Question

2. Regression review II, problem 6 Aa Aa E This question aims to review the La Quinta Inn model building exercise as discussed in lecture and described in the course packet. The data collected can be obtained in this Excel file. (Note: Reload this file each time you go through this problem.) The coefficient of multiple determination for the regression of profit margin (MARGIN) on all the other variables is The adjusted coefficient of multiple determination is From the regression output, at a 10% level of significance, which of the following variables are insignificant individually? Check all that apply. ROOMS O INCOME O OFFICE I DISTTWN ONEAREST D COLLEGE Perform a partial F-test to see whether these variables are really useless as a group in explaining the behavior of profit margin. The F-test statistic for testing the significance of the subset variables is . The p-value of the test statistic for testing the significance of the subset variables is . At a 5% level of significance, these variables significant as a group. Therefore, you choose as your final model. Now, using this final model, predict the profit margin in each of the following locations: Ann Arbor 2,672 1.3 Characteristic Rooms Competitor distance Office space ('000s) Students ('000s) Income ('000s) Distance to downtown Predicted profit margin Bloomington 2,500 1.2 604 21 37 952 Champaign 2,300 0.5 1,430 45 33.5 1.4 D- 42 35 3.4 - 4.5 1 C C Flach player MAC 32 270

Answer 1

using excel>data analysis>regression

we have

Regression Statistics
Multiple R	0.724953
R Square	0.525556
Adjusted R Square	0.494947
Standard Error	5.517757
Observations	100
ANOVA
	df	SS	MS	F	Significance F
Regression	6	3136.483	522.7472	17.16985	2.9E-13
Residual	93	2831.445	30.44564
Total	99	5967.928
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	74.08432	7.985766	9.277046	6.93E-15	58.22617	89.94247
Rooms	-0.00797	0.001249	-6.38667	6.61E-09	-0.01045	-0.0055
Nearest	-1.56552	0.632113	-2.47665	0.01507	-2.82077	-0.31027
Ofice	0.019463	0.003417	5.695413	1.43E-07	0.012677	0.026249
College	0.199082	0.137898	1.443691	0.152186	-0.07476	0.47292
Income	-0.42306	0.143796	-2.94211	0.004115	-0.70861	-0.13751
DISTTwn	0.229487	0.173906	1.319599	0.190208	-0.11586	0.57483

the coefficient of multiple determination is 0.5256

the adjusted coefficient of multiple determination is 0.4950

the only College and DiSSTWN variable is insignificant at 10% level of significance because p value 0.152 and 0.190 are >0.10

the f test statistic is 17.20. the p-value of f test statistic is 0.0000. at 5 % level of significance, these variable are significant , therefore you choose this model as your final model.

characterstics	Ann Arbor	Bloomington	Champaign
Rooms	2672	2500	2300
Competitor distance	1.3	1.2	0.5
Office Space	952	604	1430
Students	42	21	45
Income	35	37	33.5
Disst to downtown	3.4	4.5	1.4
predicted profit margin	63.61236	53.593	77.90432