Question

A fire insurance company wants to estimate the amount of fire damage in major residential fires based on distance between the residence and the nearest fire station. The study is to be conducted in a large suburb of a major city, a sample of 16 recent fires in this suburb is selected.

–Explanatory Variable (x): Distance
–Response Variable (y): Damage

Give a 95% Confidence Interval for slope.

(  ,  )

Answer 1

The 95% Confidence Interval for slope is between 4.0709 and 5.7678.

Distance	Damage
3.4	26.2
1.8	17.8
4.6	31.3
2.3	23.1
3.1	27.5
5.5	36
0.7	14.1
3	22.3
2.6	19.6
4.3	31.3
2.1	24
1.1	17.3
6.1	43.2
4.8	36.4
3.8	26.1

	r²	0.923
	r	0.961
	Std. Error	2.316
	n	15
	k	1
	Dep. Var.	Damage
ANOVA table
Source	SS	df	MS	F	p-value
Regression	841.7664	1	841.7664	156.89	1.25E-08
Residual	69.7510	13	5.3655
Total	911.5173	14
Regression output				confidence interval
variables	coefficients	std. error	t (df=13)	p-value	95% lower	95% upper
Intercept	10.2779
Distance	4.9193	0.3927	12.525	1.25E-08	4.0709	5.7678