE STATISTICS
total_sat
Mean
Standard Error
Median
Mode
Standard Deviation
Sample Variance
Kurtosis
Skewness
Range
Minimum
Maximum
Sum
Count
Confidence Level(95.0%)
teacher_pay
1061.176471
9.533293811
1044
1003
68.08133544
4635.068235
-1.216442702
0.283549916
241
954
1195
54120
51
19.14818377
Mean
Standard Error
Median
Mode
Standard Deviation
Sample Variance
Kurtosis
Skewness
Range
Minimum
Maximum
Sum
Count
Confidence Level(95.0%)
35.89019608
0.871807925
35
33.1
6.2259539
38.76250196
-0.330967678
0.656093973
24
26.3
50.3
1830.4
51
1.751077717
DESCRIPTIVE STATISTICS #2
percent_taking
Mean
Standard Error
Median
Mode
Standard Deviation
Sample Variance
Kurtosis
Skewness
Range
Minimum
Maximum
Sum
Count
Confidence Level(95.0%)
percent_no_hs
35.49019608
3.680832445
30
9
26.28640146
690.974902
-1.610838305
0.22477161
76
4
80
1810
51
7.393169401
Mean
Standard Error
Median
Mode
Standard Deviation
Sample Variance
Kurtosis
Skewness
Range
Minimum
Maximum
Sum
Count
Confidence Level(95.0%)
23.77647059
0.783048784
23.3
23.8
5.592086846
31.27143529
-0.436344214
0.469814998
22.3
13.4
35.7
1212.6
51
1.572799739
STATISTICAL ANALYSIS
Average SAT Scores vs. Teacher Pay
1250
y = -4.823x + 1234.
R² = .2
1200
1150
SAT Score 1100
1050
1000
950
15
20
25
30
35
40
Teacher Pay ('000)
45
50
55
Table 2. Regress SAT on TEACHER_PAY
Method: Least Squares
Date: 12/03/08 Time: 13:07
Sample: 1 51
Included observations: 51
Variable
Coefficient
Std. Error
t-Statistic
Prob.
TEACHER_PAY
-4.823482
1.401967
-3.440510
0.0012
C
1234.292
51.05373
24.17634
0.0000
R-squared
0.194571
Mean dependent var
1061.176
Adjusted R-squared
0.178133
S.D. dependent var
68.08134
S.E. of regression
61.72041
Akaike info criterion
11.12153
Sum squared resid
186661.0
Schwarz criterion
11.19729
F-statistic
11.83711
Prob(F-statistic)
0.001196
Log likelihood
Durbin-Watson stat
-281.5991
1.053667
STATISTICAL ANAYLSIS
Dependent Variable: SAT
Table 3. Regress SAT on all the Regions
Method: Least Squares
Date: 12/03/08 Time: 13:10
Sample: 1 51
Included observations: 51
Variable
Coefficient
Std. Error
t-Statistic
Prob.
REGION_WSC
62.35000
24.43549
2.551616
0.0145
REGION_WNC
137.1714
21.32905
6.431203
0.0000
REGION_SA
-34.95556
20.31761
-1.720456
0.0927
REGION_NE
-14.06667
22.05721
-0.637736
0.5271
REGION_MTN
58.47500
20.76618
2.815877
0.0074
REGION_MA
-27.06667
26.60200
-1.017468
0.3148
REGION_ESC
90.85000
24.43549
3.717952
0.0006
REGION_ENS
73.20000
23.03800
3.177359
0.0028
C
1023.400
16.29033
62.82255
0.0000
R-squared
0.759534
Mean dependent var
1061.176
Adjusted R-squared
0.713731
S.D. dependent var
68.08134
S.E. of regression
36.42628
Akaike info criterion
10.18724
Sum squared resid
55728.71
Schwarz criterion
10.52815
F-statistic
16.58265
Prob(F-statistic)
0.000000
Log likelihood
Durbin-Watson stat
-250.7747
2.296261
STATISTICAL ANAYLSIS
Dependent Variable: SAT
Table 4. Wald Test for all the Regions
Equation: Untitled
Null Hypothesis:
C(3)=C(10)
C(4)=C(10)
C(5)=C(10)
C(6)=C(10)
C(7)=C(10)
C(8)=C(10)
C(9)=C(10)
F-statistic
8.370558
Probability
0.000003
Chi-square
58.59391
Probability
0.000000
STATISTICAL ANAYLSIS
Wald Test:
Table 5. Regress SAT on all the independent variables
Method: Least Squares
Date: 12/03/08 Time: 13:19
Sample: 1 51
Included observations: 51
Variable
Coefficient
Std. Error
t-Statistic
Prob.
PERCENT_NO_HS
-4.603835
1.060346
-4.341824
0.0001
PERCENT_TAKING
-2.559609
0.289039
-8.855574
0.0000
POPULATION
-2.76E-06
0.000633
-0.004354
0.9965
TEACHER_PAY
-0.188369
0.834608
-0.225697
0.8226
REGION_WSC
33.19694
19.44261
1.707433
0.0959
REGION_WNC
41.58660
17.30477
2.403187
0.0212
REGION_SA
20.95284
15.59610
1.343467
0.1871
REGION_NE
60.22151
15.99922
3.764029
0.0006
REGION_MTN
-14.82679
15.55241
-0.953344
0.3464
REGION_MA
60.16609
18.87989
3.186782
0.0029
REGION_ESC
62.15848
22.31379
2.785653
0.0083
REGION_ENS
30.20575
15.31225
1.972652
0.0558
C
1240.111
46.13991
26.87720
0.0000
R-squared
0.929925
Mean dependent var
1061.176
Adjusted R-squared
0.907796
S.D. dependent var
68.08134
S.E. of regression
20.67293
Akaike info criterion
9.111091
Sum squared resid
16240.05
Schwarz criterion
9.603517
F-statistic
42.02320
Prob(F-statistic)
0.000000
Log likelihood
Durbin-Watson stat
-219.3328
2.834804
STATISTICAL ANAYLSIS
Dependent Variable: SAT
CONCLUSIONS




As education level of state increases, the average
SAT Scores decreases
As average teacher pay increases test scores tend
to decrease
Differences in regional test scores are significant
Test scores decreased as the percentage of the
population taking the test increased