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)
5	1.57
11	.75
13	.50
18	.35
24	.30
26	.35

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

- No, or Yes; the relationship appears to be - curvilinear or linear

c. Develop an estimated regression equation for the data that you believe will best explain the relationship between these two variables. (Enter negative values as negative numbers).

Several possible models can be fitted to these data, as shown below: (to 3 decimals)

Y=____+____X+_____X^2

What is the value of the coefficient of determination? R2 between 0 and 1. (to 3 decimals)

________

Y=________+_________ 1/X

What is the value of the coefficient of determination? R2 between 0 and 1. (to 3 decimals)

Answer 1

excel scatterplot output given below-

from scatterplot, we observe, relationship is not linear.

a simple linear regression model appear to be appropriate?

- No, the relationship appears to be - curvilinear

c)

Y	X	X²
1.57	5	25
0.75	11	121
0.5	13	169
0.35	18	324
0.3	24	576
0.35	26	676

using excel data analysis tool for regression, o/p given below

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.995962
R Square	0.991941
Adjusted R Square	0.986568
Standard Error	0.05631
Observations	6
ANOVA
	df	SS	MS	F	Significance F
Regression	2	1.170821	0.58541	184.6263	0.000723
Residual	3	0.009512	0.003171
Total	5	1.180333
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	2.505153	0.117231	21.3694	0.000224	2.132072	2.878234	2.132072	2.878234
X	-0.21622	0.016672	-12.9693	0.00099	-0.26928	-0.16316	-0.26928	-0.16316
X²	0.005163	0.000513	10.07268	0.002084	0.003532	0.006794	0.003532	0.006794

Y = 2.505 -0.216X + 0.005X²

value of the coefficient of determination R2 = 0.992

--------------------------------------------

Y	1/X
1.57	0.200
0.75	0.091
0.5	0.077
0.35	0.056
0.3	0.042
0.35	0.038

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.99178
R Square	0.983628
Adjusted R Square	0.979535
Standard Error	0.069507
Observations	6
ANOVA
	df	SS	MS	F	Significance F
Regression	1	1.161009	1.161009	240.3169	0.000101
Residual	4	0.019325	0.004831
Total	5	1.180333
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	-0.03307	0.051688	-0.63972	0.557154	-0.17658	0.110443	-0.17658	0.110443
1/X	7.980674	0.514811	15.50216	0.000101	6.55133	9.410017	6.55133	9.410017

Y = -0.033 + 7.981*1/X

value of the coefficient of determination R2 = 0.984