Table 4

Summary of regression output for the selected eight best predictors

Independent variable	Ordinary least squares estimation			Spatial* lag model—Maximum likelihood estimation			Spatial* error model—Maximum likelihood estimation
	R-squared: 0.529 Akaike info: 2093.5 Jarque-Bera prob: 0.000			R-squared: 0.541 Akaike info: 2089.7 Breusch-Pagan test: 0.000			R-squared: 0.537 Akaike info: 2090.43 Breusch-Pagan test: 0.000
	Coeff.	t-stat.	P value	Coeff.	z-value	P value	Coeff.	z-value	P value
No central heating	−32.188	−3.827	0.000	−30.778	−3.749	0.000	−31.776	−3.875	0.000
Unemployment	39.025	5.561	0.000	37.957	5.526	0.000	39.568	5.71	0.000
WPS recipients – Veterans	21.492	2.594	0.01	18.506	2.283	0.022	18.31	2.236	0.025
SIMD	13.248	1.911	0.057	13.136	1.947	0.052	12.984	1.872	0.061
AFCS recipients – Veterans	7.389	1.242	0.215	6.794	1.172	0.241	6.99	1.208	0.227
No qualifications	−8.976	−1.095	0.275	−9.342	−1.171	0.242	−9.837	−1.207	0.227
AFPS recipients – Veterans	10.607	1.08	0.281	15.126	1.564	0.118	14.674	1.5	0.134
Alcohol	−7.212	−1.05	0.295	−7.134	−1.067	0.286	−8.736	−1.27	0.204
Spatial lag	---	---	---	0.372	2.672	0.008	---	---	---
Lambda	---	---	---	---	---	---	0.450	2.224	0.026

Breusch-Pagan: tests whether the variance of the spatial errors from a regression is dependent on the values of the independent variables.
Spatial lag and the spatially correlated errors (λ) reflect the spatial dependence inherent, measuring the average influence on observations by their neighbouring observations. Both coefficients have a positive effect and are highly significant. As a result, the general model fit improved. The effects of other independent variables remain virtually the same.
*Spatial distance weights: (a) Bandwidth: 162 km; (b) Min neighbours: 1; (c) Max neighbours: 203; (d) Mean neighbours: 130.
AFCS, Armed Forces Compensation Scheme; SIMD, Scottish Index of Multiple Deprivation; WPS, War Pension Scheme.