Question

Consider the following table summarizing the speed limit of a certain road and the number of accidents occurring on that road in January. Posted Speed Limit 52 50 43 36 21 22. Reported Number of Accidents 27 26 23 18 18 11. 1) Find the slope of the regression line predicting the number of accidents from the posted speed limit.Round to 3 decimal places. 2) Find the intercept of the regression line predicting the number of accidents from the posted speed limit. Round to 3 decimal places. 3) Predict the number of reported accidents for a posted speed limit of 25mph. Round to the nearest whole number.

Answer 1

Consider the following table summarizing the speed limit of a certain road and the number of accidents occurring on that road in January. Posted Speed Limit 52 50 43 36 21 22. Reported Number of Accidents 27 26 23 18 18 11.

Find the slope of the regression line predicting the number of accidents from the posted speed limit.Round to 3 decimal places.

Slope= 0.405

2) Find the intercept of the regression line predicting the number of accidents from the posted speed limit. Round to 3 decimal places.

Intercept=5.384

3) Predict the number of reported accidents for a posted speed limit of 25mph. Round to the nearest whole number.

The estimated regression line is number of accidents =5.384+0.405*speed limit

When speed limit is 25,

Predicted number of accidents =5.384+0.405*25=15.509

=16 ( rounded)

Excel Addon Megastat used.

Menu used: correlation/Regression ---- Regression Analysis

Regression Analysis
	r²	0.823	n	6
	r	0.907	k	1
	Std. Error of Estimate	2.832	Dep. Var.	Number of Accidents
Regression output						confidence interval
variables		coefficients	std. error	t (df=4)	p-value	95% lower	95% upper
Intercept	a =	5.384
Speed	b =	0.405	0.094	4.315	.0125	0.144	0.665
ANOVA table
Source	SS	df	MS	F	p-value
Regression	149.409	1	149.409	18.62	.0125
Residual	32.091	4	8.023
Total	181.500	5
Predicted values for: Number of Accidents
		95% Confidence Interval		95% Prediction Interval
Speed	Predicted	lower	upper	lower	upper	Leverage
25	15.51	10.96	20.05	6.42	24.59	0.334