SMART45 Report

Dataset statistics

Number of variables	9
Number of observations	846
Missing cells	0
Missing cells (%)	0.0%
Duplicate rows	0
Duplicate rows (%)	0.0%
Total size in memory	59.6 KiB
Average record size in memory	72.2 B

Variable types

NUM	7
DATE	1
CAT	1

Warnings

`df_index` has unique values	Unique
`data` has unique values	Unique

Reproduction

Analysis started	2020-12-02 17:48:23.786745
Analysis finished	2020-12-02 17:48:32.003231
Duration	8.22 seconds
Software version	pandas-profiling v2.9.0
Download configuration	config.yaml

df_index
Date

UNIQUE

Distinct	846
Distinct (%)	100.0%
Missing	0
Missing (%)	0.0%
Memory size	6.6 KiB

Minimum	2020-10-11 00:00:00
Maximum	2020-11-30 23:00:00

Histogram

Histogram with fixed size bins (bins=50)

data
Categorical

UNIQUE

Distinct	846
Distinct (%)	100.0%
Missing	0
Missing (%)	0.0%
Memory size	6.6 KiB

16/11/2020 16:00	1
19/11/2020 23:00	1
19/11/2020 15:00	1
13/11/2020 01:00	1
20/11/2020 12:00	1
Other values (841)	841

Frequencies
Length

Common Values
Overview

Value	Count	Frequency (%)
16/11/2020 16:00	1	0.1%
19/11/2020 23:00	1	0.1%
19/11/2020 15:00	1	0.1%
13/11/2020 01:00	1	0.1%
20/11/2020 12:00	1	0.1%
24/11/2020 03:00	1	0.1%
24/10/2020 06:00	1	0.1%
19/10/2020 21:00	1	0.1%
16/11/2020 10:00	1	0.1%
17/11/2020 10:00	1	0.1%
Other values (836)	836	98.8%

Frequencies of value counts

Unique

Unique	846 ?
Unique (%)	100.0%

Histogram of lengths of the category

Length

Max length	16
Median length	16
Mean length	16
Min length	16

NO2Arpat
Real number (ℝ_≥0)

Distinct	92
Distinct (%)	10.9%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	32.90661939
Minimum	1
Maximum	100
Zeros	0
Zeros (%)	0.0%
Memory size	6.6 KiB

Quantile statistics

Minimum	1
5-th percentile	8
Q1	18
median	29
Q3	44
95-th percentile	69.75
Maximum	100
Range	99
Interquartile range (IQR)	26

Descriptive statistics

Standard deviation	19.21265679
Coefficient of variation (CV)	0.5838538613
Kurtosis	0.2337327023
Mean	32.90661939
Median Absolute Deviation (MAD)	12
Skewness	0.7911693392
Sum	27839
Variance	369.126181
Monotocity	Not monotonic

Histogram with fixed size bins (bins=50)

Value	Count	Frequency (%)
18	26	3.1%
22	23	2.7%
16	22	2.6%
24	22	2.6%
23	22	2.6%
41	21	2.5%
25	21	2.5%
28	21	2.5%
12	20	2.4%
26	20	2.4%
Other values (82)	628	74.2%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
1	5	0.6%
2	1	0.1%
3	6	0.7%
4	6	0.7%
5	5	0.6%

Value	Count	Frequency (%)
100	1	0.1%
98	1	0.1%
94	1	0.1%
92	2	0.2%
91	1	0.1%

tair
Real number (ℝ_≥0)

Distinct	843
Distinct (%)	99.6%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	14.481751
Minimum	1.176315789
Maximum	26.43589744
Zeros	0
Zeros (%)	0.0%
Memory size	6.6 KiB

Quantile statistics

Minimum	1.176315789
5-th percentile	5.916666667
Q1	11.1974359
median	14.28471154
Q3	17.85675676
95-th percentile	22.74381757
Maximum	26.43589744
Range	25.25958165
Interquartile range (IQR)	6.659320859

Descriptive statistics

Standard deviation	4.954726645
Coefficient of variation (CV)	0.3421358815
Kurtosis	-0.3295811056
Mean	14.481751
Median Absolute Deviation (MAD)	3.369230769
Skewness	-0.03068165098
Sum	12251.56135
Variance	24.54931612
Monotocity	Not monotonic

Histogram with fixed size bins (bins=50)

Value	Count	Frequency (%)
15.26923077	2	0.2%
19.38205128	2	0.2%
10.82307692	2	0.2%
13.66666667	1	0.1%
3.05	1	0.1%
12.61	1	0.1%
5.07	1	0.1%
14.43513514	1	0.1%
17.93333333	1	0.1%
14.76111111	1	0.1%
Other values (833)	833	98.5%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
1.176315789	1	0.1%
1.446153846	1	0.1%
1.702564103	1	0.1%
2.125	1	0.1%
2.1875	1	0.1%

Value	Count	Frequency (%)
26.43589744	1	0.1%
26.25405405	1	0.1%
26.21538462	1	0.1%
26.15526316	1	0.1%
25.74871795	1	0.1%

rad
Real number (ℝ_≥0)

Distinct	821
Distinct (%)	97.0%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	75.88133125
Minimum	19.33684211
Maximum	99.9
Zeros	0
Zeros (%)	0.0%
Memory size	6.6 KiB

Quantile statistics

Minimum	19.33684211
5-th percentile	36.62845816
Q1	60.97348739
median	82.33996795
Q3	93.71083333
95-th percentile	99.3381891
Maximum	99.9
Range	80.56315789
Interquartile range (IQR)	32.73734594

Descriptive statistics

Standard deviation	20.45013106
Coefficient of variation (CV)	0.2695014798
Kurtosis	-0.5675791449
Mean	75.88133125
Median Absolute Deviation (MAD)	14.06887821
Skewness	-0.7123314644
Sum	64195.60624
Variance	418.2078604
Monotocity	Not monotonic

Histogram with fixed size bins (bins=50)

Value	Count	Frequency (%)
99.9	19	2.2%
99.9	6	0.7%
97.4	2	0.2%
98.5775	2	0.2%
62.38888889	1	0.1%
95.3425	1	0.1%
99.3	1	0.1%
91.81025641	1	0.1%
50.18461538	1	0.1%
90.63076923	1	0.1%
Other values (811)	811	95.9%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
19.33684211	1	0.1%
19.6	1	0.1%
20.2125	1	0.1%
22.20769231	1	0.1%
23.04594595	1	0.1%

Value	Count	Frequency (%)
99.9	19	2.2%
99.9	6	0.7%
99.9	1	0.1%
99.87	1	0.1%
99.82571429	1	0.1%

o3
Real number (ℝ_≥0)

Distinct	836
Distinct (%)	98.8%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	761.3314002
Minimum	46.66666667
Maximum	914.5384615
Zeros	0
Zeros (%)	0.0%
Memory size	6.6 KiB

Quantile statistics

Minimum	46.66666667
5-th percentile	292.9838141
Q1	750.3397436
median	827.6076923
Q3	864.3012821
95-th percentile	893.8853695
Maximum	914.5384615
Range	867.8717949
Interquartile range (IQR)	113.9615385

Descriptive statistics

Standard deviation	179.4971704
Coefficient of variation (CV)	0.23576746
Kurtosis	4.654643893
Mean	761.3314002
Median Absolute Deviation (MAD)	46.1625
Skewness	-2.269225402
Sum	644086.3646
Variance	32219.23419
Monotocity	Not monotonic

Histogram with fixed size bins (bins=50)

Value	Count	Frequency (%)
890.35	3	0.4%
872.7	2	0.2%
883	2	0.2%
874.8974359	2	0.2%
858	2	0.2%
838.9487179	2	0.2%
840.3	2	0.2%
699	2	0.2%
892.5384615	2	0.2%
618.2702703	1	0.1%
Other values (826)	826	97.6%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
46.66666667	1	0.1%
46.975	1	0.1%
51.43589744	1	0.1%
51.51282051	1	0.1%
62.225	1	0.1%

Value	Count	Frequency (%)
914.5384615	1	0.1%
914.1	1	0.1%
911.5384615	1	0.1%
910.5128205	1	0.1%
910.3076923	1	0.1%

no2
Real number (ℝ_≥0)

Distinct	831
Distinct (%)	98.2%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	190.2322978
Minimum	40.35
Maximum	282.974359
Zeros	0
Zeros (%)	0.0%
Memory size	6.6 KiB

Quantile statistics

Minimum	40.35
5-th percentile	85.65144231
Q1	155.6032095
median	200.0259784
Q3	232.9038462
95-th percentile	262.9153418
Maximum	282.974359
Range	242.624359
Interquartile range (IQR)	77.30063669

Descriptive statistics

Standard deviation	53.91284455
Coefficient of variation (CV)	0.2834053164
Kurtosis	-0.09057386816
Mean	190.2322978
Median Absolute Deviation (MAD)	37.14102564
Skewness	-0.679053604
Sum	160936.524
Variance	2906.594808
Monotocity	Not monotonic

Histogram with fixed size bins (bins=50)

Value	Count	Frequency (%)
146.3846154	2	0.2%
154.3846154	2	0.2%
92.69230769	2	0.2%
215.2307692	2	0.2%
232.4102564	2	0.2%
163	2	0.2%
175	2	0.2%
243.75	2	0.2%
238.825	2	0.2%
208.1	2	0.2%
Other values (821)	826	97.6%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
40.35	1	0.1%
41.3	1	0.1%
42.20512821	1	0.1%
42.43589744	1	0.1%
43.46153846	1	0.1%

Value	Count	Frequency (%)
282.974359	1	0.1%
281.975	1	0.1%
277.7179487	1	0.1%
276	1	0.1%
275.35	1	0.1%

noAlpha
Real number (ℝ_≥0)

Distinct	449
Distinct (%)	53.1%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	91.14762683
Minimum	89.05263158
Maximum	93.81081081
Zeros	0
Zeros (%)	0.0%
Memory size	6.6 KiB

Quantile statistics

Minimum	89.05263158
5-th percentile	89.81205548
Q1	90.51761364
median	91.025
Q3	91.69230769
95-th percentile	92.8872549
Maximum	93.81081081
Range	4.758179232
Interquartile range (IQR)	1.174694056

Descriptive statistics

Standard deviation	0.9204398679
Coefficient of variation (CV)	0.01009834156
Kurtosis	-0.1639007852
Mean	91.14762683
Median Absolute Deviation (MAD)	0.575
Skewness	0.4515707662
Sum	77110.89229
Variance	0.8472095505
Monotocity	Not monotonic

Histogram with fixed size bins (bins=50)

Value	Count	Frequency (%)
91	11	1.3%
90.8974359	10	1.2%
91.02564103	8	0.9%
90.84615385	8	0.9%
90.87179487	7	0.8%
91.69230769	7	0.8%
90.82051282	6	0.7%
90.41025641	6	0.7%
90.74358974	6	0.7%
90.9	6	0.7%
Other values (439)	771	91.1%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
89.05263158	1	0.1%
89.05405405	1	0.1%
89.10526316	1	0.1%
89.11111111	1	0.1%
89.12121212	1	0.1%

Value	Count	Frequency (%)
93.81081081	1	0.1%
93.7027027	1	0.1%
93.67567568	1	0.1%
93.66666667	1	0.1%
93.60526316	1	0.1%

no2Alpha
Real number (ℝ_≥0)

Distinct	560
Distinct (%)	66.2%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	89.17862518
Minimum	85.71794872
Maximum	99.81081081
Zeros	0
Zeros (%)	0.0%
Memory size	6.6 KiB

Quantile statistics

Minimum	85.71794872
5-th percentile	86.64326923
Q1	87.51370656
median	88.64102564
Q3	90.42291667
95-th percentile	93.09615385
Maximum	99.81081081
Range	14.09286209
Interquartile range (IQR)	2.909210103

Descriptive statistics

Standard deviation	2.14911548
Coefficient of variation (CV)	0.02409899767
Kurtosis	1.640512446
Mean	89.17862518
Median Absolute Deviation (MAD)	1.331175131
Skewness	1.148867842
Sum	75445.1169
Variance	4.618697347
Monotocity	Not monotonic

Histogram with fixed size bins (bins=50)

Value	Count	Frequency (%)
87.92307692	7	0.8%
87.69230769	7	0.8%
87.76923077	7	0.8%
87.5	6	0.7%
87.1	5	0.6%
87.8	5	0.6%
87.17948718	5	0.6%
87.275	5	0.6%
86.69230769	4	0.5%
87.23076923	4	0.5%
Other values (550)	791	93.5%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
85.71794872	1	0.1%
85.84615385	1	0.1%
85.875	1	0.1%
85.975	1	0.1%
86	1	0.1%

Value	Count	Frequency (%)
99.81081081	1	0.1%
98.2972973	1	0.1%
98.25641026	1	0.1%
98.12820513	1	0.1%
97.3	1	0.1%

Pearson's r

The Pearson's correlation coefficient (r) is a measure of linear correlation between two variables. It's value lies between -1 and +1, -1 indicating total negative linear correlation, 0 indicating no linear correlation and 1 indicating total positive linear correlation. Furthermore, r is invariant under separate changes in location and scale of the two variables, implying that for a linear function the angle to the x-axis does not affect r.

To calculate r for two variables X and Y, one divides the covariance of X and Y by the product of their standard deviations.

Spearman's ρ

The Spearman's rank correlation coefficient (ρ) is a measure of monotonic correlation between two variables, and is therefore better in catching nonlinear monotonic correlations than Pearson's r. It's value lies between -1 and +1, -1 indicating total negative monotonic correlation, 0 indicating no monotonic correlation and 1 indicating total positive monotonic correlation.

To calculate ρ for two variables X and Y, one divides the covariance of the rank variables of X and Y by the product of their standard deviations.

Kendall's τ

Similarly to Spearman's rank correlation coefficient, the Kendall rank correlation coefficient (τ) measures ordinal association between two variables. It's value lies between -1 and +1, -1 indicating total negative correlation, 0 indicating no correlation and 1 indicating total positive correlation.

To calculate τ for two variables X and Y, one determines the number of concordant and discordant pairs of observations. τ is given by the number of concordant pairs minus the discordant pairs divided by the total number of pairs.

Phik (φk)

Phik (φk) is a new and practical correlation coefficient that works consistently between categorical, ordinal and interval variables, captures non-linear dependency and reverts to the Pearson correlation coefficient in case of a bivariate normal input distribution. There is extensive documentation available here.

Count
Matrix

First rows

	df_index	data	NO2Arpat	tair	rad	o3	no2	noAlpha	no2Alpha
0	2020-10-16 13:00:00	16/10/2020 13:00	32.0	16.128947	78.426316	829.973684	195.500000	91.157895	89.210526
1	2020-10-16 14:00:00	16/10/2020 14:00	26.0	17.792105	70.884211	847.657895	211.578947	91.052632	90.763158
2	2020-10-16 15:00:00	16/10/2020 15:00	34.0	20.611111	54.911111	870.944444	194.055556	89.861111	91.666667
3	2020-10-16 16:00:00	16/10/2020 16:00	33.0	20.522500	53.110000	897.400000	205.150000	91.000000	91.175000
4	2020-10-16 17:00:00	16/10/2020 17:00	54.0	18.324324	63.116216	870.513514	226.675676	92.243243	91.864865
5	2020-10-16 18:00:00	16/10/2020 18:00	58.0	15.188889	77.044444	859.194444	242.944444	92.416667	89.583333
6	2020-10-16 19:00:00	16/10/2020 19:00	56.0	13.643243	86.251351	869.459459	255.864865	93.135135	91.108108
7	2020-10-16 20:00:00	16/10/2020 20:00	41.0	12.323684	92.392105	874.552632	257.473684	91.657895	88.421053
8	2020-10-16 21:00:00	16/10/2020 21:00	38.0	11.344737	95.597368	869.842105	251.736842	91.210526	89.052632
9	2020-10-16 22:00:00	16/10/2020 22:00	39.0	10.902632	96.413158	866.000000	249.447368	91.052632	88.947368

Last rows

	df_index	data	NO2Arpat	tair	rad	o3	no2	noAlpha	no2Alpha
836	2020-11-30 14:00:00	30/11/2020 14:00	20.0	19.256410	30.951282	725.000000	106.820513	89.820513	89.384615
837	2020-11-30 15:00:00	30/11/2020 15:00	39.0	19.063158	33.521053	719.263158	126.421053	91.973684	88.342105
838	2020-11-30 16:00:00	30/11/2020 16:00	74.0	14.218919	46.145946	733.702703	154.189189	92.216216	88.702703
839	2020-11-30 17:00:00	30/11/2020 17:00	57.0	11.555263	56.257895	776.736842	185.605263	93.105263	88.394737
840	2020-11-30 18:00:00	30/11/2020 18:00	80.0	10.294444	63.538889	839.583333	204.555556	92.888889	89.500000
841	2020-11-30 19:00:00	30/11/2020 19:00	62.0	8.977500	71.537500	861.275000	211.175000	92.950000	91.050000
842	2020-11-30 20:00:00	30/11/2020 20:00	73.0	8.061111	77.361111	887.583333	215.388889	92.722222	93.555556
843	2020-11-30 21:00:00	30/11/2020 21:00	60.0	7.385000	72.305000	891.875000	211.275000	91.575000	88.850000
844	2020-11-30 22:00:00	30/11/2020 22:00	51.0	7.968421	66.963158	872.368421	160.605263	91.052632	88.131579
845	2020-11-30 23:00:00	30/11/2020 23:00	30.0	8.852941	63.150000	836.411765	154.323529	90.323529	87.411765

Overview

Variables

Interactions

Correlations

Pearson's r

Spearman's ρ

Kendall's τ

Phik (φk)

Missing values

Sample

First rows

Last rows