John Doe
Edit these links below
in _config.yml
LinkedIn
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Portfolio
GitHub
Twitter
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Read this part
This webpage is created from a file we made in a class. To convert it to a webpage,
- In JupyterLab, click File, then “Export Notebook as”, then markdown.
- Add that file into this repo.
- Edit that file. At the top of the file, add 3 lines with exactly this and save/commit/push it.
--- layout: wide_default ---These lines make the report part of the webpage wider, which is usually a good idea for reports.
Note 1: You can do this on any page in the website.
Note 2: The site won’t look great on Mobile.
- Naturally, you’ll want to add a link to the new page you just made in your portfolio section on the main page.
- Read the chapter on the website! It contains a lot of extra information we won’t cover in class extensively.
- After reading that, I recommend this webpage as a complimentary place to get additional intuition.
Today
Finish picking teams and declare initial project interests in the project sheet
Today is mostly about INTERPRETING COEFFICIENTS (5.2.4 in the book)
- 25 min reading groups: Talk/read through two regression pages (5.2.3 and 5.2.4)
- Assemble your own notes. Perhaps in the “Module 4 notes” file, but you can do this in any file you want.
- After class, each group will email their notes to Julio/me for participation. (Effort grading.)
- 10 min: class builds joint “big takeaways and nuanced observations”
- 5 min: Interpret models 1-2 as class as practice.
- 20 min reading groups: Work through remaining problems below.
- 10 min: wrap up
Our notes (920am class)
- R2 is the % variation in y captured by the model
- You can never DECREASE r2 by adding variables to the model… but this is a problem, leads to overfitting and even adding “random noise” variables
-
Instead - focus on Adj R2: it penalizes adding adtl variables
- John/Theo R2: % of variation in y that our model explains
- “higher is better”
- when you are vars to a model, R2 can’t decrease… tendency to overfit
- so use Adj R2: R2 with a penalty for additional variables
- Ian: by transforming variables, we change the interpretation of the relationship
- logs, polynomails, etc
- Colin: Categorical variables: a regression will give you a coefficient for each level EXCEPT ONE
- The coefficients on the levels in the reg are “relative” to the omitted group
- interpration is mechanical
- A (1 unit) increase in X is assoc with a ( ) change in Y, holding all else constant
import pandas as pd
from statsmodels.formula.api import ols as sm_ols
import numpy as np
import seaborn as sns
from statsmodels.iolib.summary2 import summary_col # nicer tables
url = 'https://github.com/LeDataSciFi/ledatascifi-2022/blob/main/data/Fannie_Mae_Plus_Data.gzip?raw=true'
fannie_mae = pd.read_csv(url,compression='gzip')
Clean the data and create variables you want
fannie_mae = (fannie_mae
# create variables
.assign(l_credscore = np.log(fannie_mae['Borrower_Credit_Score_at_Origination']),
l_LTV = np.log(fannie_mae['Original_LTV_(OLTV)']),
l_int = np.log(fannie_mae['Original_Interest_Rate']),
Origination_Date = lambda x: pd.to_datetime(x['Origination_Date']),
Origination_Year = lambda x: x['Origination_Date'].dt.year,
const = 1
)
.rename(columns={'Original_Interest_Rate':'int'}) # shorter name will help the table formatting
)
# create a categorical credit bin var with "pd.cut()"
fannie_mae['creditbins']= pd.cut(fannie_mae['Co-borrower_credit_score_at_origination'],
[0,579,669,739,799,850],
labels=['Very Poor','Fair','Good','Very Good','Exceptional'])
fannie_mae['Borrower_Credit_Score_at_Origination'].describe()
count 134481.000000
mean 742.428797
std 53.428076
min 361.000000
25% 707.000000
50% 755.000000
75% 786.000000
max 850.000000
Name: Borrower_Credit_Score_at_Origination, dtype: float64
Statsmodels
As before, the psuedocode:
model = sm_ols(<formula>, data=<dataframe>)
result=model.fit()
# you use result to print summary, get predicted values (.predict) or residuals (.resid)
Now, let’s save each regression’s result with a different name, and below this, output them all in one nice table:
# one var: 'y ~ x' means fit y = a + b*X
reg1 = sm_ols('int ~ Borrower_Credit_Score_at_Origination ', data=fannie_mae).fit()
reg1b= sm_ols('int ~ l_credscore ', data=fannie_mae).fit()
reg1c= sm_ols('l_int ~ Borrower_Credit_Score_at_Origination ', data=fannie_mae).fit()
reg1d= sm_ols('l_int ~ l_credscore ', data=fannie_mae).fit()
# multiple variables: just add them to the formula
# 'y ~ x1 + x2' means fit y = a + b*x1 + c*x2
reg2 = sm_ols('int ~ l_credscore + l_LTV ', data=fannie_mae).fit()
# interaction terms: Just use *
# Note: always include each variable separately too! (not just x1*x2, but x1+x2+x1*x2)
reg3 = sm_ols('int ~ l_credscore + l_LTV + l_credscore*l_LTV', data=fannie_mae).fit()
# categorical dummies: C()
reg4 = sm_ols('int ~ C(creditbins) ', data=fannie_mae).fit()
reg5 = sm_ols('int ~ C(creditbins) -1', data=fannie_mae).fit()
Ok, time to output them:
# now I'll format an output table
# I'd like to include extra info in the table (not just coefficients)
info_dict={'R-squared' : lambda x: f"{x.rsquared:.2f}",
'Adj R-squared' : lambda x: f"{x.rsquared_adj:.2f}",
'No. observations' : lambda x: f"{int(x.nobs):d}"}
# q4b1 and q4b2 name the dummies differently in the table, so this is a silly fix
reg4.model.exog_names[1:] = reg5.model.exog_names[1:]
# This summary col function combines a bunch of regressions into one nice table
print('='*108)
print(' y = interest rate if not specified, log(interest rate else)')
print(summary_col(results=[reg1,reg1b,reg1c,reg1d,reg2,reg3,reg4,reg5], # list the result obj here
float_format='%0.2f',
stars = True, # stars are easy way to see if anything is statistically significant
model_names=['1','2',' 3 (log)','4 (log)','5','6','7','8'], # these are bad names, lol. Usually, just use the y variable name
info_dict=info_dict,
regressor_order=[ 'Intercept','Borrower_Credit_Score_at_Origination','l_credscore','l_LTV','l_credscore:l_LTV',
'C(creditbins)[Very Poor]','C(creditbins)[Fair]','C(creditbins)[Good]','C(creditbins)[Vrey Good]','C(creditbins)[Exceptional]']
)
)
============================================================================================================
y = interest rate if not specified, log(interest rate else)
============================================================================================================
1 2 3 (log) 4 (log) 5 6 7 8
------------------------------------------------------------------------------------------------------------
Intercept 11.58*** 45.37*** 2.87*** 9.50*** 44.13*** -16.81*** 6.65***
(0.05) (0.29) (0.01) (0.06) (0.30) (4.11) (0.08)
Borrower_Credit_Score_at_Origination -0.01*** -0.00***
(0.00) (0.00)
l_credscore -6.07*** -1.19*** -5.99*** 3.22***
(0.04) (0.01) (0.04) (0.62)
l_LTV 0.15*** 14.61***
(0.01) (0.97)
l_credscore:l_LTV -2.18***
(0.15)
C(creditbins)[Very Poor] 6.65***
(0.08)
C(creditbins)[Fair] -0.63*** 6.02***
(0.08) (0.02)
C(creditbins)[Good] -1.17*** 5.48***
(0.08) (0.01)
C(creditbins)[Exceptional] -2.25*** 4.40***
(0.08) (0.01)
C(creditbins)[Very Good] -1.65*** 5.00***
(0.08) (0.01)
R-squared 0.13 0.12 0.13 0.12 0.13 0.13 0.11 0.11
R-squared Adj. 0.13 0.12 0.13 0.12 0.13 0.13 0.11 0.11
R-squared 0.13 0.12 0.13 0.12 0.13 0.13 0.11 0.11
Adj R-squared 0.13 0.12 0.13 0.12 0.13 0.13 0.11 0.11
No. observations 134481 134481 134481 134481 134481 134481 67366 67366
============================================================================================================
Standard errors in parentheses.
* p<.1, ** p<.05, ***p<.01
fannie_mae['int'].describe()
count 135038.000000
mean 5.238376
std 1.289895
min 2.250000
25% 4.250000
50% 5.250000
75% 6.125000
max 11.000000
Name: int, dtype: float64
Today. Work in groups. Refer to the lectures.
You might need to print out a few individual regressions with more decimals.
- Interpret coefs in model 1-4
- Model 1: The predicted interest rate for borrowers with a credit score of 0 is 11.5%.
- Model 1: A 1 unit inc in credit score is assoc with a 1 b.p. decrease in interest rates, holding all other X constant.
- If credit score goes from 700 to 707: rate falls 7 b.p.
- If credit score goes from 600 to 606: rate falls 6 b.p.
- Model 2: A 1% inc in credit score is assoc with a 6.07 b.p. decrease in interest rates, holding all other X constant.
- If credit score goes from 700 to 707: rate falls 6.07 b.p.
- If credit score goes from 600 to 606: rate falls 6.07 b.p.
- Model 3: A 1 unit inc in credit score is assoc with a 0.17% (percent! not p.p.) decrease in interest rates, holding all other X constant.
- If credit score goes from 700 to 707: rate falls by 6 b.p. (assuming y starts at avg y of 5.23)
- Model 4: A 1% inc in credit score is assoc with a 1.19% decrease in interest rates, holding all other X constant.
- If credit score goes from 700 to 707: rate falls by 6 b.p. (assuming y starts at avg y of 5.23)
- Interpret coefs in model 5
- Model 5: A 1% inc in credit score is assoc with a 5.99 b.p. decrease in interest rates, holding constant log_LTV.
- Interpret coefs in model 6 (and visually?)
- int = a + cl_credscore + dl_LTV + el_credscorel_LTV
- deriv of int w.r.t to credit score: 3.22 - 2.18 * log(LTV)
- For loans with an average log(LTV) of 4.2= 3.22-2.18*4.2 = -5.936
- A 1 % increase in credit score is assoc with interest rates that are 5.936 bp lower, ceterus paribus
- Interpret coefs in model 7 (and visually? + comp to table)
- Interpret coefs in model 8 (and visually? + comp to table)
- Add l_LTV to Model 8 and interpret (and visually?)