Question

In an article, Bissell, et. al., study bridge safety (measured in accident rates per 100 million vehicles) and the difference between the width of the bridge and the width of the roadway approach (road plus shoulder). The raw data points are:

WidthDiff.	-6	-4	-2	0	2	4	6	8	10	12
Accidents	120	103	87	72	58	44	31	20	12	7

The Excel output of a simple linear regression analysis relating accident to width difference is as follows:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.9913
R Square	0.9827
Adjusted R Square	0.9802
Standard Error	4.7942
Observations	9
ANOVA
	df	SS	MS	F	Significance F
Regression	1	9126.6667	9126.6667	397.0856	0.0000
Residual	7	160.8889	22.9841
Total	8	9287.5556
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	72.8889	2.0214	36.0586	0.0000	68.1090	77.6687	68.1090	77.6687
Width	-6.1667	0.3095	-19.9270	0.0000	-6.8984	-5.4349	-6.8984	-5.4349

Identify and interpret the least squares estimate of slope.

The slope is 72.889. For every unit increase in width difference, the mean number of accidents are increased by 72.8889.

The slope is -6.167. For every unit increase in width difference, the mean number of accidents are increased by 6.167.

The slope is 72.889. For every unit increase in width difference, the mean number of accidents are decreased by 72.8889.

The slope is -6.167. For every unit increase in width difference, the mean number of accidents are decreased by 6.167.

Answer 1

From Given table we have Slope = -6.1667

R squared= 0.9827

r(correlation)= sqrt(0.9827)= -0.9913 (Correlation will be negative because the slope has negative sign).

So r=-0.9913 . Negative correlation.

So the correct interpretation of the least squares estimate of slope is OPTION D

The slope is -6.167. For every unit increase in width difference, the mean number of accidents are decreased by 6.167.

OPTION A and OPTION C can not be correct because the slope value is NOT 72.889. OPTION B can not be TRUE because data are negatively correlated. So correct answer is OPTION D.