chicago insurance redlining example were insurance companies in chicago denying insurance in...
Post on 16-Dec-2015
213 Views
Preview:
TRANSCRIPT
Chicago Insurance Redlining Example
Were insurance companies in Chicago denying insurance in
neighborhoods based on race?
The background
• In some US cities, services such as insurance are denied based on race
• This is sometimes called “redlining.”• For insurance, many states have a “FAIR” plan
available, for (and limited to) those who cannot obtain insurance in the regular market.
• So an area with high numbers of FAIR plan policies is an area where it is hard to get insurance in the regular market.
The data (for 47 zip codes near Chicago)
• involact = # of new FAIR plan policies and renewals per 100 housing units
• race = % minority
• theft = theft per 1000 population
• fire = fires per 100 housing units
• income = median family income in $1000s
First, some description
• Descriptive statistics for the variables
• Box plots
• Histograms
• Matrix plots
• etc.
Descriptive Statistics: race, fire, theft, age, involact, income
Variable N N* Mean SE Mean StDev Minimum Q1 Median Q3
race 47 0 34.99 4.75 32.59 1.00 3.10 24.50 59.80
fire 47 0 12.28 1.36 9.30 2.00 5.60 10.40 16.50
theft 47 0 32.36 3.25 22.29 3.00 22.00 29.00 39.00
age 47 0 60.33 3.29 22.57 2.00 48.00 65.00 78.10
involact 47 0 0.6149 0.0925 0.6338 0.0000 0.0000 0.4000 0.9000
income 47 0 10.696 0.402 2.754 5.583 8.330 10.694 12.102
Variable Maximum
race 99.70
fire 39.70
theft 147.00
age 90.10
involact 2.2000
income 21.480
100806040200
16
12
8
4
0403020100
16
12
8
4
01501209060300
20
15
10
5
0
806040200
10.0
7.5
5.0
2.5
0.02.01.51.00.50.0
16
12
8
4
02016128
16
12
8
4
0
race
Frequency
fire theft
age involact income
Histogram of race, fire, theft, age, involact, income
100
75
50
25
0
40
30
20
10
0
160
120
80
40
0
80
60
40
20
0
2.0
1.5
1.0
0.5
0.0
20
15
10
5
race fire theft
age involact income
Boxplot of race, fire, theft, age, involact, income
40200 100500 18126
100
50
040
20
0 160
80
0100
50
02
1
0
100500
18
12
6
160800 210
race
fire
thef
tag
ein
vola
ct
race
inco
me
fire theft age involact income
Matrix Plot of race, fire, theft, ... vs race, fire, theft, ...
Simple linear regression model
• Fit a model with involact as the response and race as the predictor
• A strong positive relationship gives some evidence for redlining
100806040200
2.5
2.0
1.5
1.0
0.5
0.0
race
invola
ct
S 0.448832R-Sq 50.9%R-Sq(adj) 49.9%
Fitted Line Plotinvolact = 0.1292 + 0.01388 race
What’s next
• The matrix plot showed that race is correlated with other predictors, e.g., income, fire, etc.
• So it’s possible that these are the important factors in influencing involact
• Next the full model is fit
The regression equation is
involact = - 0.609 + 0.00913 race + 0.0388 fire - 0.0103 theft + 0.00827 age
+ 0.0245 income
Predictor Coef SE Coef T P
Constant -0.6090 0.4953 -1.23 0.226
race 0.009133 0.002316 3.94 0.000
fire 0.038817 0.008436 4.60 0.000
theft -0.010298 0.002853 -3.61 0.001
age 0.008271 0.002782 2.97 0.005
income 0.02450 0.03170 0.77 0.444
S = 0.335126 R-Sq = 75.1% R-Sq(adj) = 72.0%
Analysis of Variance
Source DF SS MS F P
Regression 5 13.8749 2.7750 24.71 0.000
Residual Error 41 4.6047 0.1123
Total 46 18.4796
What have we learned?
• Race is still highly significant (t = 3.94, p-value ≈ 0) in the full model
• Income is not significant (this isn’t surprising, since race and income are highly correlated).
Diagnostics
• Some plots are next.
• Uninteresting (good!)
• We’ll ignore more substantial diagnostics such as looking at leverage and influence, although these should be done.
1.00.50.0-0.5-1.0
99
90
50
10
1
Residual
Perc
ent
2.01.51.00.50.0
1.0
0.5
0.0
-0.5
-1.0
Fitted Value
Resi
dual
0.80.40.0-0.4-0.8
16
12
8
4
0
Residual
Fre
quency
454035302520151051
1.0
0.5
0.0
-0.5
-1.0
Observation Order
Resi
dual
Normal Probability Plot Versus Fits
Histogram Versus Order
Residual Plots for involact
Model selectionResponse is involact
i t n r f h c a i e a o Mallows c r f g mVars R-Sq R-Sq(adj) Cp S e e t e e 1 50.9 49.9 37.7 0.44883 X 2 63.0 61.3 19.8 0.39406 X X 3 69.3 67.2 11.5 0.36310 X X X 4 74.7 72.3 4.6 0.33352 X X X X 5 75.1 72.0 6.0 0.33513 X X X X X
top related