Using Statistical Regressions to Identify Factors Influencing PM_2.5 Concentrations: The Pittsburgh Supersite as a Case Study

Figures & data

TABLE 1 Results of the linear regression Model 1 for PM_2.5 concentration as the dependent variable. The symbols *, **, and § indicate significance at 0.05, 0.01, and 0.001 levels, respectively. The adjusted r² for this model is 0.59

Explanatory variable x	j Average value	j Estimate	j Standard dev.	j j	t value	Pr(> |t|)
Intercept	—	−12.6	1.57	−12.6	−8.05	2.1E-15§
[SO2]	10.5ppb	0.450	3.05E-02	4.73	14.73	< 2E-16§
Temp	14.1°C	0.449	4.93E-02	6.31	9.09	< 2E-16§
Humidity	59.0%	0.158	1.78E-02	9.32	8.87	< 2E-16§
fsummer	—	7.53	0.950	7.53	7.93	5.3E-15§
ffall	—	−0.267	0.768	−0.267	−0.35	0.73
fwinter	—	−1.28	0.780	−1.28	−1.64	0.10
iMHc	0.00587m^− 1	319	75.4	1.87	4.23	2.6E-05§
[O3]	29.7ppb	0.194	2.06E-02	5.76	9.44	< 2E-16§
UV	7.84watts/m^2	−0.247	3.93E-02	−1.94	−6.29	4.5E-10§
rSE	0.0847	8.41	1.24	0.712	6.80	1.7E-11§
rS	0.174	5.05	0.905	0.878	5.58	3.0E-08§
rSW	0.143	3.67	1.12	0.526	3.27	1.1E-3**

TABLE 2 Results of the linear regression Model 2 for PM_2.5 concentration as the dependent variable. The symbols *, **, and § indicate significance at 0.05, 0.01, and 0.001 levels, respectively. The adjusted r² for this model is 0.66.

Explanatory variable x	j Average value	j Estimate	j Standard dev.	j j	t value	Pr(> |t|)
Intercept	—	1.70	4.29	1.70	0.396	0.69
[SO2]	10.5ppb	0.589	0.220	6.19	2.678	7.5E-03**
Temp	14.1°C	−1.20	0.204	−16.9	−5.896	4.9E-09§
Humidity	59.0%	8.66E-02	0.104	5.11	0.831	0.41
[SO2]^2	180ppb^2	−8.14E-03	1.45E-03	−1.47	−5.616	2.5E-08§
Temp^2	294(°C)^2	4.02E-02	4.15E-03	11.8	9.700	< 2e-16§
Humid^2	3840(%)^2	−1.09E-03	7.03E-04	−4.19	−1.555	0.12
fsummer	—	2.70	0.973	2.70	2.773	5.7E-03**
ffall	—	−0.455	0.720	−0.455	−0.632	0.53
fwinter	—	−2.10	0.753	−2.10	−2.789	5.4E-03**
iMHc	0.00587m^− 1	353	69.2	2.07	5.105	3.9E-07§
[O3]	29.7ppb	0.101	2.44E-02	2.99	4.139	3.8E-05§
UV	7.84watts/m^2	−0.278	3.61E-02	−2.18	−7.692	3.1E-14§
rSE	0.0847	8.69	1.15	0.736	7.588	6.8E-14§
rS	0.174	4.29	0.838	0.745	5.114	3.7E-07§
rSW	0.143	1.73	1.04	0.247	1.664	9.6E-02
[SO2]× Temp	136ppb×°C	−5.00E-04	1.14E-02	−6.80E–02	−0.044	0.96
[SO2]× Humid	604ppb× %	−1.12E-04	3.04E-03	−6.73E–02	−0.037	0.97
Temp× Humid	776°C× %	1.12E-02	2.58E-03	8.66	4.317	1.7E-05§
[SO2]× Temp× Humid	7350 ppb×°C× %	2.25E-04	1.94E-04	1.65	1.158	0.25

TABLE 3 Results of the linear regression Model 3 for PM_2.5 concentration as the dependent variable. The symbols *, **, and § indicate significance at 0.05, 0.01, and 0.001 levels, respectively. The adjusted r² for this model is 0.52.

Explanatory variable x	j Average value	j Estimate	j Standard dev.	j j	t value	Pr(> |t|)
Intercept	—	15.6	2.05	15.6	7.59	6.7e-14§
Temp	14.1°C	−1.59	0.176	−22.3	−9.03	< 2e-16§
Humidity	59.0%	−7.42E-02	2.83E-02	−4.38	−2.62	9.0E-3**
Temp^2	294(°C)^2	4.96E-02	3.83E-03	14.6	12.9	< 2e-16§
fsummer	—	1.83	1.10	1.83	1.67	0.096
ffall	—	−4.14E-02	0.814	−4.14E-02	−0.051	0.96
fwinter	—	−0.554	0.813	−0.554	−0.681	0.50
Temp× Humid	776°C× %	1.71E–02	1.81E–03	13.3	9.50	< 2e-16§

FIG. 1 Fitted PM_2.5 vs. Observed PM_2.5. A random sample with size 100 is taken from all 3-h observations with valid observed data and fitted values. The length of error bars of the fitted values is set to the standard error from the linear regression.

TABLE 4 Results of the linear regression Model 4 for PM_2.5 concentration as the dependent variable with autocorrelated errors. The symbols *, **, and § indicate significance at 0.05, 0.01, and 0.001 levels, respectively. The adjusted r² equals 0.54, slightly lower than Model 2 without autocorrelation, but Model 2 incorrectly assumes independent errors. Model 4 gives an estimate for the first order autocorrelation coefficient of 0.77.

Explanatory variable x	j Average value	j Estimate	j Standard dev.	j j	t value	Pr(> |t|)
Intercept	—	6.87	4.11	6.87	1.67	9.45E-02
[SO2]	10.5ppb	0.293	0.153	3.08	1.91	5.62E-02
Temp	14.1°C	−1.57	0.246	−22.1	−6.39	< 3E-10§
Humidity	59.0%	0.122	8.67E-02	7.22	1.41	0.16
[SO2]^2	180ppb^2	−4.96E-03	8.90E-04	−0.893	−5.58	< 3E-8§
Temp^2	294(°C)^2	4.72E-02	5.16E-03	13.9	9.16	< 2E-16§
Humid^2	3840(%)^2	−1.32E-03	5.40E-04	−5.05	−2.45	1.46E-02*
fsummer	—	2.20	2.12	2.20	1.04	0.30
ffall	—	−0.915	1.98	−0.915	−0.462	0.64
fwinter	—	−1.86	1.89	−1.86	−0.985	0.32
iMHc	0.00587m^− 1	7.96	46.7	4.67E-02	0.170	0.86
[O3]	29.7ppb	−4.02E-02	1.99E-02	−1.19	−2.02	4.36E-02
UV	7.84watts/m^2	−6.84E-02	2.48E-02	−0.536	−2.76	5.80E-03**
rSE	0.0847	4.36	0.843	0.369	5.17	< 3E-7§
rS	0.174	3.17	0.612	0.552	5.18	< 3E-7§
rSW	0.143	1.52	0.760	0.217	2.00	4.61E-02*
[SO2] × Temp	136ppb×°C	2.52E-03	7.43E-03	0.343	0.339	0.73
[SO2] × Humid	604ppb× %	1.32E-03	2.11E-03	0.794	0.624	0.53
Temp× Humid	776°C× %	1.75E-02	2.47E-03	13.6	7.10	< 3E-12§
[SO2] × Temp× H	7350 ppb×°C× %	−9.62E-08	1.30E-04	−7.07E-04	−0.001	> 0.99