Results

Linear Regression

Looking at the output below, we can see that the number of pubs significantly predicts mortality, t(6) = 3.33, p = 0.016. The positive beta value (0.806) indicates a positive relationship between number of pubs and death rate in that, the more pubs in an area, the higher the rate of mortality (as we would expect). The value of 𝑅² tells us that number of pubs accounts for 64.9% of the variance in mortality rate – that’s over half!

Model Summary - mortality
Model	R	R²	Adjusted R²	RMSE
M₀	0.000	0.000	0.000	2915.476
M₁	0.806	0.649	0.591	1864.431

Note. M₁ includes pubs

ANOVA
Model		Sum of Squares	df	Mean Square	F	p
M₁	Regression	3.864×10⁺⁷	1	3.864×10⁺⁷	11.117	0.016
	Residual	2.086×10⁺⁷	6	3.476×10⁺⁶
	Total	5.950×10⁺⁷	7

Note. M₁ includes pubs
Note. The intercept model is omitted, as no meaningful information can be shown.

Coefficients
							95% CI
Model		Unstandardized	Standard Error	Standardized	t	p	Lower	Upper
M₀	(Intercept)	4750.000	1030.776		4.608	0.002	2312.601	7187.399
M₁	(Intercept)	3351.955	781.236		4.291	0.005	1440.341	5263.570
	pubs	14.339	4.301	0.806	3.334	0.016	3.816	24.862

Bootstrap Coefficients
						95% CI*
Model		Unstandardized	Bias	Standard Error	p*	Lower	Upper
M₀	(Intercept)	4625.000	-9.250	948.008	< .001	3125.000	6750.000
M₁	(Intercept)	2890.632	-1098.015	1723.410	0.105	-7.375×10^-13	5934.906
	pubs	15.005	28.718	40.819	NaN	8.288	100.000

Note. Bootstrapping based on 1000 replicates.
Note. Coefficient estimate is based on the median of the bootstrap distribution.
Note. Some bootstrap results could not be computed.
* Bias corrected accelerated.

Bootstrap Coefficients shows that the bootstrapped confidence intervals are both positive values – they do not cross zero (8.288, 100.00). Assuming this interval is one of the 95% that contain the population value then it appears that there is a positive and non-zero relationship between number of pubs in an area and its mortality rate.