#This is for jupyter notebook
from IPython.display import display, Markdown

def print_header(text, level=2):
    display(Markdown(f"{'#'*level} {text}"))

Predicting Tomorrow's Weather From Yesterday's Data

This notebook builds a simple weather forecaster for Basel, Switzerland. It looks at 10 years of daily weather readings from 18 European cities and learns the patterns that go with hot/cold, humid/dry, and high/low pressure days in Basel. It then uses that learning to guess temperature, humidity, and pressure it has never seen before, and checks how close the guesses were.

Step 1: Get Our Tools Ready

%pip install pandas numpy matplotlib seaborn scikit-learn

Requirement already satisfied: pandas in /opt/hostedtoolcache/Python/3.11.15/x64/lib/python3.11/site-packages (3.0.5)
Requirement already satisfied: numpy in /opt/hostedtoolcache/Python/3.11.15/x64/lib/python3.11/site-packages (2.4.6)
Requirement already satisfied: matplotlib in /opt/hostedtoolcache/Python/3.11.15/x64/lib/python3.11/site-packages (3.11.1)
Requirement already satisfied: seaborn in /opt/hostedtoolcache/Python/3.11.15/x64/lib/python3.11/site-packages (0.13.2)
Requirement already satisfied: scikit-learn in /opt/hostedtoolcache/Python/3.11.15/x64/lib/python3.11/site-packages (1.9.0)
Requirement already satisfied: python-dateutil>=2.8.2 in /opt/hostedtoolcache/Python/3.11.15/x64/lib/python3.11/site-packages (from pandas) (2.9.0.post0)

Requirement already satisfied: contourpy>=1.0.1 in /opt/hostedtoolcache/Python/3.11.15/x64/lib/python3.11/site-packages (from matplotlib) (1.3.3)
Requirement already satisfied: cycler>=0.10 in /opt/hostedtoolcache/Python/3.11.15/x64/lib/python3.11/site-packages (from matplotlib) (0.12.1)
Requirement already satisfied: fonttools>=4.28.2 in /opt/hostedtoolcache/Python/3.11.15/x64/lib/python3.11/site-packages (from matplotlib) (4.63.0)
Requirement already satisfied: kiwisolver>=1.3.1 in /opt/hostedtoolcache/Python/3.11.15/x64/lib/python3.11/site-packages (from matplotlib) (1.5.0)
Requirement already satisfied: packaging>=20.0 in /opt/hostedtoolcache/Python/3.11.15/x64/lib/python3.11/site-packages (from matplotlib) (26.3)
Requirement already satisfied: pillow>=9 in /opt/hostedtoolcache/Python/3.11.15/x64/lib/python3.11/site-packages (from matplotlib) (12.3.0)
Requirement already satisfied: pyparsing>=3 in /opt/hostedtoolcache/Python/3.11.15/x64/lib/python3.11/site-packages (from matplotlib) (3.3.2)
Requirement already satisfied: scipy>=1.10.0 in /opt/hostedtoolcache/Python/3.11.15/x64/lib/python3.11/site-packages (from scikit-learn) (1.17.1)
Requirement already satisfied: joblib>=1.4.0 in /opt/hostedtoolcache/Python/3.11.15/x64/lib/python3.11/site-packages (from scikit-learn) (1.5.3)
Requirement already satisfied: narwhals>=2.0.1 in /opt/hostedtoolcache/Python/3.11.15/x64/lib/python3.11/site-packages (from scikit-learn) (2.24.0)
Requirement already satisfied: threadpoolctl>=3.5.0 in /opt/hostedtoolcache/Python/3.11.15/x64/lib/python3.11/site-packages (from scikit-learn) (3.6.0)
Requirement already satisfied: six>=1.5 in /opt/hostedtoolcache/Python/3.11.15/x64/lib/python3.11/site-packages (from python-dateutil>=2.8.2->pandas) (1.17.0)

Note: you may need to restart the kernel to use updated packages.

We use four free, well-known Python toolkits:

• pandas — opens and organizes the weather data like a spreadsheet
• numpy — does the number-crunching underneath
• matplotlib / seaborn — draws the charts
• scikit-learn — contains the actual prediction ("machine learning") algorithm

None of this is exotic — it's the standard starter kit for any data analysis in Python.

Step 2: Load the Weather Data

The dataset comes from Zenodo, a public research data archive, and holds one row per day from 2000–2010, with weather readings (temperature, humidity, pressure, wind, sunshine, etc.) for 18 European cities side by side.

import pandas as pd

# URL of Dataset on Zenodo, across locations in Europe
url = 'https://zenodo.org/records/4770937/files/weather_prediction_dataset.csv'

# Load Dataset
df = pd.read_csv(url)

# Display basic information about dataset
df.info()

<class 'pandas.DataFrame'>
RangeIndex: 3654 entries, 0 to 3653
Columns: 165 entries, DATE to TOURS_temp_max
dtypes: float64(150), int64(15)
memory usage: 4.6 MB

# Display Preview and Summary of Dataset

print_header("Dataset Preview")
display(df.head().style.set_caption("First 5 Rows").background_gradient(cmap='Blues'))

print_header("Dataset Summary")
display(df.describe().T.style.bar(color='#5fba7d'))

Dataset Preview

First 5 Rows

	DATE	MONTH	BASEL_cloud_cover	BASEL_humidity	BASEL_pressure	BASEL_global_radiation	BASEL_precipitation	BASEL_sunshine	BASEL_temp_mean	BASEL_temp_min	BASEL_temp_max	BUDAPEST_cloud_cover	BUDAPEST_humidity	BUDAPEST_pressure	BUDAPEST_global_radiation	BUDAPEST_precipitation	BUDAPEST_sunshine	BUDAPEST_temp_mean	BUDAPEST_temp_max	DE_BILT_cloud_cover	DE_BILT_wind_speed	DE_BILT_wind_gust	DE_BILT_humidity	DE_BILT_pressure	DE_BILT_global_radiation	DE_BILT_precipitation	DE_BILT_sunshine	DE_BILT_temp_mean	DE_BILT_temp_min	DE_BILT_temp_max	DRESDEN_cloud_cover	DRESDEN_wind_speed	DRESDEN_wind_gust	DRESDEN_humidity	DRESDEN_global_radiation	DRESDEN_precipitation	DRESDEN_sunshine	DRESDEN_temp_mean	DRESDEN_temp_min	DRESDEN_temp_max	DUSSELDORF_cloud_cover	DUSSELDORF_wind_speed	DUSSELDORF_wind_gust	DUSSELDORF_humidity	DUSSELDORF_pressure	DUSSELDORF_global_radiation	DUSSELDORF_precipitation	DUSSELDORF_sunshine	DUSSELDORF_temp_mean	DUSSELDORF_temp_min	DUSSELDORF_temp_max	HEATHROW_cloud_cover	HEATHROW_humidity	HEATHROW_pressure	HEATHROW_global_radiation	HEATHROW_precipitation	HEATHROW_sunshine	HEATHROW_temp_mean	HEATHROW_temp_min	HEATHROW_temp_max	KASSEL_wind_speed	KASSEL_wind_gust	KASSEL_humidity	KASSEL_pressure	KASSEL_global_radiation	KASSEL_precipitation	KASSEL_sunshine	KASSEL_temp_mean	KASSEL_temp_min	KASSEL_temp_max	LJUBLJANA_cloud_cover	LJUBLJANA_wind_speed	LJUBLJANA_humidity	LJUBLJANA_pressure	LJUBLJANA_global_radiation	LJUBLJANA_precipitation	LJUBLJANA_sunshine	LJUBLJANA_temp_mean	LJUBLJANA_temp_min	LJUBLJANA_temp_max	MAASTRICHT_cloud_cover	MAASTRICHT_wind_speed	MAASTRICHT_wind_gust	MAASTRICHT_humidity	MAASTRICHT_pressure	MAASTRICHT_global_radiation	MAASTRICHT_precipitation	MAASTRICHT_sunshine	MAASTRICHT_temp_mean	MAASTRICHT_temp_min	MAASTRICHT_temp_max	MALMO_wind_speed	MALMO_precipitation	MALMO_temp_mean	MALMO_temp_min	MALMO_temp_max	MONTELIMAR_wind_speed	MONTELIMAR_humidity	MONTELIMAR_pressure	MONTELIMAR_global_radiation	MONTELIMAR_precipitation	MONTELIMAR_temp_mean	MONTELIMAR_temp_min	MONTELIMAR_temp_max	MUENCHEN_cloud_cover	MUENCHEN_wind_speed	MUENCHEN_wind_gust	MUENCHEN_humidity	MUENCHEN_pressure	MUENCHEN_global_radiation	MUENCHEN_precipitation	MUENCHEN_sunshine	MUENCHEN_temp_mean	MUENCHEN_temp_min	MUENCHEN_temp_max	OSLO_cloud_cover	OSLO_wind_speed	OSLO_wind_gust	OSLO_humidity	OSLO_pressure	OSLO_global_radiation	OSLO_precipitation	OSLO_sunshine	OSLO_temp_mean	OSLO_temp_min	OSLO_temp_max	PERPIGNAN_wind_speed	PERPIGNAN_humidity	PERPIGNAN_pressure	PERPIGNAN_global_radiation	PERPIGNAN_precipitation	PERPIGNAN_temp_mean	PERPIGNAN_temp_min	PERPIGNAN_temp_max	ROMA_cloud_cover	ROMA_humidity	ROMA_pressure	ROMA_global_radiation	ROMA_sunshine	ROMA_temp_mean	ROMA_temp_min	ROMA_temp_max	SONNBLICK_cloud_cover	SONNBLICK_humidity	SONNBLICK_global_radiation	SONNBLICK_precipitation	SONNBLICK_sunshine	SONNBLICK_temp_mean	SONNBLICK_temp_min	SONNBLICK_temp_max	STOCKHOLM_cloud_cover	STOCKHOLM_pressure	STOCKHOLM_precipitation	STOCKHOLM_sunshine	STOCKHOLM_temp_mean	STOCKHOLM_temp_min	STOCKHOLM_temp_max	TOURS_wind_speed	TOURS_humidity	TOURS_pressure	TOURS_global_radiation	TOURS_precipitation	TOURS_temp_mean	TOURS_temp_min	TOURS_temp_max
0	20000101	1	8	0.890000	1.028600	0.200000	0.030000	0.000000	2.900000	1.600000	3.900000	3	0.920000	1.026800	0.520000	0.000000	3.700000	-4.900000	-0.700000	7	2.500000	8.000000	0.970000	1.024000	0.110000	0.100000	0.000000	6.100000	3.500000	8.100000	8	3.200000	7.200000	0.890000	0.090000	0.320000	0.000000	1.000000	-1.800000	2.000000	8	2.500000	5.900000	0.920000	1.024000	0.120000	0.220000	0.000000	4.200000	2.500000	6.900000	7	0.940000	1.024500	0.180000	0.000000	0.400000	7.000000	4.900000	10.800000	2.500000	8.200000	0.930000	1.023700	0.060000	0.130000	0.000000	3.500000	1.500000	5.000000	6	0.400000	0.830000	1.029400	0.570000	0.000000	5.200000	-4.800000	-9.100000	-1.300000	8	3.100000	7.000000	0.980000	1.025100	0.060000	0.170000	0.000000	5.600000	4.100000	6.900000	2.500000	0.270000	2.900000	0.900000	3.600000	3.800000	0.850000	1.026900	0.300000	0.000000	5.500000	2.500000	8.500000	8	2.600000	9.400000	0.910000	1.027300	0.200000	0.200000	0.000000	1.700000	-0.500000	2.600000	7	0.900000	5.100000	0.940000	1.013000	0.040000	0.600000	0.000000	-5.000000	-8.600000	-3.200000	4.400000	0.710000	1.026700	0.600000	0.000000	12.200000	10.300000	14.000000	0	0.720000	1.024400	0.920000	8.400000	1.600000	3.000000	8.000000	7	0.890000	0.820000	1.340000	0.000000	-15.200000	-17.000000	-13.400000	8	1.016300	0.170000	0.000000	-2.300000	-9.300000	0.700000	1.600000	0.970000	1.027500	0.250000	0.040000	8.500000	7.200000	9.800000
1	20000102	1	8	0.870000	1.031800	0.250000	0.000000	0.000000	3.600000	2.700000	4.800000	8	0.940000	1.029700	0.140000	0.000000	0.400000	-3.600000	-1.900000	8	3.700000	9.000000	0.970000	1.026700	0.110000	0.000000	0.000000	7.300000	5.400000	8.700000	7	4.000000	8.800000	0.890000	0.230000	0.000000	0.400000	2.500000	1.400000	4.000000	6	3.000000	7.400000	0.870000	1.028300	0.190000	0.000000	0.700000	6.500000	2.700000	7.900000	7	0.890000	1.025300	0.200000	0.020000	0.700000	7.900000	5.000000	11.500000	2.900000	9.600000	0.920000	1.029000	0.330000	0.000000	2.900000	2.300000	0.300000	4.700000	6	0.400000	0.760000	1.031000	0.590000	0.000000	5.000000	-0.900000	-4.900000	2.000000	7	3.800000	9.000000	0.950000	1.028600	0.140000	0.000000	0.000000	6.200000	4.200000	7.500000	3.800000	0.000000	3.700000	1.000000	5.400000	5.800000	0.820000	1.028700	0.540000	0.000000	8.300000	6.800000	9.800000	6	2.100000	8.200000	0.900000	1.032100	0.660000	0.000000	6.100000	1.900000	-0.200000	5.800000	6	1.900000	5.700000	0.940000	1.007600	0.110000	0.000000	1.600000	-0.800000	-6.700000	2.400000	2.900000	0.670000	1.027800	0.960000	0.000000	9.800000	5.100000	14.600000	2	0.740000	1.026300	0.810000	6.500000	4.200000	0.000000	8.400000	5	0.860000	0.600000	0.390000	2.800000	-13.700000	-15.000000	-12.300000	8	1.010800	0.200000	0.000000	1.300000	0.500000	2.000000	2.000000	0.990000	1.029300	0.170000	0.160000	7.900000	6.600000	9.200000
2	20000103	1	5	0.810000	1.031400	0.500000	0.000000	3.700000	2.200000	0.100000	4.800000	6	0.950000	1.029500	0.190000	0.000000	0.000000	-0.800000	1.100000	8	6.100000	13.000000	0.940000	1.020300	0.110000	0.450000	0.000000	8.400000	6.400000	9.600000	7	5.400000	12.100000	0.790000	0.180000	0.000000	0.000000	4.200000	1.300000	5.100000	7	5.500000	14.300000	0.780000	1.023500	0.120000	0.280000	0.000000	7.700000	6.900000	9.100000	8	0.910000	1.018600	0.130000	0.600000	0.000000	9.400000	7.200000	9.500000	4.800000	11.900000	0.900000	1.025100	0.200000	0.010000	0.000000	3.500000	2.200000	4.600000	6	0.300000	0.830000	1.030900	0.510000	0.000000	2.400000	-0.300000	-1.800000	3.300000	7	7.400000	14.000000	0.870000	1.023600	0.150000	0.020000	0.900000	6.800000	6.100000	7.900000	4.300000	0.060000	5.600000	4.000000	6.900000	0.400000	0.920000	1.031600	0.530000	0.000000	3.200000	-2.100000	8.500000	7	2.100000	6.900000	0.920000	1.031700	0.280000	0.000000	0.400000	-0.400000	-3.300000	0.900000	6	1.700000	8.700000	0.880000	1.001600	0.040000	0.000000	0.000000	1.200000	-1.100000	3.800000	2.500000	0.850000	1.028800	0.930000	0.000000	8.600000	4.100000	13.200000	0	0.770000	1.028800	0.890000	0.000000	3.800000	11.100000	21.100000	3	0.410000	0.810000	0.000000	5.100000	-9.200000	-12.500000	-5.800000	7	1.007100	0.080000	1.800000	0.800000	-1.000000	2.800000	3.400000	0.910000	1.026700	0.270000	0.000000	8.100000	6.600000	9.600000
3	20000104	1	7	0.790000	1.026200	0.630000	0.350000	6.900000	3.900000	0.500000	7.500000	8	0.940000	1.025200	0.210000	0.000000	0.000000	-1.000000	0.100000	7	3.800000	15.000000	0.940000	1.014200	0.110000	1.090000	0.000000	6.400000	4.300000	9.400000	8	6.000000	14.400000	0.880000	0.110000	0.220000	0.000000	4.400000	3.400000	5.200000	7	6.000000	16.800000	0.870000	1.016200	0.120000	0.970000	0.000000	7.800000	6.600000	9.200000	5	0.890000	1.014800	0.340000	0.020000	2.900000	7.000000	4.400000	11.000000	4.500000	12.700000	0.940000	1.017400	0.060000	0.440000	0.000000	4.800000	3.500000	5.600000	2	0.400000	0.880000	1.026200	0.700000	0.000000	3.500000	-3.600000	-6.100000	0.400000	8	7.200000	15.000000	0.920000	1.016500	0.070000	1.330000	0.000000	7.300000	6.100000	9.000000	3.900000	0.750000	4.500000	3.000000	6.400000	1.100000	0.850000	1.027400	0.640000	0.000000	7.200000	2.300000	12.100000	6	2.700000	11.700000	0.750000	1.026000	0.580000	0.040000	4.500000	3.800000	-2.800000	6.600000	1	3.400000	11.800000	0.580000	0.998200	0.130000	0.000000	5.300000	2.100000	-0.500000	5.100000	1.500000	0.850000	1.026900	0.560000	0.020000	8.600000	4.300000	12.800000	1	0.850000	1.027300	0.890000	8.200000	6.000000	2.000000	10.000000	1	0.250000	1.050000	0.110000	8.700000	-5.600000	-7.000000	-4.200000	2	0.994700	0.000000	5.000000	3.500000	2.500000	4.600000	4.900000	0.950000	1.022200	0.110000	0.440000	8.600000	6.400000	10.800000
4	20000105	1	5	0.900000	1.024600	0.510000	0.070000	3.700000	6.000000	3.800000	8.600000	5	0.880000	1.023500	0.430000	0.000000	0.800000	0.200000	3.900000	3	4.000000	12.000000	0.900000	1.018300	0.480000	0.000000	6.500000	4.400000	1.400000	7.400000	2	5.600000	15.800000	0.760000	0.490000	0.000000	5.700000	1.800000	-0.500000	6.900000	4	4.500000	11.200000	0.800000	1.020300	0.510000	0.000000	6.500000	5.200000	0.400000	8.600000	5	0.850000	1.014200	0.250000	0.080000	1.300000	6.400000	1.900000	10.800000	2.400000	8.800000	0.840000	1.021000	0.480000	0.000000	6.700000	2.300000	0.200000	6.300000	4	0.600000	0.850000	1.027100	0.570000	0.000000	4.600000	-3.000000	-6.100000	1.100000	4	4.100000	10.000000	0.870000	1.020500	0.440000	0.000000	6.200000	5.200000	0.600000	8.400000	3.200000	0.030000	3.800000	2.500000	5.500000	3.400000	0.820000	1.023400	0.700000	0.000000	8.200000	1.500000	14.800000	5	3.300000	13.200000	0.870000	1.024800	0.260000	0.000000	0.200000	5.300000	4.300000	7.300000	8	1.200000	5.700000	0.940000	1.005500	0.050000	0.060000	0.000000	-0.700000	-4.000000	0.500000	2.600000	0.740000	1.021900	0.830000	0.020000	9.200000	3.600000	14.900000	2	0.920000	1.023800	0.740000	7.500000	5.000000	-1.200000	11.200000	4	0.770000	0.690000	0.170000	3.400000	-7.600000	-9.400000	-5.800000	5	1.007200	0.000000	2.200000	-0.600000	-1.800000	2.900000	3.600000	0.950000	1.020900	0.390000	0.040000	8.000000	6.400000	9.500000

Dataset Summary

	count	mean	std	min	25%	50%	75%	max
DATE	3654.000000	20045678.754242	28742.871733	20000101.000000	20020702.250000	20045666.000000	20070702.750000	20100101.000000
MONTH	3654.000000	6.520799	3.450083	1.000000	4.000000	7.000000	10.000000	12.000000
BASEL_cloud_cover	3654.000000	5.418446	2.325497	0.000000	4.000000	6.000000	7.000000	8.000000
BASEL_humidity	3654.000000	0.745107	0.107788	0.380000	0.670000	0.760000	0.830000	0.980000
BASEL_pressure	3654.000000	1.017876	0.007962	0.985600	1.013300	1.017700	1.022700	1.040800
BASEL_global_radiation	3654.000000	1.330380	0.935348	0.050000	0.530000	1.110000	2.060000	3.550000
BASEL_precipitation	3654.000000	0.234849	0.536267	0.000000	0.000000	0.000000	0.210000	7.570000
BASEL_sunshine	3654.000000	4.661193	4.330112	0.000000	0.500000	3.600000	8.000000	15.300000
BASEL_temp_mean	3654.000000	11.022797	7.414754	-9.300000	5.300000	11.400000	16.900000	29.000000
BASEL_temp_min	3654.000000	6.989135	6.653356	-16.000000	2.000000	7.300000	12.400000	20.800000
BASEL_temp_max	3654.000000	15.536782	8.721323	-5.700000	8.700000	15.800000	22.300000	38.600000
BUDAPEST_cloud_cover	3654.000000	4.890531	2.386442	0.000000	3.000000	5.000000	7.000000	8.000000
BUDAPEST_humidity	3654.000000	0.656505	0.149603	0.260000	0.540000	0.650000	0.770000	1.000000
BUDAPEST_pressure	3654.000000	1.016935	0.007795	0.989100	1.012100	1.016500	1.021475	1.043800
BUDAPEST_global_radiation	3654.000000	1.465487	0.977986	0.040000	0.580000	1.340000	2.310000	3.490000
BUDAPEST_precipitation	3654.000000	0.136442	0.408932	0.000000	0.000000	0.000000	0.030000	6.960000
BUDAPEST_sunshine	3654.000000	5.753229	4.475439	0.000000	1.100000	5.900000	9.600000	14.900000
BUDAPEST_temp_mean	3654.000000	12.174849	8.744451	-9.800000	5.100000	12.800000	19.300000	33.100000
BUDAPEST_temp_max	3654.000000	16.629091	9.981538	-6.600000	8.400000	17.400000	25.000000	40.100000
DE_BILT_cloud_cover	3654.000000	5.303229	2.279416	0.000000	4.000000	6.000000	7.000000	8.000000
DE_BILT_wind_speed	3654.000000	3.395293	1.422020	0.700000	2.300000	3.200000	4.200000	10.300000
DE_BILT_wind_gust	3654.000000	9.986316	3.582408	2.000000	7.000000	10.000000	12.000000	28.000000
DE_BILT_humidity	3654.000000	0.817882	0.097465	0.370000	0.760000	0.830000	0.890000	1.000000
DE_BILT_pressure	3654.000000	1.015299	0.009861	0.973200	1.009400	1.015700	1.021700	1.044900
DE_BILT_global_radiation	3654.000000	1.190903	0.870267	0.110000	0.410000	1.020000	1.860000	3.410000
DE_BILT_precipitation	3654.000000	0.236888	0.459495	0.000000	0.000000	0.010000	0.290000	4.250000
DE_BILT_sunshine	3654.000000	4.744444	3.995637	0.000000	1.100000	4.100000	7.500000	15.500000
DE_BILT_temp_mean	3654.000000	10.703530	6.190770	-7.900000	6.200000	11.000000	15.500000	26.900000
DE_BILT_temp_min	3654.000000	6.397099	5.639597	-14.400000	2.300000	6.800000	10.800000	20.800000
DE_BILT_temp_max	3654.000000	14.798604	7.210740	-4.700000	9.200000	14.900000	20.200000	35.700000
DRESDEN_cloud_cover	3654.000000	5.405036	2.194769	0.000000	4.000000	6.000000	7.000000	8.000000
DRESDEN_wind_speed	3654.000000	4.256924	1.775045	1.000000	2.900000	3.900000	5.200000	12.200000
DRESDEN_wind_gust	3654.000000	10.924576	4.031649	2.900000	8.000000	10.300000	13.200000	34.300000
DRESDEN_humidity	3654.000000	0.759023	0.132420	0.320000	0.670000	0.770000	0.860000	1.000000
DRESDEN_global_radiation	3654.000000	1.263432	0.936443	0.030000	0.440000	1.090000	1.980000	3.660000
DRESDEN_precipitation	3654.000000	0.175881	0.459725	0.000000	0.000000	0.000000	0.170000	15.800000
DRESDEN_sunshine	3654.000000	4.815736	4.426682	0.000000	0.600000	3.900000	8.200000	15.800000
DRESDEN_temp_mean	3654.000000	9.800629	7.854752	-16.300000	3.700000	10.200000	16.100000	30.400000
DRESDEN_temp_min	3654.000000	5.924056	6.934514	-20.400000	0.800000	6.300000	11.500000	23.500000
DRESDEN_temp_max	3654.000000	13.671346	9.038833	-13.600000	6.300000	13.900000	20.900000	36.400000
DUSSELDORF_cloud_cover	3654.000000	5.141762	2.115639	0.000000	4.000000	6.000000	7.000000	8.000000
DUSSELDORF_wind_speed	3654.000000	3.963738	1.718106	1.000000	2.600000	3.700000	5.000000	12.200000
DUSSELDORF_wind_gust	3654.000000	10.591680	3.884296	2.800000	7.800000	10.100000	12.700000	40.300000
DUSSELDORF_humidity	3654.000000	0.755744	0.111595	0.260000	0.690000	0.770000	0.840000	1.000000
DUSSELDORF_pressure	3654.000000	1.016000	0.009302	0.975900	1.010400	1.016200	1.021800	1.045000
DUSSELDORF_global_radiation	3654.000000	1.147362	0.880692	0.110000	0.380000	0.920000	1.780000	3.490000
DUSSELDORF_precipitation	3654.000000	0.218043	0.439578	0.000000	0.000000	0.010000	0.250000	5.740000
DUSSELDORF_sunshine	3654.000000	4.324111	4.209463	0.000000	0.400000	3.200000	7.300000	16.000000
DUSSELDORF_temp_mean	3654.000000	11.142009	6.689373	-11.100000	6.125000	11.500000	16.200000	29.200000
DUSSELDORF_temp_min	3654.000000	6.865736	6.150650	-19.900000	2.500000	7.300000	11.600000	21.500000
DUSSELDORF_temp_max	3654.000000	15.312014	7.778961	-8.500000	9.300000	15.400000	21.200000	38.500000
HEATHROW_cloud_cover	3654.000000	5.272031	2.011846	0.000000	4.000000	6.000000	7.000000	8.000000
HEATHROW_humidity	3654.000000	0.758358	0.102410	0.420000	0.690000	0.760000	0.840000	1.000000
HEATHROW_pressure	3654.000000	1.015192	0.010561	0.971500	1.009000	1.016000	1.022100	1.043800
HEATHROW_global_radiation	3654.000000	1.196970	0.881638	0.120000	0.430000	0.960000	1.860000	3.490000
HEATHROW_precipitation	3654.000000	0.178279	0.367572	0.000000	0.000000	0.020000	0.180000	3.660000
HEATHROW_sunshine	3654.000000	4.433498	3.982646	0.000000	0.600000	3.700000	7.200000	15.500000
HEATHROW_temp_mean	3654.000000	11.822386	5.610018	-2.200000	7.600000	11.700000	16.300000	29.000000
HEATHROW_temp_min	3654.000000	8.002737	5.230449	-6.800000	4.100000	8.250000	12.100000	20.600000
HEATHROW_temp_max	3654.000000	15.637438	6.385440	0.200000	10.800000	15.400000	20.500000	37.900000
KASSEL_wind_speed	3654.000000	2.478079	0.999386	0.000000	1.700000	2.300000	3.000000	7.600000
KASSEL_wind_gust	3654.000000	9.329557	3.373451	2.100000	6.900000	8.900000	11.200000	41.000000
KASSEL_humidity	3654.000000	0.785200	0.120909	0.340000	0.710000	0.800000	0.880000	1.000000
KASSEL_pressure	3654.000000	1.016373	0.009107	0.978600	1.010800	1.016500	1.022200	1.045900
KASSEL_global_radiation	3654.000000	1.183087	0.882655	0.030000	0.390000	1.020000	1.830000	3.470000
KASSEL_precipitation	3654.000000	0.202211	0.407147	0.000000	0.000000	0.010000	0.210000	5.420000
KASSEL_sunshine	3654.000000	4.136836	4.159699	0.000000	0.300000	2.900000	7.000000	15.000000
KASSEL_temp_mean	3654.000000	9.581007	7.203922	-14.500000	4.100000	9.800000	15.300000	28.400000
KASSEL_temp_min	3654.000000	5.586864	6.349421	-19.000000	0.900000	5.900000	10.600000	21.100000
KASSEL_temp_max	3654.000000	13.821702	8.546460	-12.100000	7.100000	13.900000	20.500000	36.700000
LJUBLJANA_cloud_cover	3654.000000	4.930213	2.367843	0.000000	3.000000	5.000000	7.000000	8.000000
LJUBLJANA_wind_speed	3654.000000	1.301423	0.629852	0.100000	0.800000	1.200000	1.600000	5.100000
LJUBLJANA_humidity	3654.000000	0.743013	0.137274	0.360000	0.640000	0.750000	0.860000	0.990000
LJUBLJANA_pressure	3654.000000	1.017947	0.007704	0.983300	1.013200	1.017500	1.022500	1.043700
LJUBLJANA_global_radiation	3654.000000	1.414031	1.000020	0.040000	0.530000	1.190000	2.270000	3.550000
LJUBLJANA_precipitation	3654.000000	0.367263	0.916321	0.000000	0.000000	0.000000	0.207500	8.640000
LJUBLJANA_sunshine	3654.000000	5.412397	4.507394	0.000000	0.600000	5.200000	9.000000	15.000000
LJUBLJANA_temp_mean	3654.000000	11.511604	8.250707	-10.800000	4.900000	11.800000	18.100000	28.400000
LJUBLJANA_temp_min	3654.000000	7.071757	7.355434	-16.200000	1.000000	7.800000	13.200000	21.500000
LJUBLJANA_temp_max	3654.000000	16.352053	9.509272	-7.500000	8.700000	16.800000	24.000000	37.300000
MAASTRICHT_cloud_cover	3654.000000	5.337712	2.401823	0.000000	4.000000	6.000000	7.000000	8.000000
MAASTRICHT_wind_speed	3654.000000	4.205720	1.883268	1.000000	2.800000	3.800000	5.300000	12.300000
MAASTRICHT_wind_gust	3654.000000	10.729338	4.069453	3.000000	8.000000	10.000000	13.000000	31.000000
MAASTRICHT_humidity	3654.000000	0.792003	0.110260	0.370000	0.720000	0.810000	0.880000	1.000000
MAASTRICHT_pressure	3654.000000	1.016035	0.009313	0.975700	1.010500	1.016300	1.022000	1.043400
MAASTRICHT_global_radiation	3654.000000	1.193410	0.902938	0.030000	0.400000	1.010000	1.860000	3.520000
MAASTRICHT_precipitation	3654.000000	0.220649	0.444137	0.000000	0.000000	0.010000	0.230000	5.870000
MAASTRICHT_sunshine	3654.000000	4.652354	4.015278	0.000000	1.000000	3.950000	7.400000	15.200000
MAASTRICHT_temp_mean	3654.000000	10.840230	6.604143	-12.100000	6.000000	11.200000	15.900000	28.800000
MAASTRICHT_temp_min	3654.000000	6.854871	5.954737	-16.200000	2.600000	7.200000	11.500000	21.300000
MAASTRICHT_temp_max	3654.000000	14.805939	7.653391	-7.800000	8.900000	15.000000	20.600000	36.300000
MALMO_wind_speed	3654.000000	2.918035	1.534168	0.000000	1.800000	2.700000	3.800000	9.500000
MALMO_precipitation	3654.000000	0.166732	0.395186	0.000000	0.000000	0.000000	0.150000	7.690000
MALMO_temp_mean	3654.000000	9.164970	6.897853	-13.800000	3.800000	9.150000	15.000000	24.700000
MALMO_temp_min	3654.000000	5.663246	6.477001	-19.500000	0.925000	5.800000	11.100000	19.700000
MALMO_temp_max	3654.000000	12.731773	7.849050	-7.500000	6.200000	12.700000	19.300000	31.400000
MONTELIMAR_wind_speed	3654.000000	3.680952	2.133979	0.000000	2.000000	3.100000	5.100000	13.200000
MONTELIMAR_humidity	3654.000000	0.690794	0.129024	0.340000	0.600000	0.690000	0.790000	0.980000
MONTELIMAR_pressure	3654.000000	1.017094	0.006988	0.986200	1.013200	1.017000	1.021100	1.038700
MONTELIMAR_global_radiation	3654.000000	1.647783	1.007065	0.020000	0.750000	1.520000	2.550000	3.640000
MONTELIMAR_precipitation	3654.000000	0.253426	0.910761	0.000000	0.000000	0.000000	0.040000	15.400000
MONTELIMAR_temp_mean	3654.000000	14.241215	7.193924	-4.000000	8.400000	14.200000	20.000000	30.800000
MONTELIMAR_temp_min	3654.000000	9.535222	6.326726	-8.800000	4.600000	9.600000	14.800000	24.900000
MONTELIMAR_temp_max	3654.000000	18.948741	8.557584	-2.000000	12.200000	18.800000	25.700000	41.100000
MUENCHEN_cloud_cover	3654.000000	5.226054	2.318547	0.000000	4.000000	6.000000	7.000000	8.000000
MUENCHEN_wind_speed	3654.000000	2.792255	1.315428	0.700000	1.900000	2.500000	3.300000	10.400000
MUENCHEN_wind_gust	3654.000000	9.769814	4.291187	2.600000	6.600000	8.700000	11.900000	30.900000
MUENCHEN_humidity	3654.000000	0.741946	0.132932	0.200000	0.650000	0.750000	0.840000	1.000000
MUENCHEN_pressure	3654.000000	1.017450	0.008226	0.984000	1.012600	1.017200	1.022500	1.044000
MUENCHEN_global_radiation	3654.000000	1.426429	0.983942	0.190000	0.580000	1.150000	2.230000	3.650000
MUENCHEN_precipitation	3654.000000	0.261700	0.599618	0.000000	0.000000	0.010000	0.280000	9.790000
MUENCHEN_sunshine	3654.000000	5.219814	4.594811	0.000000	0.700000	4.400000	8.900000	15.700000
MUENCHEN_temp_mean	3654.000000	10.051587	7.903211	-12.900000	3.900000	10.400000	16.300000	29.200000
MUENCHEN_temp_min	3654.000000	5.997126	7.055925	-16.400000	0.600000	6.300000	11.675000	22.000000
MUENCHEN_temp_max	3654.000000	14.540285	9.170164	-9.900000	7.300000	14.800000	21.875000	37.000000
OSLO_cloud_cover	3654.000000	5.608101	2.170706	0.000000	4.000000	6.000000	8.000000	8.000000
OSLO_wind_speed	3654.000000	2.663656	1.364321	0.000000	1.700000	2.400000	3.400000	11.000000
OSLO_wind_gust	3654.000000	9.094800	3.471479	1.500000	6.700000	8.700000	11.300000	27.300000
OSLO_humidity	3654.000000	0.723298	0.151112	0.240000	0.620000	0.750000	0.850000	1.000000
OSLO_pressure	3654.000000	1.011396	0.012005	0.959000	1.003700	1.011600	1.019400	1.051100
OSLO_global_radiation	3654.000000	1.047244	0.978529	0.010000	0.170000	0.705000	1.767500	3.530000
OSLO_precipitation	3654.000000	0.239792	0.512402	0.000000	0.000000	0.000000	0.240000	5.600000
OSLO_sunshine	3654.000000	4.848714	4.879549	0.000000	0.000000	3.900000	8.200000	24.000000
OSLO_temp_mean	3654.000000	7.198194	7.990930	-18.100000	1.100000	7.000000	13.900000	25.400000
OSLO_temp_min	3654.000000	3.845484	7.502278	-20.700000	-1.300000	3.700000	10.000000	20.700000
OSLO_temp_max	3654.000000	11.033443	9.002142	-15.600000	3.700000	10.900000	18.475000	33.000000
PERPIGNAN_wind_speed	3654.000000	4.669376	2.651377	0.800000	2.600000	3.900000	6.200000	16.300000
PERPIGNAN_humidity	3654.000000	0.651522	0.149114	0.220000	0.540000	0.650000	0.770000	0.970000
PERPIGNAN_pressure	3654.000000	1.016451	0.006809	0.983000	1.012800	1.016500	1.020400	1.036500
PERPIGNAN_global_radiation	3654.000000	1.711773	0.941671	0.030000	0.930000	1.570000	2.510000	3.660000
PERPIGNAN_precipitation	3654.000000	0.150733	0.772949	0.000000	0.000000	0.000000	0.020000	16.040000
PERPIGNAN_temp_mean	3654.000000	16.035468	6.476893	-0.600000	11.000000	15.800000	21.400000	31.800000
PERPIGNAN_temp_min	3654.000000	11.615900	6.373871	-5.900000	6.900000	11.500000	16.900000	26.300000
PERPIGNAN_temp_max	3654.000000	20.455337	6.974910	1.300000	14.900000	20.300000	26.000000	38.200000
ROMA_cloud_cover	3654.000000	3.520799	2.198344	0.000000	2.000000	3.000000	5.000000	8.000000
ROMA_humidity	3654.000000	0.735025	0.121004	0.180000	0.650000	0.740000	0.830000	0.990000
ROMA_pressure	3654.000000	1.015247	0.006743	0.982900	1.011400	1.015300	1.019200	1.039100
ROMA_global_radiation	3654.000000	1.568177	0.878505	0.050000	0.820000	1.505000	2.390000	3.330000
ROMA_sunshine	3654.000000	7.162397	4.015933	0.000000	3.900000	8.000000	10.500000	13.800000
ROMA_temp_mean	3654.000000	16.059579	6.941017	-0.700000	10.300000	15.900000	21.900000	31.500000
ROMA_temp_min	3654.000000	11.170115	6.424980	-4.400000	6.000000	11.100000	16.600000	25.000000
ROMA_temp_max	3654.000000	21.103229	7.626300	0.000000	14.800000	21.000000	27.400000	40.000000
SONNBLICK_cloud_cover	3654.000000	5.446907	2.437457	0.000000	4.000000	6.000000	8.000000	8.000000
SONNBLICK_humidity	3654.000000	0.853952	0.174900	0.100000	0.800000	0.930000	0.970000	1.000000
SONNBLICK_global_radiation	3654.000000	1.693919	0.898277	0.170000	0.930000	1.600000	2.300000	4.420000
SONNBLICK_precipitation	3654.000000	0.541475	0.771348	0.000000	0.000000	0.180000	0.840000	5.950000
SONNBLICK_sunshine	3654.000000	4.891078	4.470904	0.000000	0.000000	4.300000	8.700000	15.600000
SONNBLICK_temp_mean	3654.000000	-4.626327	6.987080	-26.600000	-9.400000	-4.400000	0.700000	13.800000
SONNBLICK_temp_min	3654.000000	-6.884319	7.120333	-30.300000	-11.800000	-6.400000	-1.100000	8.700000
SONNBLICK_temp_max	3654.000000	-2.352244	6.972886	-24.700000	-7.100000	-2.200000	2.700000	14.300000
STOCKHOLM_cloud_cover	3654.000000	5.245758	3.362460	-99.000000	4.000000	6.000000	7.000000	9.000000
STOCKHOLM_pressure	3654.000000	1.011074	0.033838	-0.099000	1.004525	1.012100	1.019800	1.051200
STOCKHOLM_precipitation	3654.000000	0.149039	0.345369	0.000000	0.000000	0.000000	0.130000	4.300000
STOCKHOLM_sunshine	3654.000000	5.101478	4.943148	-1.700000	0.200000	4.300000	8.700000	17.800000
STOCKHOLM_temp_mean	3654.000000	8.049808	7.829552	-17.000000	2.000000	7.900000	14.675000	26.200000
STOCKHOLM_temp_min	3654.000000	5.104215	7.250744	-19.700000	0.000000	5.000000	11.200000	21.200000
STOCKHOLM_temp_max	3654.000000	11.470635	8.950217	-14.500000	4.100000	11.000000	19.000000	32.900000
TOURS_wind_speed	3654.000000	3.677258	1.519866	0.700000	2.600000	3.400000	4.600000	10.800000
TOURS_humidity	3654.000000	0.781872	0.115572	0.330000	0.700000	0.800000	0.870000	1.000000
TOURS_pressure	3654.000000	1.016639	0.018885	0.000300	1.012100	1.017300	1.022200	1.041400
TOURS_global_radiation	3654.000000	1.369787	0.926472	0.050000	0.550000	1.235000	2.090000	3.560000
TOURS_precipitation	3654.000000	0.186100	0.422151	0.000000	0.000000	0.000000	0.160000	6.200000
TOURS_temp_mean	3654.000000	12.205802	6.467155	-6.200000	7.600000	12.300000	17.200000	31.200000
TOURS_temp_min	3654.000000	7.860536	5.692256	-13.000000	3.700000	8.300000	12.300000	22.600000
TOURS_temp_max	3654.000000	16.551779	7.714924	-3.100000	10.800000	16.600000	22.400000	39.800000

What these summary numbers mean:

• count — how many days have a real reading (not blank)
• mean — the average value across all those days
• std — how spread out the values are; a bigger number means more day-to-day swing
• min / max — the lowest and highest value ever recorded
• 25% / 50% / 75% — if you lined up every value from lowest to highest, these are the values 1/4, 1/2, and 3/4 of the way along

Step 3: Check for Missing Data

Real-world sensors sometimes fail to record a reading. Before doing anything else, we check every column for blanks ("missing values") so we know how much clean-up is needed.

print_header("Data Types & Missing Values")
display(pd.DataFrame({
    'Data Type': df.dtypes,
    'Missing Values': df.isna().sum(),
    '% Missing': (df.isna().mean()*100).round(2)
}))

Data Types & Missing Values

	Data Type	Missing Values	% Missing
DATE	int64	0	0.0
MONTH	int64	0	0.0
BASEL_cloud_cover	int64	0	0.0
BASEL_humidity	float64	0	0.0
BASEL_pressure	float64	0	0.0
...	...	...	...
TOURS_global_radiation	float64	0	0.0
TOURS_precipitation	float64	0	0.0
TOURS_temp_mean	float64	0	0.0
TOURS_temp_min	float64	0	0.0
TOURS_temp_max	float64	0	0.0

165 rows × 3 columns

Step 4: Clean the Data

Four clean-up steps happen here, in order:

1. Throw out physically impossible readings — the check below; this turned out to matter enormously
2. Remove incomplete days — any day missing a reading is dropped, since a forecaster cannot learn from a blank
3. Remove the raw calendar date — a number like 20000101 looks meaningful to a person but is meaningless to the model as a plain number, so we drop it and keep MONTH instead, which does capture the season
4. Check which readings move together — see the correlation chart below

4.1 Hunting for impossible readings

Checking for blanks is the obvious clean-up step, and almost every tutorial stops there. But a sensor can also fail by reporting a number that is simply wrong — and a blank-check will never notice, because a wrong number is still a number.

Air pressure at sea level is always somewhere around 1 bar; it has never been recorded below about 0.87 or above 1.09. So any reading far outside that window is not weather, it is a broken sensor. Let's look.

# Air pressure at sea level physically cannot fall outside roughly 0.87-1.09 bar.
# Anything beyond that is a sensor failure, not weather.
PRESSURE_MIN, PRESSURE_MAX = 0.87, 1.09
pressure_cols = [c for c in df.columns if c.endswith('_pressure')]

implausible = pd.Series(False, index=df.index)
for col in pressure_cols:
    bad = (df[col] < PRESSURE_MIN) | (df[col] > PRESSURE_MAX)
    if bad.any():
        print(f"{col}: {bad.sum()} impossible reading(s) -> {df.loc[bad, col].tolist()}")
    implausible |= bad

print(f"\nFound {implausible.sum()} corrupted days out of {len(df)} "
      f"({implausible.sum() / len(df) * 100:.2f}% of the data)")

# Remove them - a handful of bad rows can do enormous damage, as we will see
df = df[~implausible].reset_index(drop=True)
print(f"{len(df)} days remain")

STOCKHOLM_pressure: 3 impossible reading(s) -> [-0.099, -0.099, -0.099]
TOURS_pressure: 1 impossible reading(s) -> [0.0003]

Found 4 corrupted days out of 3654 (0.11% of the data)
3650 days remain

Why this tiny clean-up matters so much. Only four days out of 3,654 carried a corrupted pressure reading — values like -0.099 bar (negative pressure, which cannot exist) and 0.0003 bar (a near-vacuum). That is roughly one hundredth of one percent of the data.

Yet leaving those four rows in was enough to make several models score worse than useless. Because the model multiplies each input by a weight, one absurd input produces one absurd output — a single day's pressure estimate missed by over 700 hPa, which by itself dragged an entire model's score below zero.

The lesson is worth remembering: dropna() only catches blanks, not nonsense. A handful of bad numbers, invisible in any summary table, can quietly ruin an entire analysis.

# 1. Handle Missing Values
rows_before = len(df)
df = df.dropna() # Drop rows with missing values
rows_after = len(df)
print(f"Dropped {rows_before - rows_after} rows with missing values ({rows_before} -> {rows_after})")

Dropped 0 rows with missing values (3650 -> 3650)

# 2. Drop DATE (raw int date has no meaningful magnitude for a linear model; MONTH already captures season)
df = df.drop('DATE', axis=1)

# 3. Visualize Correlation Matrix
import seaborn as sns
import matplotlib.pyplot as plt

plt.figure(figsize=(12, 10))
sns.heatmap(df.corr(numeric_only=True), cmap='coolwarm', annot=False)
plt.title("Correlation Matrix of Numerical Features")
plt.show()

What is a correlation matrix?

It's a grid that shows, for every pair of weather readings, how closely they move together — from -1 (perfectly opposite) to +1 (perfectly together), with 0 meaning no relationship at all.

Value	Meaning
+1.0	Move perfectly together
+0.7 to +0.9	Strong same-direction relationship
+0.4 to +0.6	Moderate same-direction relationship
+0.1 to +0.3	Weak same-direction relationship
0	No relationship
-0.1 to -0.3	Weak opposite-direction relationship
-0.4 to -0.6	Moderate opposite-direction relationship
-0.7 to -0.9	Strong opposite-direction relationship
-1.0	Move perfectly opposite

This helps us sanity-check the data before training — e.g. we'd expect sunshine and temperature to move together.

# 4. Feature Selection
# Define Features and Target Variable
# Each target is dropped from every feature set, including the OTHER two targets,
# so no model can see another target's answer as an input feature
targets = ['BASEL_temp_mean', 'BASEL_humidity', 'BASEL_pressure']

X1 = df.drop(columns=targets) #axis is column
y1 = df['BASEL_temp_mean']

X2 = df.drop(columns=targets)
y2 = df['BASEL_humidity']

X3 = df.drop(columns=targets)
y3 = df['BASEL_pressure']

Step 5: Set Aside Recent Years for Testing

We split the data by time, not at random: the model learns from the earliest 80% of days (2000 to the start of 2008) and is tested on the most recent 20% (2008 to 2010), which it never sees during training.

Why this matters: if we shuffled the days randomly, the model could learn from 2009 and then be tested on 2003 — effectively studying the future to answer questions about the past. No real forecaster gets that luxury, so a random split would flatter the results. Training on the past and testing on the future is the honest way.

We also build the feature sets so that no model can peek at the other two targets. When predicting Basel's humidity, the model is never shown Basel's actual temperature or pressure for that same day.

# Chronological split: rows are already in date order, so the first 80% of rows
# are the earliest days and the last 20% are the most recent.
split_idx = int(len(df) * 0.8)

# Split Data Temperature
X1_train, X1_test = X1.iloc[:split_idx], X1.iloc[split_idx:]
y1_train, y1_test = y1.iloc[:split_idx], y1.iloc[split_idx:]

# Split Data Humidity
X2_train, X2_test = X2.iloc[:split_idx], X2.iloc[split_idx:]
y2_train, y2_test = y2.iloc[:split_idx], y2.iloc[split_idx:]

# Split Data Pressure
X3_train, X3_test = X3.iloc[:split_idx], X3.iloc[split_idx:]
y3_train, y3_test = y3.iloc[:split_idx], y3.iloc[split_idx:]

print(f"Training on {split_idx} earliest days, testing on {len(df) - split_idx} most recent days")

Training on 2920 earliest days, testing on 730 most recent days

Step 6: Train Three Separate Forecasters

We train three independent models, one for temperature, one for humidity, one for pressure. Each one uses Linear Regression — a straightforward technique that looks for the best straight-line relationship between the input readings (other cities' weather, month, etc.) and the target it's trying to predict.

from sklearn.linear_model import LinearRegression

# Init Temperature Model
model_temp = LinearRegression()
# Train Temperature Model
model_temp.fit(X1_train, y1_train)

# Init Humidity Model
model_humidity = LinearRegression()
# Train Humidity Model
model_humidity.fit(X2_train, y2_train)

# Init Pressure Model
model_pressure = LinearRegression()
# Train Pressure Model
model_pressure.fit(X3_train, y3_train)

LinearRegression()

In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.
On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.

Step 7: Check How Good the Estimates Are

Now we ask each model to estimate the test days it never saw, and compare its answers to what actually happened.

A note on units. The raw dataset stores humidity as a fraction (0.89 meaning 89%) and pressure in bar (1.0286 meaning 1028.6 hPa). Scores in those raw units are hard to interpret, so below we convert every error back into units a person actually recognises: °C, %, and hPa.

from sklearn.metrics import mean_squared_error, mean_absolute_error, r2_score

# Convert each target back into human-readable units:
#   temperature is already in degrees C
#   humidity is stored as a fraction, so x100 gives percent
#   pressure is stored in bar, so x1000 gives hPa
UNITS = {
    'Temperature': ('°C', 1),
    'Humidity':    ('%', 100),
    'Pressure':    ('hPa', 1000),
}

def evaluate(name, y_true, y_pred):
    """Print MAE (in real units), MSE and R2 for one target."""
    unit, factor = UNITS[name]
    mae = mean_absolute_error(y_true, y_pred) * factor
    mse = mean_squared_error(y_true, y_pred)
    r2 = r2_score(y_true, y_pred)

    print(f"{name} Evaluation")
    print(f"  Average error (MAE): {mae:.2f} {unit}")
    print(f"  Mean Squared Error:  {mse:.6g}")
    print(f"  R2 Score:            {r2:.4f}")
    print()
    return {'target': name, 'mae': mae, 'unit': unit, 'r2': r2}

y1_pred = model_temp.predict(X1_test)
y2_pred = model_humidity.predict(X2_test)
y3_pred = model_pressure.predict(X3_test)

results = [
    evaluate('Temperature', y1_test, y1_pred),
    evaluate('Humidity',    y2_test, y2_pred),
    evaluate('Pressure',    y3_test, y3_pred),
]

Temperature Evaluation
  Average error (MAE): 0.38 °C
  Mean Squared Error:  0.239053
  R2 Score:            0.9956

Humidity Evaluation
  Average error (MAE): 3.54 %
  Mean Squared Error:  0.00207507
  R2 Score:            0.7952

Pressure Evaluation
  Average error (MAE): 0.54 hPa
  Mean Squared Error:  4.74644e-07
  R2 Score:            0.9935

How to read the scores:

• Average error (MAE) — the most human-readable one. It is the typical size of the model's mistake, in real units. "1.2 °C" means that on an average day the estimate was off by about 1.2 degrees.
• Mean Squared Error (MSE) — similar idea, but mistakes are squared before averaging, so a few big misses count much more heavily than many small ones. Lower is better. It is not in readable units, which is exactly why MAE is shown alongside it.
• R² Score — a 0-to-1 score for how much of the day-to-day pattern the model explains. 1.0 means it explains everything; 0 means it is no better than always guessing the long-term average.

A good score on its own does not prove a model is useful, though — that needs a comparison, which is the next step.

Step 8: See the Predictions vs. Reality

Each chart below plots what actually happened (x-axis) against what the model predicted (y-axis) for every test day. The red dashed line is where a perfect forecaster would land — the closer the blue dots hug that line, the more accurate the model.

import matplotlib.pyplot as plt

def plot_regression(y_true, y_pred, title, unit):
    plt.figure(figsize=(6, 6)) # Set figure size
    plt.scatter(y_true, y_pred, color='skyblue', edgecolors='k', alpha=0.7)
    max_val = max(max(y_true), max(y_pred))
    min_val = min(min(y_true), min(y_pred))
    plt.plot([min_val, max_val], [min_val, max_val], 'r--', label='Ideal Prediction')

    plt.xlabel(f'Actual Values ({unit})')
    plt.ylabel(f'Predicted Values ({unit})')
    plt.title(title)
    plt.legend()
    plt.grid(True)
    plt.axis('equal')
    plt.tight_layout()
    plt.show()

# Temperature Plot (°C)
plot_regression(y1_test, y1_pred, 'Actual Temperature vs Predicted Temperature', '°C')

# Humidity Plot (%)
plot_regression(y2_test, y2_pred, 'Actual Humidity vs Predicted Humidity', '%')

# Pressure Plot (hPa)
plot_regression(y3_test, y3_pred, 'Actual Pressure vs Predicted Pressure', 'hPa')

Step 9: Is the Model Actually Better Than a Lazy Guess?

A high score means nothing on its own. Before trusting any model you have to ask: could something far simpler have done just as well?

So we compare against a seasonal average baseline - a "model" that ignores all the clever inputs and simply answers with the historical average for that month. If our model cannot clearly beat that, it is not earning its keep.

# Seasonal average baseline: for each month, use the average value seen in TRAINING data only
def seasonal_baseline(y_train, X_train, X_test):
    month_avg = y_train.groupby(X_train['MONTH']).mean()
    return X_test['MONTH'].map(month_avg)

print("Model vs. seasonal-average baseline (lower average error is better)\n")

comparison = []
for name, (y_tr, X_tr, X_te, y_te, y_pr) in {
    'Temperature': (y1_train, X1_train, X1_test, y1_test, y1_pred),
    'Humidity':    (y2_train, X2_train, X2_test, y2_test, y2_pred),
    'Pressure':    (y3_train, X3_train, X3_test, y3_test, y3_pred),
}.items():
    unit, factor = UNITS[name]
    base_pred = seasonal_baseline(y_tr, X_tr, X_te)

    model_mae = mean_absolute_error(y_te, y_pr) * factor
    base_mae = mean_absolute_error(y_te, base_pred) * factor
    improvement = (1 - model_mae / base_mae) * 100

    print(f"{name}")
    print(f"  Seasonal average guess: off by {base_mae:.2f} {unit}")
    print(f"  Our model:              off by {model_mae:.2f} {unit}")
    print(f"  -> {improvement:.0f}% smaller error than the lazy guess")
    print()
    comparison.append({'target': name, 'unit': unit,
                       'baseline_mae': base_mae, 'model_mae': model_mae,
                       'improvement': improvement})

Model vs. seasonal-average baseline (lower average error is better)

Temperature
  Seasonal average guess: off by 2.81 °C
  Our model:              off by 0.38 °C
  -> 86% smaller error than the lazy guess

Humidity
  Seasonal average guess: off by 6.93 %
  Our model:              off by 3.54 %
  -> 49% smaller error than the lazy guess

Pressure
  Seasonal average guess: off by 6.41 hPa
  Our model:              off by 0.54 hPa
  -> 92% smaller error than the lazy guess

Step 10: A Real Forecast - Predicting Tomorrow

Everything up to this point does something subtly different from forecasting. The models above estimate Basel's weather for the same day, using other cities' readings from that same day. That is genuinely useful - it is how you would fill in a broken sensor - but it is not predicting the future. It is more like looking around the room to work out the temperature where you are standing.

A real forecast has to use only what is known today to say something about tomorrow. So here we rebuild the problem honestly:

• Inputs: every reading from today - including Basel's own temperature, humidity and pressure, which a real forecaster obviously knows
• Target: Basel's weather the following day

We also compare against the toughest simple baseline in weather forecasting: persistence, which just guesses "tomorrow will be the same as today." That is a genuinely hard benchmark to beat, because weather really is sluggish from one day to the next.

# Build the next-day problem: today's readings (row t) predict Basel's weather on row t+1
X_next = df.iloc[:-1].reset_index(drop=True)          # today's conditions, all cities
next_targets = {t: df[t].iloc[1:].reset_index(drop=True) for t in targets}

split_next = int(len(X_next) * 0.8)
Xn_train, Xn_test = X_next.iloc[:split_next], X_next.iloc[split_next:]

print("Forecasting tomorrow from today (model vs. 'tomorrow = today' persistence)\n")

forecast_results = []
forecast_preds = {}
for name, col in [('Temperature', 'BASEL_temp_mean'),
                  ('Humidity', 'BASEL_humidity'),
                  ('Pressure', 'BASEL_pressure')]:
    unit, factor = UNITS[name]
    y_next = next_targets[col]
    yn_train, yn_test = y_next.iloc[:split_next], y_next.iloc[split_next:]

    model = LinearRegression()
    model.fit(Xn_train, yn_train)
    pred = model.predict(Xn_test)

    # Persistence baseline: tomorrow will be whatever today was
    persistence = Xn_test[col]

    model_mae = mean_absolute_error(yn_test, pred) * factor
    persist_mae = mean_absolute_error(yn_test, persistence) * factor
    r2 = r2_score(yn_test, pred)

    print(f"{name}")
    print(f"  'Same as today' guess: off by {persist_mae:.2f} {unit}")
    print(f"  Our forecast:          off by {model_mae:.2f} {unit}  (R2 = {r2:.3f})")
    print(f"  -> {(1 - model_mae / persist_mae) * 100:.0f}% smaller error than persistence")
    print()

    forecast_preds[name] = (yn_test, pred)
    forecast_results.append({'target': name, 'unit': unit, 'r2': r2,
                             'model_mae': model_mae, 'persist_mae': persist_mae})

Forecasting tomorrow from today (model vs. 'tomorrow = today' persistence)

Temperature
  'Same as today' guess: off by 1.64 °C
  Our forecast:          off by 1.30 °C  (R2 = 0.950)
  -> 21% smaller error than persistence

Humidity
  'Same as today' guess: off by 6.71 %
  Our forecast:          off by 5.49 %  (R2 = 0.508)
  -> 18% smaller error than persistence

Pressure
  'Same as today' guess: off by 3.64 hPa
  Our forecast:          off by 2.84 hPa  (R2 = 0.821)
  -> 22% smaller error than persistence

Notice how much lower these scores are than the same-day numbers. That drop is the honest cost of actually predicting the future - and it is exactly why you should be suspicious of any weather model reporting near-perfect accuracy.

Step 11: Which Cities Tell Us Most About Basel?

A linear model assigns a weight to every input. By looking at which weights are largest, we can ask a genuinely interesting question: whose weather is the best clue to Basel's?

One catch: the inputs are on wildly different scales (cloud cover runs 0-8, pressure sits near 1.03). Comparing raw weights would be meaningless, so we scale each weight by how much that reading actually varies. The result estimates how much each input really moves the answer.

import numpy as np

# Weight each coefficient by the spread of its feature, so inputs on different
# scales can be compared fairly. Result is roughly "degrees C of influence".
influence = (pd.Series(model_temp.coef_, index=X1.columns).abs()
             * X1_train.std()).sort_values(ascending=False)

top = influence.head(12).sort_values()

plt.figure(figsize=(8, 6))
plt.barh(top.index, top.values, color='#2e6f6a')
plt.xlabel('Influence on the temperature estimate (°C)')
plt.title("Which readings tell us most about Basel's temperature?")
plt.tight_layout()
plt.show()

print("Top 5 most influential readings:")
for rank, (feature, value) in enumerate(influence.head(5).items(), start=1):
    print(f"  {rank}. {feature}  ({value:.2f} °C of influence)")

Top 5 most influential readings:
  1. TOURS_temp_mean  (3.73 °C of influence)
  2. BASEL_temp_max  (3.51 °C of influence)
  3. BASEL_temp_min  (2.74 °C of influence)
  4. PERPIGNAN_temp_mean  (2.31 °C of influence)
  5. TOURS_temp_max  (2.13 °C of influence)

Step 12: When Does the Forecast Struggle?

An average error hides a lot. A model can be excellent in summer and unreliable in winter, and a single number would never show it. So we break the next-day temperature forecast's error down month by month.

# Average forecast error for each calendar month, using the next-day temperature model
yn_test_temp, pred_temp = forecast_preds['Temperature']
errors = pd.DataFrame({
    'month': Xn_test['MONTH'].values,
    'error': np.abs(yn_test_temp.values - pred_temp),
})
monthly = errors.groupby('month')['error'].mean()

month_names = ['Jan', 'Feb', 'Mar', 'Apr', 'May', 'Jun',
               'Jul', 'Aug', 'Sep', 'Oct', 'Nov', 'Dec']

plt.figure(figsize=(9, 5))
plt.bar([month_names[m - 1] for m in monthly.index], monthly.values, color='#2e6f6a')
plt.axhline(monthly.mean(), color='#c26b5f', linestyle='--',
            label=f'Year-round average ({monthly.mean():.2f} °C)')
plt.ylabel('Average error (°C)')
plt.title('Next-day temperature forecast error by month')
plt.legend()
plt.tight_layout()
plt.show()

print(f"Hardest month: {month_names[monthly.idxmax() - 1]} "
      f"(off by {monthly.max():.2f} °C on average)")
print(f"Easiest month: {month_names[monthly.idxmin() - 1]} "
      f"(off by {monthly.min():.2f} °C on average)")

Hardest month: Dec (off by 1.46 °C on average)
Easiest month: Sep (off by 1.09 °C on average)

Step 13: What We Learned

Pulling the whole analysis together:

1. Filling in the same day is easy. Given what 17 other European cities recorded today, Basel's temperature and pressure for that same day can be reconstructed almost exactly. Regional weather moves as one connected system, so the neighbours give the answer away.

2. Humidity is the stubborn one. It scores noticeably worse than temperature and pressure in every version of the experiment, because local effects like fog, rain and cloud cover can change it quickly without the whole region shifting.

3. Predicting tomorrow is a completely different, much harder problem. Once the model may only use today's information, accuracy drops sharply - and beating the plain "tomorrow will be like today" guess is a real challenge. This gap is the single most important result here.

4. Always compare to a lazy baseline. A 99% score sounds impressive until you notice a trivial rule scores nearly as well. Baselines are what turn a number into evidence.

5. How you split the data changes the answer. Testing on random days lets a model peek at the future. Testing on the most recent years - as we do here - is harder and far more honest.

Limitations worth stating plainly: this covers one city over 2000-2010, uses a straight-line model, and forecasts only one day ahead. It is a learning exercise in how to evaluate a model honestly, not a working weather service.