Question

Distance	3.4	1.8	4.6	2.3	3.1	5.5	0.7	3.0
Damage	26.2	17.8	31.3	23.1	27.5	36.0	14.1	22.3

Distance	2.6	4.3	2.1	1.1	6.1	4.8	3.8
Damage	19.6	31.3	24.0	17.3	43.2	36.4	26.1

Refer to the Model Summary table from Minitab Express (or Simple linear regression results from StatCrunch) generated in part (e). What is the name and observed value of the measure that tells us the “percent of variation in the amount of damage for major residential fires that can be explained by the [linear] relationship with the distance between the fire and nearest fire station?” Based on this value, would you expect the estimates of the response (predictions) made by using this particular regression equation to be accurate? See pp. 203-205 in the course text.

Answer 1

Refer to the Model Summary table from Minitab Express (or Simple linear regression results from StatCrunch) generated in part (e). What is the name and observed value of the measure that tells us the “percent of variation in the amount of damage for major residential fires that can be explained by the [linear] relationship with the distance between the fire and nearest fire station?” Based on this value, would you expect the estimates of the response (predictions) made by using this particular regression equation to be accurate? See pp. 203-205 in the course text.

Name: R square or coefficient of determination.

observed value of the measure = 92.35%    ( or R square = 0.9235)

92.35% of variation in the damage for major residential fires that can be explained by the [linear] relationship with the distance between the fire and nearest fire station.

Therefore we expect the estimates of the response (predictions) made by using this particular regression equation is accurate.

Regression Analysis: Damage versus Distance

Analysis of Variance

Source	DF	Adj SS	Adj MS	F-Value	P-Value
Regression	1	841.77	841.766	156.89	0.000
Distance	1	841.77	841.766	156.89	0.000
Error	13	69.75	5.365
Total	14	911.52

Model Summary

S	R-sq	R-sq(adj)	R-sq(pred)
2.31635	92.35%	91.76%	89.77%

Coefficients

Term	Coef	SE Coef	T-Value	P-Value	VIF
Constant	10.28	1.42	7.24	0.000
Distance	4.919	0.393	12.53	0.000	1.00

Regression Equation

Damage

=

10.28 + 4.919 Distance