GIS-based regression modeling of the extreme weather patterns in Arkansas, USA

Geoenvironmental Disasters

Table 3 Ordinary Least Squares results for hail

	Variable	Coefficient	StdError	t-Statistic	Probability	Robust_SE	Robust_t	Robust_Pr	VIF
Event	Intercept	−0.0296	0.2200	−0.1346	0.8929	0.2050	−0.1444	0.8852	–
	SUM_MAG	0.8729	0.0009	1023.3266	0.000000*	0.0016	561.5929	0.000000*	1.0212
	MO	0.0409	0.0076	5.3547	0.000000*	0.0078	5.2433	0.000000*	1.0241
	HAIL_TIM_2	−0.0082	0.0033	−2.4808	0.013107*	0.0033	−2.4926	0.012680*	1.0196
	ELEVATION	0.0015	0.0001	10.8536	0.000000*	0.0001	12.5462	0.000000*	1.2704
	AR_ECO_ID	−0.0004	0.0002	−2.1620	0.030620*	0.0002	−2.2770	0.022785*	1.2861
Magnitude	Intercept	−0.2115	0.2501	−0.8456	0.3978	0.2248	−0.9406	0.3469	–
	SUM_EVENT	1.1281	0.0011	1023.3266	0.000000*	0.0021	533.7691	0.000000*	1.0215
	MO	−0.0422	0.0087	−4.8542	0.000002*	0.0088	−4.7753	0.000003*	1.0244
	HAIL_TIM_2	0.0115	0.0037	3.0678	0.002173*	0.0037	3.0856	0.002049*	1.0194
	ELEVATION	−0.0018	0.0002	−11.2164	0.000000*	0.0001	−12.8938	0.000000*	1.2698
	AR_ECO_ID	0.0008	0.0002	4.1671	0.000037*	0.0002	4.5625	0.000007*	1.2851
			Joint Wald	Jarque-Bera	Koenker (BP) Statistic	AICc	Adjusted R2
			47,365.25	2445.7748	1057.0264	190,276.91	0.84911

OLS analysis shows very low VIF values meaning low model redundancy and all explanatory variables prove to be statistically significant denoted by asterisk. Significant p-values (p< 0.01) are denoted by *, StdError is the standard deviation error, t-Statistic is the ratio between estimated and hypothesized values relative to StdError, probability and robust probability (Pr) are significant when (p<0.01), Koenker statistic determines significance of coefficients, and VIF is the variance inflation factor with values >7.5 are indicative of redundancy. Joint Wald determines overall significance if Koenker value is significant, AICc and R2 represent overall fit and performance