Question

D. b. Does a simple linear regression model appear to be appropriate? Explain. ;the relationship appears to be curvilinear Yes 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 x + X2 (to 3 decimals) What is the value of the coefficient of determination? Not report R between 0 and 1 (to 3 decimals) L(to 3 decimals) What is the value of the coefficient of determination? Note:report R betee and 1 (to 3 decimal)

Answer 1

Independent variable (x): Number of facilities

Dependent variable (y): Average Distance (miles)

(a)

Following is the scatter plot of the data:

1.8 1.6 1.4 1.2 ()箭 0.6 0.4 0.2 0 20 25 30 35 10 15 01

(b)

The relationship appears to be curvilinear linear .

(c)

Following is the data for regression model:

Y	X	X^2
1.59	5	25
0.76	11	121
0.47	16	256
0.32	20	400
0.35	24	576
0.37	29	841

Following is the output of Quardatic model generated by excel:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.993511819
R Square	0.987065735
Adjusted R Square	0.978442891
Standard Error	0.072082162
Observations	6
ANOVA
	df	SS	MS	F	Significance F
Regression	2	1.189545819	0.59477291	114.4710243	0.001471
Residual	3	0.015587514	0.005195838
Total	5	1.205133333
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	2.357073882	0.132304749	17.81548955	0.000385632	1.936021121	2.778126643
X	-0.181111865	0.017340445	-10.44447623	0.001873532	-0.2362969	-0.12592683
X^2	0.003936144	0.000499813	7.875240205	0.004266066	0.002345517	0.00552677

The required regression model is

Y=2.357 -0.181* X+ 0.004*x^2

The R-square is: 0.987

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Following is the data for regression model:

Y	1/X
1.59	0.2
0.76	0.090909
0.47	0.0625
0.32	0.05
0.35	0.041667
0.37	0.034483

Following is the required regression model:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.992880057
R Square	0.985810808
Adjusted R Square	0.98226351
Standard Error	0.065383231
Observations	6
ANOVA
	df	SS	MS	F	Significance F
Regression	1	1.188033466	1.188033466	277.9047131	7.58599E-05
Residual	4	0.017099868	0.004274967
Total	5	1.205133333
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	0.015703759	0.046151433	0.340265904	0.750774783	-0.11243316	0.143840678
1/X	7.852592163	0.471047915	16.67047429	7.58599E-05	6.544753484	9.160430842

The required regression model is

Y=0.016+7.853 *(1/x)

The value of the coefficient of determination is

The R-square is: 0.986