
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
import pandas as pd

df = pd.read_csv("https://www.mth548.org/_static/kde_marathon_results/marathon_results.csv")
df["tot_minutes"] = pd.to_timedelta(df["Finish"]).dt.total_seconds()/60

df


from scipy.stats import gaussian_kde


kde = gaussian_kde(df['tot_minutes'])


kde(200)

array([0.01028678])


kde.integrate_box(120, 180)

0.09945655722252811


plt.style.use('bmh')
plt.figure(figsize=(10, 5))
kde = gaussian_kde(df['tot_minutes'], bw_method=0.01)
x = np.linspace(120, 500, 400)
plt.plot(x, kde(x));


kde2 = gaussian_kde(df['tot_minutes'], bw_method=0.5)
plt.figure(figsize=(10, 5))
x = np.linspace(120, 500, 400)
plt.plot(x, kde2(x));


dfm = df[df["M/F"] == 'M']
dff = df[df["M/F"] == 'F']

kdem = gaussian_kde(dfm['tot_minutes'])
kdef = gaussian_kde(dff['tot_minutes'])


plt.figure(figsize=(10, 5))
x = np.linspace(120, 500, 400)
plt.plot(x, kdem(x), label='M')
plt.plot(x, kdef(x), label='F')
plt.legend()
plt.show()


from sklearn.model_selection import train_test_split


train_df, test_df = train_test_split(df, test_size=0.5, random_state=123)


train_df


test_df


from sklearn.neighbors import KNeighborsClassifier


k = 50

neigh = KNeighborsClassifier(n_neighbors=k)
neigh.fit(train_df[['tot_minutes']], train_df['M/F'])

KNeighborsClassifier(n_neighbors=50)


knn_pred  = neigh.predict(test_df[['tot_minutes']])


knn_pred

array(['F', 'M', 'M', ..., 'F', 'M', 'F'], dtype=object)


(knn_pred == test_df['M/F']).sum()/len(test_df)

0.6453722716556393


neigh.predict_proba([[200]])

/Users/bb/opt/anaconda3/lib/python3.8/site-packages/sklearn/base.py:450: UserWarning: X does not have valid feature names, but KNeighborsClassifier was fitted with feature names
  warnings.warn(

array([[0.36, 0.64]])


neigh.classes_

array(['F', 'M'], dtype=object)


plt.figure(figsize=(10, 5))
x = np.linspace(120, 360, 400)
plt.plot(x, neigh.predict_proba(x.reshape(-1, 1))[:, 0])
plt.plot

/Users/bb/opt/anaconda3/lib/python3.8/site-packages/sklearn/base.py:450: UserWarning: X does not have valid feature names, but KNeighborsClassifier was fitted with feature names
  warnings.warn(

<function matplotlib.pyplot.plot(*args, scalex=True, scaley=True, data=None, **kwargs)>


neigh.predict_proba(x.reshape(-1, 1))[:, 0]

/Users/bb/opt/anaconda3/lib/python3.8/site-packages/sklearn/base.py:450: UserWarning: X does not have valid feature names, but KNeighborsClassifier was fitted with feature names
  warnings.warn(

array([0.1 , 0.1 , 0.1 , 0.1 , 0.1 , 0.1 , 0.1 , 0.1 , 0.1 , 0.1 , 0.1 ,
       0.1 , 0.1 , 0.1 , 0.1 , 0.1 , 0.1 , 0.1 , 0.1 , 0.1 , 0.1 , 0.1 ,
       0.1 , 0.1 , 0.1 , 0.1 , 0.1 , 0.1 , 0.1 , 0.1 , 0.1 , 0.1 , 0.1 ,
       0.1 , 0.1 , 0.1 , 0.1 , 0.1 , 0.1 , 0.1 , 0.1 , 0.1 , 0.1 , 0.1 ,
       0.1 , 0.1 , 0.1 , 0.1 , 0.06, 0.04, 0.04, 0.02, 0.  , 0.  , 0.  ,
       0.  , 0.  , 0.  , 0.  , 0.  , 0.  , 0.  , 0.  , 0.  , 0.  , 0.  ,
       0.02, 0.02, 0.02, 0.02, 0.02, 0.  , 0.  , 0.04, 0.04, 0.04, 0.02,
       0.  , 0.  , 0.  , 0.04, 0.08, 0.06, 0.08, 0.12, 0.08, 0.08, 0.06,
       0.  , 0.04, 0.08, 0.06, 0.14, 0.08, 0.02, 0.12, 0.06, 0.06, 0.1 ,
       0.1 , 0.08, 0.14, 0.1 , 0.06, 0.06, 0.06, 0.1 , 0.1 , 0.14, 0.2 ,
       0.1 , 0.12, 0.1 , 0.18, 0.22, 0.14, 0.18, 0.32, 0.22, 0.18, 0.24,
       0.28, 0.24, 0.14, 0.38, 0.36, 0.32, 0.2 , 0.22, 0.28, 0.26, 0.28,
       0.3 , 0.36, 0.34, 0.38, 0.34, 0.32, 0.46, 0.26, 0.44, 0.44, 0.48,
       0.54, 0.44, 0.56, 0.42, 0.52, 0.44, 0.5 , 0.52, 0.58, 0.54, 0.7 ,
       0.76, 0.68, 0.68, 0.56, 0.62, 0.56, 0.52, 0.58, 0.54, 0.58, 0.52,
       0.52, 0.52, 0.58, 0.54, 0.68, 0.7 , 0.62, 0.54, 0.6 , 0.58, 0.66,
       0.74, 0.66, 0.68, 0.5 , 0.76, 0.68, 0.6 , 0.62, 0.54, 0.44, 0.66,
       0.48, 0.6 , 0.7 , 0.64, 0.56, 0.62, 0.58, 0.56, 0.52, 0.38, 0.56,
       0.58, 0.56, 0.56, 0.68, 0.54, 0.62, 0.6 , 0.62, 0.64, 0.58, 0.58,
       0.74, 0.56, 0.72, 0.5 , 0.68, 0.52, 0.7 , 0.6 , 0.62, 0.62, 0.58,
       0.64, 0.74, 0.64, 0.52, 0.48, 0.56, 0.5 , 0.6 , 0.56, 0.52, 0.5 ,
       0.66, 0.58, 0.54, 0.52, 0.7 , 0.56, 0.5 , 0.64, 0.66, 0.58, 0.58,
       0.56, 0.48, 0.42, 0.36, 0.52, 0.58, 0.52, 0.5 , 0.46, 0.5 , 0.58,
       0.62, 0.6 , 0.58, 0.6 , 0.68, 0.64, 0.6 , 0.54, 0.38, 0.54, 0.66,
       0.62, 0.46, 0.46, 0.4 , 0.44, 0.56, 0.54, 0.54, 0.46, 0.58, 0.6 ,
       0.56, 0.52, 0.54, 0.58, 0.56, 0.6 , 0.56, 0.62, 0.6 , 0.6 , 0.6 ,
       0.6 , 0.58, 0.58, 0.52, 0.62, 0.62, 0.5 , 0.5 , 0.5 , 0.58, 0.62,
       0.64, 0.64, 0.6 , 0.58, 0.62, 0.62, 0.68, 0.62, 0.6 , 0.64, 0.54,
       0.5 , 0.52, 0.48, 0.42, 0.48, 0.42, 0.38, 0.42, 0.42, 0.52, 0.58,
       0.64, 0.66, 0.6 , 0.64, 0.58, 0.54, 0.62, 0.66, 0.54, 0.58, 0.64,
       0.58, 0.52, 0.5 , 0.48, 0.46, 0.44, 0.46, 0.56, 0.6 , 0.64, 0.66,
       0.64, 0.62, 0.62, 0.6 , 0.58, 0.58, 0.54, 0.52, 0.48, 0.5 , 0.5 ,
       0.5 , 0.5 , 0.5 , 0.58, 0.6 , 0.62, 0.64, 0.64, 0.66, 0.66, 0.7 ,
       0.64, 0.62, 0.62, 0.62, 0.62, 0.66, 0.68, 0.72, 0.68, 0.66, 0.72,
       0.74, 0.74, 0.74, 0.7 , 0.68, 0.68, 0.68, 0.72, 0.72, 0.7 , 0.68,
       0.64, 0.58, 0.58, 0.58, 0.56, 0.5 , 0.44, 0.42, 0.42, 0.46, 0.42,
       0.44, 0.46, 0.46, 0.46])


train_df


test_df


kde = gaussian_kde(train_df['tot_minutes'], bw_method = 0.3)

plt.figure(figsize=(10, 5))
x = np.linspace(120, 500, 400)
plt.plot(x, kde(x));


kde(180)

array([0.00662687])


likelihood = kde(test_df['tot_minutes']).prod()
likelihood

0.0


0.5**2000

0.0


log_likelihood = np.log10(kde(test_df['tot_minutes'])).sum()


log_likelihood

-28746.170695622182


choices = []
for bw in np.linspace(0.01, 0.3, 20):
    kde = gaussian_kde(train_df['tot_minutes'], bw_method=bw)
    log_likelihood = np.log10(kde(test_df['tot_minutes'])).sum()
    print(bw, log_likelihood)
    choices.append((bw, log_likelihood))

0.01 -28817.917595202038
0.02526315789473684 -28709.48265025039
0.04052631578947368 -28696.36462240536
0.05578947368421053 -28692.098901252437
0.07105263157894737 -28690.45313426285
0.0863157894736842 -28690.196250451263
0.10157894736842105 -28690.79905684394
0.11684210526315789 -28691.982108391796
0.13210526315789473 -28693.63706897139
0.1473684210526316 -28695.755302217007
0.16263157894736843 -28698.366808507242
0.17789473684210527 -28701.504011156496
0.1931578947368421 -28705.187108819886
0.20842105263157895 -28709.422653258458
0.2236842105263158 -28714.207903649116
0.23894736842105263 -28719.53606510508
0.25421052631578944 -28725.400168116994
0.2694736842105263 -28731.79516403717
0.2847368421052632 -28738.718637586047
0.3 -28746.170695622182


choices

[(0.01, -28817.917595202038),
 (0.02526315789473684, -28709.48265025039),
 (0.04052631578947368, -28696.36462240536),
 (0.05578947368421053, -28692.098901252437),
 (0.07105263157894737, -28690.45313426285),
 (0.0863157894736842, -28690.196250451263),
 (0.10157894736842105, -28690.79905684394),
 (0.11684210526315789, -28691.982108391796),
 (0.13210526315789473, -28693.63706897139),
 (0.1473684210526316, -28695.755302217007),
 (0.16263157894736843, -28698.366808507242),
 (0.17789473684210527, -28701.504011156496),
 (0.1931578947368421, -28705.187108819886),
 (0.20842105263157895, -28709.422653258458),
 (0.2236842105263158, -28714.207903649116),
 (0.23894736842105263, -28719.53606510508),
 (0.25421052631578944, -28725.400168116994),
 (0.2694736842105263, -28731.79516403717),
 (0.2847368421052632, -28738.718637586047),
 (0.3, -28746.170695622182)]


bw = 0.0863157894736842
kde = gaussian_kde(train_df['tot_minutes'], bw_method = bw)

plt.figure(figsize=(10, 5))
x = np.linspace(120, 500, 400)
plt.plot(x, kde(x));


import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
import pandas as pd

df = pd.read_csv("https://www.mth548.org/_static/kde_marathon_results/marathon_results.csv")
df["tot_minutes"] = pd.to_timedelta(df["Finish"]).dt.total_seconds()/60

df


def f(x, y):
    return (x**2 + y - 11)**2 + (x + y**2 - 7)**2 - 150


f(1, 2)

-82


x = np.linspace(0, 5, 6)
y = np.linspace(0, 5, 6)

x

array([0., 1., 2., 3., 4., 5.])


X, Y = np.meshgrid(x, y)


X, Y

(array([[0., 1., 2., 3., 4., 5.],
        [0., 1., 2., 3., 4., 5.],
        [0., 1., 2., 3., 4., 5.],
        [0., 1., 2., 3., 4., 5.],
        [0., 1., 2., 3., 4., 5.],
        [0., 1., 2., 3., 4., 5.]]),
 array([[0., 0., 0., 0., 0., 0.],
        [1., 1., 1., 1., 1., 1.],
        [2., 2., 2., 2., 2., 2.],
        [3., 3., 3., 3., 3., 3.],
        [4., 4., 4., 4., 4., 4.],
        [5., 5., 5., 5., 5., 5.]]))


plt.plot(X, Y, 'r.');


Z = f(X, Y)
Z

array([[  20.,  -14.,  -76., -130., -116.,   50.],
       [ -14.,  -44.,  -98., -140., -110.,   76.],
       [ -60.,  -82., -124., -150., -100.,  110.],
       [ -82.,  -92., -118., -124.,  -50.,  188.],
       [ -20.,  -14.,  -20.,   -2.,  100.,  370.],
       [ 210.,  236.,  254.,  300.,  434.,  740.]])


import plotly.graph_objects as go

fig = go.Figure(go.Surface(x=X, y=Y, z=Z))
fig.show()


x = np.linspace(-5, 5, 400)
y = np.linspace(-5, 5, 400)
X, Y = np.meshgrid(x, y)
Z = f(X, Y)


fig = go.Figure(go.Surface(x=X, y=Y, z=Z, colorscale="Picnic"))
fig.show()


plt.plot(figsize=(6, 6))
plt.contour(X, Y, Z, levels=20, colors='k');


plt.plot(figsize=(6, 6))
plt.contour(X, Y, Z, levels=20, cmap='jet');


plt.plot(figsize=(6, 6))
plt.contourf(X, Y, Z, levels=20, cmap='jet');


plt.plot(figsize=(6, 6))
plt.contourf(X, Y, Z, levels=20, cmap='jet')
plt.contour(X, Y, Z, levels=20, colors='k');


plt.figure(figsize=(10, 6))
plt.plot(df['tot_minutes'], df['Age'], 'r.', alpha=0.2);


data = np.array([[0, 0],
                 [1, 0],
                 [0, 1],
                 [1, 1]
                ])
data

array([[0, 0],
       [1, 0],
       [0, 1],
       [1, 1]])


data.T

array([[0, 1, 0, 1],
       [0, 0, 1, 1]])


from scipy.stats import gaussian_kde

kde = gaussian_kde(data.T, bw_method=0.7)


kde([0.5, 0.7])

array([0.22263723])


x = np.linspace(-1, 2, 400)
y = np.linspace(-1, 2, 400)
X, Y = np.meshgrid(x, y)
Z = kde([X.reshape(-1), Y.reshape(-1)]).reshape(X.shape)

Z

array([[0.00053435, 0.00055943, 0.00058549, ..., 0.00058549, 0.00055943,
        0.00053435],
       [0.00055943, 0.00058569, 0.00061296, ..., 0.00061296, 0.00058569,
        0.00055943],
       [0.00058549, 0.00061296, 0.00064151, ..., 0.00064151, 0.00061296,
        0.00058549],
       ...,
       [0.00058549, 0.00061296, 0.00064151, ..., 0.00064151, 0.00061296,
        0.00058549],
       [0.00055943, 0.00058569, 0.00061296, ..., 0.00061296, 0.00058569,
        0.00055943],
       [0.00053435, 0.00055943, 0.00058549, ..., 0.00058549, 0.00055943,
        0.00053435]])


fig = go.Figure(go.Surface(x=X, y=Y, z=Z))
fig.show()


plt.figure(figsize=(6, 6))
plt.contourf(X, Y, Z, levels=10, cmap="Reds")
plt.contour(X, Y, Z, levels=10, colors='k')
plt.show()


bw_method = 0.2
kde = gaussian_kde(df[["tot_minutes", "Age"]].T, bw_method=bw_method)


df[["tot_minutes", "Age"]].T


kde([180, 30])

array([0.00024693])


kde.integrate_box([180, 30], [240, 40])

0.15874527277356906


x = np.linspace(120, 360, 100)
y = np.linspace(10, 70, 100)

X, Y = np.meshgrid(x, y)
Z = kde([X.reshape(-1), Y.reshape(-1)]).reshape(X.shape)

plt.figure(figsize=(10, 6))
plt.contourf(X, Y, Z, levels=10, cmap='Reds')
plt.contour(X, Y, Z, levels=10, colors='k')

<matplotlib.contour.QuadContourSet at 0x7fa9f65e02e0>


import seaborn as sns

df = sns.load_dataset('tips')
df


from ipywidgets import interact, fixed
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns

plt.style.use('ggplot')
sns.set_context("notebook")


df = sns.load_dataset('tips')

def tip_plot(frac):
    frac=frac/100
    plt.figure(figsize=(12,7))
    sns.scatterplot(data=df, x="total_bill", y="tip", marker='o')
    x = np.arange(0, 55)
    plt.plot(x, frac*x, c='b', label=f"{frac:.0%} tip")
    plt.ylim(0, 11)
    plt.title("Total bill vs tip amount")
    plt.legend()
    plt.show()

interact(tip_plot, frac=(10, 20));

interactive(children=(IntSlider(value=15, description='frac', max=20, min=10), Output()), _dom_classes=('widge…


df['tip_fraction'] = df['tip']/df['total_bill']

df


mean_tip = df['tip_fraction'].mean()
mean_tip

0.16080258172250478


df['naive_tip_prediction'] = mean_tip*df['total_bill']

df


df['naive_prediction_error'] = df['naive_tip_prediction'] - df['tip']
df


df['naive_prediction_error'].mean()

0.18335196705924947


np.abs(df['naive_prediction_error']).mean()

0.7968739185842583


np.abs(df['naive_prediction_error']).describe()

count    244.000000
mean       0.796874
std        0.826432
min        0.002699
25%        0.234597
50%        0.509510
75%        1.068028
max        4.623554
Name: naive_prediction_error, dtype: float64


def cost(a, b):
    prediction = a*df['total_bill'] + b
    return ((prediction - df['tip'])**2).sum()


cost(0.16, 0)

317.83711808


cost(0.2, 0)

650.866652


cost(0.14, 0.5)

294.36668427999996

	Age	M/F	Country	5K	10K	15K	20K	Half	25K	30K	35K	40K	Finish	Pace	Overall	Gender	Division	tot_minutes
0	25	M	ETH	00:14:43	00:29:43	00:44:57	01:00:29	01:04:02	01:16:07	01:32:00	01:47:59	02:02:39	02:09:17	00:04:56	1	1	1	129.283333
1	30	M	ETH	00:14:43	00:29:43	00:44:58	01:00:28	01:04:01	01:16:07	01:31:59	01:47:59	02:02:42	02:09:48	00:04:58	2	2	2	129.800000
2	29	M	KEN	00:14:43	00:29:43	00:44:57	01:00:29	01:04:02	01:16:07	01:32:00	01:47:59	02:03:01	02:10:22	00:04:59	3	3	3	130.366667
3	28	M	KEN	00:14:43	00:29:44	00:45:01	01:00:29	01:04:02	01:16:07	01:32:00	01:48:03	02:03:47	02:10:47	00:05:00	4	4	4	130.783333
4	32	M	KEN	00:14:43	00:29:44	00:44:58	01:00:28	01:04:01	01:16:07	01:32:00	01:47:59	02:03:27	02:10:49	00:05:00	5	5	5	130.816667
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
26293	64	F	USA	00:50:15	01:43:31	02:36:53	03:32:26	03:43:46	04:25:53	05:19:44	06:17:19	07:13:34	07:38:56	00:17:31	26594	12015	269	458.933333
26294	61	F	USA	00:48:36	01:39:39	02:39:13	03:35:58	03:47:55	04:32:44	05:31:58	06:28:56	07:26:19	07:51:30	00:17:59	26595	12016	270	471.500000
26295	66	F	USA	00:53:03	01:47:16	02:41:45	03:37:07	03:48:21	04:33:51	05:38:56	06:38:51	07:36:18	07:59:33	00:18:18	26596	12017	91	479.550000
26296	53	M	USA	00:49:04	01:40:12	02:33:31	03:31:41	03:43:35	04:29:20	05:31:11	06:33:35	07:35:38	08:00:37	00:18:20	26597	14580	2055	480.616667
26297	62	M	USA	00:40:14	01:28:18	02:26:46	03:28:41	03:40:36	04:36:06	05:43:44	06:51:31	07:41:28	08:06:01	00:18:33	26598	14581	898	486.016667

	Age	M/F	Country	5K	10K	15K	20K	Half	25K	30K	35K	40K	Finish	Pace	Overall	Gender	Division	tot_minutes
1024	33	M	USA	00:18:33	00:37:18	00:56:26	01:15:51	01:20:12	01:35:51	01:56:38	02:18:35	02:40:36	02:50:47	00:06:31	1026	985	825	170.783333
14892	40	F	USA	00:26:44	00:53:34	01:20:44	01:47:42	01:53:30	02:14:47	02:42:09	03:09:04	03:34:16	03:45:06	00:08:36	14970	5196	914	225.100000
13216	55	M	USA	00:25:14	00:49:51	01:14:52	01:41:52	01:47:19	02:07:11	02:33:40	03:01:24	03:27:57	03:39:35	00:08:23	13277	9100	653	219.583333
10302	37	M	USA	00:26:17	00:50:37	01:15:09	01:40:43	01:46:17	02:07:12	02:33:12	02:57:48	03:21:09	03:30:35	00:08:02	10337	7833	3560	210.583333
13164	57	M	USA	00:25:18	00:49:50	01:14:45	01:39:49	01:45:22	02:05:06	02:31:41	02:59:42	03:27:39	03:39:26	00:08:23	13224	9080	647	219.433333
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
15377	26	F	USA	00:25:18	00:51:06	01:16:33	01:41:52	01:47:26	02:08:08	02:35:55	03:05:23	03:34:32	03:46:50	00:08:40	15463	5505	3578	226.833333
21602	60	F	CAN	00:31:03	01:01:33	01:30:58	02:00:14	02:06:34	02:30:29	03:02:19	03:33:13	04:05:01	04:19:26	00:09:54	21787	9327	114	259.433333
17730	43	F	USA	00:27:06	00:53:30	01:20:51	01:48:06	01:54:00	02:16:06	02:44:59	03:14:54	03:42:59	03:55:26	00:08:59	17852	6994	1297	235.433333
15725	47	F	USA	00:27:22	00:53:47	01:19:38	01:47:14	01:53:03	02:13:46	02:41:02	03:08:51	03:36:21	03:48:11	00:08:43	15818	5737	649	228.183333
19966	37	F	USA	00:28:36	00:55:46	01:24:31	01:52:27	01:58:58	02:23:39	02:55:00	03:25:49	03:54:46	04:07:24	00:09:27	20116	8325	4424	247.400000

	Age	M/F	Country	5K	10K	15K	20K	Half	25K	30K	35K	40K	Finish	Pace	Overall	Gender	Division	tot_minutes
15955	47	F	USA	00:27:31	00:53:43	01:19:39	01:45:57	01:51:39	02:12:27	02:40:08	03:08:26	03:36:40	03:48:56	00:08:44	16054	5886	682	228.933333
1083	37	M	NED	00:18:30	00:37:13	00:56:19	01:15:54	01:20:10	01:35:53	01:57:06	02:20:18	02:42:10	02:51:28	00:06:33	1085	1039	870	171.466667
358	40	M	CAN	00:18:31	00:37:16	00:56:05	01:15:04	01:19:12	01:34:06	01:53:31	02:13:14	02:33:04	02:42:01	00:06:11	359	343	21	162.016667
5136	34	F	USA	00:20:19	00:41:00	01:01:57	01:23:14	01:27:55	01:44:44	02:07:58	02:34:10	03:00:20	03:12:22	00:07:21	5149	515	449	192.366667
16029	40	F	CAN	00:25:02	00:51:08	01:19:07	01:45:56	01:51:43	02:13:12	02:41:19	03:11:08	03:37:51	03:49:11	00:08:45	16128	5935	1083	229.183333
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
19657	48	F	USA	00:27:53	00:58:05	01:26:21	01:54:59	02:01:09	02:23:39	02:52:50	03:23:20	03:52:51	04:05:29	00:09:22	19804	8137	1247	245.483333
10744	42	F	GBR	00:25:47	00:50:38	01:15:34	01:40:12	01:45:37	02:05:56	02:30:53	02:56:18	03:21:03	03:31:57	00:08:06	10781	2736	349	211.950000
17175	41	M	USA	00:24:40	00:53:59	01:21:15	01:48:49	01:54:28	02:16:23	02:44:47	03:13:03	03:40:48	03:53:21	00:08:55	17291	10665	1671	233.350000
3806	27	M	USA	00:21:44	00:43:56	01:06:09	01:28:25	01:33:19	01:50:49	02:13:21	02:35:36	02:56:51	03:06:07	00:07:06	3814	3546	2458	186.116667
10433	24	F	USA	00:23:43	00:46:45	01:09:57	01:33:42	01:38:51	01:57:49	02:24:02	02:51:45	03:18:56	03:30:59	00:08:03	10469	2570	2027	210.983333

	Age	M/F	Country	5K	10K	15K	20K	Half	25K	30K	35K	40K	Finish	Pace	Overall	Gender	Division	tot_minutes
1024	33	M	USA	00:18:33	00:37:18	00:56:26	01:15:51	01:20:12	01:35:51	01:56:38	02:18:35	02:40:36	02:50:47	00:06:31	1026	985	825	170.783333
14892	40	F	USA	00:26:44	00:53:34	01:20:44	01:47:42	01:53:30	02:14:47	02:42:09	03:09:04	03:34:16	03:45:06	00:08:36	14970	5196	914	225.100000
13216	55	M	USA	00:25:14	00:49:51	01:14:52	01:41:52	01:47:19	02:07:11	02:33:40	03:01:24	03:27:57	03:39:35	00:08:23	13277	9100	653	219.583333
10302	37	M	USA	00:26:17	00:50:37	01:15:09	01:40:43	01:46:17	02:07:12	02:33:12	02:57:48	03:21:09	03:30:35	00:08:02	10337	7833	3560	210.583333
13164	57	M	USA	00:25:18	00:49:50	01:14:45	01:39:49	01:45:22	02:05:06	02:31:41	02:59:42	03:27:39	03:39:26	00:08:23	13224	9080	647	219.433333
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
15377	26	F	USA	00:25:18	00:51:06	01:16:33	01:41:52	01:47:26	02:08:08	02:35:55	03:05:23	03:34:32	03:46:50	00:08:40	15463	5505	3578	226.833333
21602	60	F	CAN	00:31:03	01:01:33	01:30:58	02:00:14	02:06:34	02:30:29	03:02:19	03:33:13	04:05:01	04:19:26	00:09:54	21787	9327	114	259.433333
17730	43	F	USA	00:27:06	00:53:30	01:20:51	01:48:06	01:54:00	02:16:06	02:44:59	03:14:54	03:42:59	03:55:26	00:08:59	17852	6994	1297	235.433333
15725	47	F	USA	00:27:22	00:53:47	01:19:38	01:47:14	01:53:03	02:13:46	02:41:02	03:08:51	03:36:21	03:48:11	00:08:43	15818	5737	649	228.183333
19966	37	F	USA	00:28:36	00:55:46	01:24:31	01:52:27	01:58:58	02:23:39	02:55:00	03:25:49	03:54:46	04:07:24	00:09:27	20116	8325	4424	247.400000

	Age	M/F	Country	5K	10K	15K	20K	Half	25K	30K	35K	40K	Finish	Pace	Overall	Gender	Division	tot_minutes
15955	47	F	USA	00:27:31	00:53:43	01:19:39	01:45:57	01:51:39	02:12:27	02:40:08	03:08:26	03:36:40	03:48:56	00:08:44	16054	5886	682	228.933333
1083	37	M	NED	00:18:30	00:37:13	00:56:19	01:15:54	01:20:10	01:35:53	01:57:06	02:20:18	02:42:10	02:51:28	00:06:33	1085	1039	870	171.466667
358	40	M	CAN	00:18:31	00:37:16	00:56:05	01:15:04	01:19:12	01:34:06	01:53:31	02:13:14	02:33:04	02:42:01	00:06:11	359	343	21	162.016667
5136	34	F	USA	00:20:19	00:41:00	01:01:57	01:23:14	01:27:55	01:44:44	02:07:58	02:34:10	03:00:20	03:12:22	00:07:21	5149	515	449	192.366667
16029	40	F	CAN	00:25:02	00:51:08	01:19:07	01:45:56	01:51:43	02:13:12	02:41:19	03:11:08	03:37:51	03:49:11	00:08:45	16128	5935	1083	229.183333
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
19657	48	F	USA	00:27:53	00:58:05	01:26:21	01:54:59	02:01:09	02:23:39	02:52:50	03:23:20	03:52:51	04:05:29	00:09:22	19804	8137	1247	245.483333
10744	42	F	GBR	00:25:47	00:50:38	01:15:34	01:40:12	01:45:37	02:05:56	02:30:53	02:56:18	03:21:03	03:31:57	00:08:06	10781	2736	349	211.950000
17175	41	M	USA	00:24:40	00:53:59	01:21:15	01:48:49	01:54:28	02:16:23	02:44:47	03:13:03	03:40:48	03:53:21	00:08:55	17291	10665	1671	233.350000
3806	27	M	USA	00:21:44	00:43:56	01:06:09	01:28:25	01:33:19	01:50:49	02:13:21	02:35:36	02:56:51	03:06:07	00:07:06	3814	3546	2458	186.116667
10433	24	F	USA	00:23:43	00:46:45	01:09:57	01:33:42	01:38:51	01:57:49	02:24:02	02:51:45	03:18:56	03:30:59	00:08:03	10469	2570	2027	210.983333

Week 10¶

Guessing if a runner was male or female based on the finish time¶

Probabilities and predictions with k-NN¶

Selection of bandwidth and maximum likelihood¶

Sidenote: 3D plots and contour plots¶

2-dimensional KDE¶

Toy example: KDE for 2-dimensional data¶

Back to the marathon data¶

Linear regression¶

	0	1	2	3	4	5	6	7	8	9	...	26288	26289	26290	26291	26292	26293	26294	26295	26296	26297
tot_minutes	129.283333	129.8	130.366667	130.783333	130.816667	130.866667	131.333333	132.7	133.583333	133.866667	...	402.016667	404.466667	416.783333	417.833333	420.5	458.933333	471.5	479.55	480.616667	486.016667
Age	25.000000	30.0	29.000000	28.000000	32.000000	30.000000	32.000000	39.0	27.000000	33.000000	...	47.000000	46.000000	71.000000	57.000000	37.0	64.000000	61.0	66.00	53.000000	62.000000

	total_bill	tip	sex	smoker	day	time	size
0	16.99	1.01	Female	No	Sun	Dinner	2
1	10.34	1.66	Male	No	Sun	Dinner	3
2	21.01	3.50	Male	No	Sun	Dinner	3
3	23.68	3.31	Male	No	Sun	Dinner	2
4	24.59	3.61	Female	No	Sun	Dinner	4
...	...	...	...	...	...	...	...
239	29.03	5.92	Male	No	Sat	Dinner	3
240	27.18	2.00	Female	Yes	Sat	Dinner	2
241	22.67	2.00	Male	Yes	Sat	Dinner	2
242	17.82	1.75	Male	No	Sat	Dinner	2
243	18.78	3.00	Female	No	Thur	Dinner	2