Question

Problem 1: USING STATPRO slice the data 3 ways

As the midwest regional manager of a chain of Heavenly Grill Restaurant, it is your responsibility to come up with the beer selections for the 50 restaurants under your management. It has been the policy of Heavenly Grill Restaurant to let each regional manager selects the beer offerings that are most appropriate for the region. However, the main office requires all regional managers to submit an annual report describing the beer offerings for their respective regions.

In the past year, you have selected 69 different beers for the drink menu. Your assistant has compiled the following information for the 69 choices:

Cost ($)	The cost of a six-pack of 12-ounce bottles
Calories	Calories per 12 fluid ounces
% of Alcohol	Percentage of alcohol content
Type	There are 5 different types of beer
City of Origin	The beer is either from U.S. or imported

Since this is your first year on the job, you need to first determine what is the best way to "describe" the beer offerings in the midwest region. However, you consider this as a rite of passage so you are "too proud" to ask the other regional managers for assistance on how to prepare the report.

How would you describe the beer offerings in the midwest region? Based on your  prelimanary analysis, how would you "describe" the Heavenly Grill's midwest beer choices?

HINT: Keep in mind that you should look at different ways to "slice" the data.

Brand	Cost ($)	Calories	% of Alcohol	Type	Cty of Origin
BrooklynBrand	6.24	159	5.2	Craft lagers	U.S.
Leinenkugel'sRed	4.79	160	5.0	Craft lagers	U.S.
SamuelAdamsBoston	5.96	160	4.9	Craft lagers	U.S.
GeorgeKillian'sIrishRed	4.70	162	4.9	Craft lagers	U.S.
RedWolf	4.11	157	5.5	Craft lagers	U.S.
HenryWeinhard'sPrivateRes.	3.85	151	4.9	Craft lagers	U.S.
Sterling	2.52	155	4.7	Craft lagers	U.S.
Legacy	5.46	135	5.1	Craft lagers	U.S.
Dominion	6.00	162	5.4	Craft lagers	U.S.
LoneStar	3.71	142	4.8	Craft lagers	U.S.
AbitaAmber	6.70	146	4.4	Craft lagers	U.S.
YuenglingPremium	4.99	148	4.3	Craft lagers	U.S.
BerghoffOriginal	4.10	170	5.1	Craft lagers	U.S.
SamuelAdamsBoston	5.96	160	5.0	Craft ales	U.S.
SierraNevadaPale	6.31	172	5.8	Craft ales	U.S.
FullSailAmber	6.42	170	5.9	Craft ales	U.S.
Liberty	7.79	184	6.0	Craft ales	U.S.
ElkMountainAmber	5.05	201	5.6	Craft ales	U.S.
CelisPaleBock	5.26	155	4.7	Craft ales	U.S.
Pete'sWicked	5.84	170	5.3	Craft ales	U.S.
AnchorSteam	7.22	158	4.9	Craft ales	U.S.
DockStreetAmber	6.12	159	5.4	Craft ales	U.S.
Bass	7.37	150	5.1	Craft ales	Imported
RedhookESB	6.47	177	5.6	Craft ales	U.S.
NewAmsterdamNewYork	6.72	146	3.7	Craft ales	U.S.
CatamountAmber	7.59	151	4.9	Craft ales	U.S.
RedNectar	6.36	163	5.3	Craft ales	U.S.
OldDetroitAmber	6.52	186	5.9	Craft ales	U.S.
BridgePortBlueHeronPale	6.34	168	5.9	Craft ales	U.S.
Geary'sPale	7.10	142	4.7	Craft ales	U.S.
MolsonGolden	4.78	148	5.0	Imported largers	Imported
LabattBlue	4.63	150	5.0	Imported largers	Imported
Foster's	5.41	140	5.0	Imported largers	Imported
Kirin	6.39	150	5.0	Imported largers	Imported
DosEquis	5.52	160	4.8	Imported largers	Imported
Heineken	6.38	160	5.0	Imported largers	Imported
CoronaExtra	5.68	148	4.6	Imported largers	Imported
St.PauliGirl	5.82	148	4.9	Imported largers	Imported
Beck's	5.83	148	4.3	Imported largers	Imported
PilsnerUrquell	7.80	160	4.1	Imported largers	Imported
OldMilwaukee	2.82	145	4.5	Regular and ice beers	U.S.
Stroh's	3.20	142	4.4	Regular and ice beers	U.S.
RedDog	3.83	147	5.0	Regular and ice beers	U.S.
Budweiser	4.02	148	4.9	Regular and ice beers	U.S.
Icehouse	3.88	149	5.5	Regular and ice beers	U.S.
MolsonIce	4.79	155	5.6	Regular and ice beers	Imported
Michelob	4.00	159	5.0	Regular and ice beers	U.S.
BudIce	3.95	148	5.5	Regular and ice beers	U.S.
Busch	3.27	143	4.9	Regular and ice beers	U.S.
CoorsOriginal	4.02	137	4.6	Regular and ice beers	U.S.
GeneseeCreamAle	3.26	153	4.6	Regular and ice beers	U.S.
MillerHighLife	3.19	143	5.0	Regular and ice beers	U.S.
PabstBlueRibbon	2.90	144	4.7	Regular and ice beers	U.S.
Milwaukee'sBest	2.36	133	4.6	Regular and ice beers	U.S.
MillerGenuineDraft	3.93	143	5.0	Regular and ice beers	U.S.
RollingRock	4.25	143	4.6	Regular and ice beers	U.S.
MichelobLight	4.03	134	4.3	Light and nonalcoholic beers	U.S.
BudLight	4.02	110	4.2	Light and nonalcoholic beers	U.S.
NaturalLight	2.86	110	4.2	Light and nonalcoholic beers	U.S.
CoorsLight	4.03	105	4.2	Light and nonalcoholic beers	U.S.
MillerLite	4.02	96	4.5	Light and nonalcoholic beers	U.S.
AmstelLight	6.49	95	3.6	Light and nonalcoholic beers	Imported
Sharp's	3.24	58	0.0	Light and nonalcoholic beers	U.S.
CoorsCutter	3.60	82	0.0	Light and nonalcoholic beers	U.S.
Kingsbury	2.99	60	0.0	Light and nonalcoholic beers	U.S.
OldMilwaukee	2.75	72	0.0	Light and nonalcoholic beers	U.S.
O'Doul's	3.90	70	0.0	Light and nonalcoholic beers	U.S.
Kaliber	5.42	71	0.0	Light and nonalcoholic beers	Imported
Clausthaler	5.63	96	0.0	Light and nonalcoholic beers	Imported

Answer 1

There are 5 different types of beer:

Craft lagers = 1

Craft ales = 2

Imported largers = 3

Regular and ice beers = 4

Light and nonalcoholic beers = 4

The beer is either from U.S. or imported:

U.S. = 1

Imported = 0

Running the regression on the data, we get:

	R²	0.420
	Adjusted R²	0.384
	R	0.648
	Std. Error	1.135
	n	69
	k	4
	Dep. Var.	Cost ($)
ANOVA table
Source	SS	df	MS	F	p-value
Regression	59.7930	4	14.9482	11.60	3.84E-07
Residual	82.4907	64	1.2889
Total	142.2837	68
Regression output					confidence interval
variables	coefficients	std. error	t (df=64)	p-value	95% lower	95% upper
Intercept	6.1104
Calories	0.0138	0.0117	1.180	.2424	-0.0096	0.0372
% of Alcohol	-0.1529	0.1903	-0.803	.4248	-0.5331	0.2274
Type	-0.4506	0.1411	-3.193	.0022	-0.7325	-0.1686
Cty of Origin	-1.3981	0.3382	-4.134	.0001	-2.0737	-0.7226

Running the backward elimination on the data, we have to remove the independent variable % of Alcohol because it is insignificant.

Running the regression on the data, we get:

	R²	0.414
	Adjusted R²	0.387
	R	0.644
	Std. Error	1.132
	n	69
	k	3
	Dep. Var.	Cost ($)
ANOVA table
Source	SS	df	MS	F	p-value
Regression	58.9614	3	19.6538	15.33	1.20E-07
Residual	83.3223	65	1.2819
Total	142.2837	68
Regression output					confidence interval
variables	coefficients	std. error	t (df=65)	p-value	95% lower	95% upper
Intercept	6.6399
Calories	0.0060	0.0065	0.925	.3585	-0.0070	0.0189
Type	-0.4730	0.1380	-3.429	.0011	-0.7485	-0.1975
Cty of Origin	-1.4286	0.3351	-4.263	.0001	-2.0978	-0.7593

Running the backward elimination on the data, we have to remove the independent variable Calories because it is insignificant.

Running the regression on the data, we get:

	R²	0.407
	Adjusted R²	0.389
	R	0.638
	Std. Error	1.131
	n	69
	k	2
	Dep. Var.	Cost ($)
ANOVA table
Source	SS	df	MS	F	p-value
Regression	57.8651	2	28.9326	22.62	3.30E-08
Residual	84.4186	66	1.2791
Total	142.2837	68
Regression output					confidence interval
variables	coefficients	std. error	t (df=66)	p-value	95% lower	95% upper
Intercept	7.7765
Type	-0.5629	0.0978	-5.755	2.45E-07	-0.7582	-0.3676
Cty of Origin	-1.4475	0.3341	-4.332	.0001	-2.1146	-0.7803

The regression model is:

Cost = 7.7765 -0.5629Type -1.4475Cty of Origin

Therefore, the data is finally sliced and this is the final model as all the variables are significant in the model.