Question

You are operating a small ice cream truck. Each day you visit a different neighborhood and spend the day there. In every neighborhood you face a different competition with varying number competitors and average prices. Up to know you did not make any price change by neighborhood. Observing that your demand varies between neighborhoods, and since now you know how to estimate regressions, you decided to use your knowledge to perform a quantitative analysis. Namely, you collected the data attached in files. (HW3Q2Data)

Demand	Average Price of Competitor	Temperature	Population	Number of Students in Nearby School	Number of Competitors
22.7531445	6.93898234	27.9208355	529.700156	31.2171286	3
25.2147947	8.01675936	15.9348508	1391.39061	89.6720582	1
20.5214464	5.33192197	27.3849726	652.336758	70.7371022	5
22.7897955	9.06488424	25.128342	678.503513	99.5443756	4
27.1711912	8.156383	27.2199228	1037.46276	92.8964586	2
16.4478283	7.01801513	20.7361169	1303.22749	71.899216	5
20.7946046	5.11029706	26.5490151	544.479962	49.6235655	4
18.9023662	5.54884794	26.2655144	574.727786	34.1467194	5
27.1931077	6.60090156	29.9430915	837.613961	91.8933829	1
20.7471855	7.5141901	17.0496574	1148.71672	144.596919	5
18.2295445	7.47057329	26.3565698	914.045764	105.065966	5
19.3883817	9.95111764	19.645012	1432.81959	109.872351	4
28.9456938	5.04072647	20.3809514	1493.04665	92.0901082	1
23.6774317	6.25812571	27.633099	792.505213	52.3548714	2
24.3311121	7.14712635	28.3438563	560.076703	42.9858266	3
22.1387031	5.25680885	29.3236071	505.197033	58.9504117	3
20.5188943	6.62839783	25.1968869	1087.06562	66.763349	4

a.) Scatter your demand on each of the variables.

b.) Begin with a model, by adding and subtracting variables select the best one. (Hint, begin with all) At each step, copy and paste only the Regression Statistics part of your result table (R2, Adjusted R2 etc. top part of result table)

c.) What is your estimated final result? (Copy and paste all result table from Excel)

d.) Is the model significant at 1%?

e.) Which variables are significant at 5% and at 1%?

Answer 1

(a)

b)

Regression results with all the variables:

The adjusted R-square is 81.88% but the four variables (highlighted with red) are insignificant at both 1% and 5% level.

We start by adding only the significant variable and then keep on adding the more significant variables to the model (the regression will be run again and again and the result is to be noted). The result is as follows:

The best model is highlighted.

(c)

Final model:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.9320
R Square	0.8685
Adjusted R Square	0.8382
Standard Error	1.3812
Observations	17.0000
ANOVA
	df	SS	MS	F	Significance F
Regression	3	163.849877	54.6166258	28.6281127	5.35515E-06
Residual	13	24.8013602	1.90779694
Total	16	188.651237
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	29.9409	1.3979	21.4185	0.0000	26.9210	32.9609
Population	-0.0027	0.0013	-2.0200	0.0645	-0.0056	0.0002
Number of Students in Nearby School	0.0308	0.0150	2.0521	0.0609	-0.0016	0.0632
Number of Competitors	-2.2329	0.2426	-9.2038	0.0000	-2.7570	-1.7088

(d)

The Significance F (i.e. the p-value) is less than 0.01. So, the model is significant at 1%

(e)

Only the 'Number of Competitors' is significant. Rest two are still having p-values > 0.05 and 0.01. So, they are insignificant at 5% (although marginally) and 1%.