Question

A study of emergency service facilities investigated the relationship between the number of facilities and the average distance traveled to provide the emergency service. The following table gives the data collected.

Number of Facilities	Average Distance (miles)
9	1.65
11	1.13
16	0.83
21	0.61
27	0.51
30	0.48

(a) Develop a scatter diagram for these data, treating average distance traveled as the dependent variable

(b) Does a simple linear regression model appear to be appropriate? Explain.

No, the scatter diagram suggests that there is a curvilinear relationship.     

(c) Develop an estimated regression equation for the data corresponding to a second-order model with one predictor variable. (Round your numerical values to four decimal places.)

ŷ =  

Answer 1

a)

b)No, the scatter diagram suggests that there is a curvilinear relationship.    

c)

applying multiple regression on above data from excel: data-data analysis: regression:

	df	SS	MS	F	Significance F
Regression	2	0.979245	0.489623	30.83382	0.009992
Residual	3	0.047638	0.015879
Total	5	1.026883
	Coefficients	Standard Error	t Stat	P-value
Intercept	2.9168	0.407422	7.159074	0.005613
x	-0.1870	0.047542	-3.93398	0.029253
x^2	0.0036	0.001211	2.9488	0.060083

c)

y^ =2.9168-0.1870x+0.0036x²