1. What is a model?

“All models are wrong…but some models are useful.” – George Box (maybe)

What are some types of models you’ve ? (let’s aim for a diverse list)

• Role model

• Linear regression model

• classification model

• arma model (time-series model)

• logistic regression model

• super model

• model organism

• clustering model

• large language model

• template

• lego model

• architectural model

• model train

Okay, then what is a model?

• input, output

• framework to follow

• function

• mold

• simplifications/abstractions of real phenomena

How are models useful? What are their limitations?

import pandas as pd
import matplotlib.pyplot as plt

sp500 = pd.read_csv('https://raw.githubusercontent.com/GettysburgDataScience/datasets/refs/heads/main/sp500_1950_2025_weekly.csv', 
                    parse_dates = ['Date'], thousands = ',')
sp500.head()

	Date	Price	Open	High	Low	Vol.	Change %
0	2025-08-31	6437.47	6386.45	6445.17	6360.53	NaN	-0.35%
1	2025-08-24	6460.26	6457.67	6508.23	6429.21	NaN	-0.10%
2	2025-08-17	6466.91	6445.02	6478.89	6343.86	NaN	0.27%
3	2025-08-10	6449.80	6389.67	6481.34	6364.06	NaN	0.94%
4	2025-08-03	6389.45	6271.71	6395.16	6271.71	NaN	2.43%

murders_df = pd.read_csv('https://raw.githubusercontent.com/GettysburgDataScience/datasets/refs/heads/main/cdc_murdermortality_2023.csv',
                         thousands = ',')
murders_df.describe()

	YEAR	RATE	DEATHS
count	502.000000	477.000000	502.000000
mean	2018.515936	6.598323	413.547809
std	2.880651	3.969087	458.695970
min	2014.000000	0.000000	10.000000
25%	2016.000000	3.600000	72.250000
50%	2019.000000	6.100000	262.000000
75%	2021.000000	8.500000	603.500000
max	2023.000000	33.100000	2495.000000

murders_df['POP'] = murders_df['DEATHS']/murders_df['RATE']
murders_df.head()

	YEAR	STATE	RATE	DEATHS	URL	POP
0	2023	AL	14.8	717	/nchs/state-stats/states/al.html	48.445946
1	2023	AK	8.5	61	/nchs/state-stats/states/ak.html	7.176471
2	2023	AZ	7.5	531	/nchs/state-stats/states/az.html	70.800000
3	2023	AR	11.3	325	/nchs/state-stats/states/ar.html	28.761062
4	2023	CA	5.1	1972	/nchs/state-stats/states/ca.html	386.666667

hw_df = pd.read_csv('https://raw.githubusercontent.com/GettysburgDataScience/datasets/refs/heads/main/SOCR-HeightWeight.csv',
                    index_col = 0)
hw_df.head()

	Height(Inches)	Weight(Pounds)
Index
1	65.78331	112.9925
2	71.51521	136.4873
3	69.39874	153.0269
4	68.21660	142.3354
5	67.78781	144.2971

fig, ax = plt.subplots(1, 3, figsize = (20, 5))

# Height vs Weight
ax[0].scatter(hw_df['Height(Inches)'], hw_df['Weight(Pounds)'], s = 1, alpha = 0.2)
ax[0].set_title('US Height vs Weight')
ax[0].set_xlabel('Height (in)')
ax[0].set_ylabel('Weight (lbs)')

# Homocides
murders2023_df = murders_df.query('YEAR==2023')
ax[1].scatter(murders2023_df['POP'], murders2023_df['DEATHS'], s = 10)

for i, row in murders2023_df.iterrows():
    ax[1].annotate(row['STATE'], (row['POP'], row['DEATHS']), fontsize=8, alpha = 0.5)

ax[1].set_title('2023 Homocides by population for US states')
ax[1].set_xlabel('Population (100K residents)')
ax[1].set_ylabel('Homocides')

# S&P 500
ax[2].plot(sp500['Date'], sp500['Price'])

ax[2].set_title('S&P500 over time')
ax[2].set_ylabel('Price at end of week ($)')
ax[2].set_xlabel('Date')

plt.show()

Answer the following questions based on the plots above.

US Height vs Weight

• Given a room of 1000 Americans, what do you think the average height and weight would be?

• Suppose a 6’ American (72 in), how much would you predict them to weigh?

• What information might change your answers above?

US Homocides

• Which states have a number of homocides above expectation?

• If there were a new state with 30M residents, how many homocides would you expect?

S&P 500

• When has the economy experienced there significant bubbles or recessions?

• What do you expect the SP500 price to be in 2030?

How did you arrive at your answers for these questions?