Question

The research firm LL Research collected data from 200 client businesses. They want to determine how the businesses compare among four variables:

2015 Profit in millions of dollars
2016 Profit in millions of dollars
2015-2016 Two-Year Change in Daily Average Customer Visits
Two-Year Average Number of Employees

Data collected for the sample of 200 businesses is contained in the file named Businesses, linked at the bottom of the page. Use all 200 data points.

Managerial Report
Prepare a report (see below) using the numerical methods of descriptive statistics presented in this module to learn how each of the variables contributes to the success of a client business. Be sure to include the following three items in your report.

Find descriptive sample statistics (mean, median, two quartiles Q1 and Q3, minimum, maximum, range, sample standard deviation, and coefficient of variation) for each of the four variables along with an explanation of what the descriptive statistics tell us about the client businesses.

Compute the percent change in profit from 2015 to 2016 for each business. Then use the z-score to determine which businesses were outliers with respect to percent change in profit.

Compute the sample correlation coefficient, showing the relationship between percent change in profit and each of the other two variables (2015-2016 Two-Year Change in Daily Average Customer Visits and Two-Year Average Number of Employees). Explain what the correlation coefficients tell us about the three pairs of relationships. Use tables, charts, or graphs to support your conclusions.

Number	Business	2015 Profit	2016 Profit	Two Year avg. change in daily no. of visits	Two Year Average Number of Employees
1	B Phillips	4436	8108	37	100
2	Barr & Edwin Co.	7452	9542	82	71
3	Lacrosse Archery	2564	2125	6	41
4	Global Fleet Sales	4547	5219	40	56
5	ALLSTATE ATHLETIC SUPPLY	8028	6160	85	79
6	ELECTROPOWER UTILITY SALES	1313	5074	-7	31
7	Bergner's	6843	7211	71	97
8	BESLEY'S	4280	7775	34	54
9	Dave Ranney & Assoc	4721	9674	40	89
10	RDI Technologies	3603	4881	17	37
11	Rocky MTN HMO - Info. & Sales	2701	7172	7	63
12	Mid-South Sweeper Supply; Inc	3119	8327	12	85
13	WestLake Supply	4308	6516	36	43
14	Old Town Artisans Galleries	4550	2305	40	48
15	Client Services Guy	5267	8804	46	32
16	Bill Reed	8973	4747	93	86
17	Game Fair Ltd	7366	2629	80	96
18	Air Supply Systems; Inc	5905	7186	54	38
19	The Webmaster	3701	9466	20	44
20	First Supply Group; Inc	1180	7572	-8	26
21	Comfyco	6980	930	73	95
22	Telson; Inc	2117	2414	4	66
23	One Plus Two	1219	1108	-8	83
24	FlowTech Supply	2817	5635	9	91
25	Brewer Business Supply	3142	2651	14	44
26	King Plaza-Management Lsng	2533	3784	6	47
27	Sales Recruiting Specialist	7021	9522	75	62
28	Lenty Sales; Inc.	1654	1841	-3	21
29	Vipbrasil	7713	6069	83	74
30	Empire State Sales Inc	6244	1063	57	26
31	Sunday Sales	8838	2851	91	26
32	Spa City Silver	5777	3058	51	24
33	Cps	4504	6606	39	65
34	WSA Sales Co. Inc	1990	6252	-2	65
35	Sun State Sales	6541	5904	67	58
36	KWICK SUPPLY INC	4541	8953	39	67
37	Power Solutions Inc	5662	5125	50	71
38	Reece & Nichols Wyandotte	9286	1158	94	42
39	Harmony Ball	5414	2769	48	98
40	Eagle Flight Safety Products	5505	4364	49	66
41	Team Vehicle Sales	3444	4977	14	50
42	Papaya Clothing	3703	4059	20	39
43	Daniels & Fry Motor Company	5009	3286	44	29
44	Home Base Solutions	8229	9303	87	50
45	SAFsystems	4800	4999	42	69
46	Robert Rytter & Associates	8424	3258	89	79
47	Arbor Consulting	6488	1039	62	30
48	DEANGELO MACHINERY SALES	6287	5524	58	44
49	JDG Sales And Service	3844	7146	25	74
50	MOSS	6730	8194	71	72
51	Sonya C. Atwell	5695	7747	51	47
52	Sentry Network Service; Inc.	3579	6245	17	39
53	SUMMIT FINANCIAL GROUP	1737	2498	-3	57
54	Lenexa Office Supply	7001	4820	74	35
55	Cyberzone	6699	8272	69	38
56	Monarch Rep Sales Inc	8868	6316	92	21
57	Eddiechamberland	7114	7116	76	63
58	EXCEL PRODUCTS	5239	7248	45	70
59	Samco Sales	6541	2355	67	49
60	Lajobi Sales; Inc	4484	4466	38	74
61	ECS Anchor Supply	8655	3577	91	100
62	Tiger Sales	4278	7425	32	39
63	Auto Graphics Sales	9678	2829	97	39
64	Algin Technology LLC	4440	3301	38	51
65	Triple T Sales	3687	6882	19	89
66	Georges Miret Salon	8906	1063	93	35
67	NICHOLSON; WILLIAM	2991	3746	11	66
68	Sears Grand	992	8233	-10	57
69	Active Fitness And Aerobics	4106	9366	29	93
70	Crosstech	3527	9840	16	69
71	Druglaunch	8190	5866	86	58
72	Brian Sullivan Enterprises	6966	1888	72	56
73	PC SALES	9268	6999	94	77
74	Starr Gennett Foundation	6132	9766	55	62
75	KCI Sales	8134	9845	85	60
76	Mapleshade Lane E	2595	962	6	26
77	Rod Dow	3136	5738	14	95
78	CC Industrial Sales	4301	9571	36	20
79	Southwest Distributing; Inc.	5513	7564	49	54
80	Robert M. Wells	1541	2515	-5	83
81	United Sales & Services; Inc	8249	4299	88	25
82	NO. Power Plant	6137	5846	55	54
83	BREWARES INC	9936	5651	100	32
84	Closeouts Attic	6720	8230	69	40
85	AGEE Sales; Inc.	6253	8833	57	80
86	Jason Golden	5564	5855	50	94
87	Shepherd Sales	2178	6106	4	22
88	John C Weigand	6376	8755	60	32
89	Discount Silks	7664	9634	83	48
90	Ban-Koe Systems Inc.	5335	1975	47	96
91	Shamrock Computer	1124	7099	-9	95
92	Margaret Lucas	4869	9725	43	40
93	Shafer Valve	7368	2085	80	96
94	RTG INDUSTRIAL SUPPLY; INC	1553	4908	-4	64
95	American Supply Group	2185	8449	4	51
96	Mr. Spindle	2045	7917	1	36
97	Jones Services Supply Co.	6135	6843	55	79
98	Factory Direct Craft Supply	9943	1268	100	70
99	Metro Sandwiches & Salads	2500	500	3	84
100	Global Industrial Sales	9843	5622	99	32
101	Fun Yards	5939	1321	54	48
102	Taylor Supply	300	6040	72	95
103	Facility Robotics; Inc	2630	1653	6	63
104	Tele-Sales Consultants; Inc	1309	3000	-3	68
105	Hometown Paintball Supply Inc.	4131	5000	30	77
106	Bales Hay Sales	2000	9956	48	39
107	Zero systems	1588	5000	-3	93
108	Agm	9655	7249	97	65
109	Simcha Sales	9842	1000	42	71
110	Pauls Motor Sales And Service	9000	9957	56	100
111	Drillers Supply	9583	1685	81	35
112	Sharper Concepts; Inc	2728	1360	7	80
113	Pat Tomek	9345	1312	43	66
114	Mbh Sales And Service	9471	3405	96	52
115	Howard Sales Co.; Inc	1488	6142	-7	23
116	SELECT SALES; INC.	3246	3549	14	24
117	John Garesche	7462	5052	82	68
118	TOP SALES COMPANY; INC	8551	3427	89	67
119	On Angels Wings	2599	2740	6	23
120	WebStar Designs	7521	7907	82	40
121	Lone Pine Sales	7937	5991	85	50
122	Associated Supply Co	9202	7112	94	95
123	John Cody	7230	4503	79	92
124	Barton Mattress Sales	6399	3312	61	71
125	InternetNow	3675	9576	19	70
126	Corrosion Guard	6536	8512	63	40
127	Comet Website Consultants	2464	4501	5	26
128	MCMAHON; JOHN	4084	5773	28	59
129	Alan Warren	7540	5068	83	83
130	ROV Supply CO	2371	4610	4	49
131	Wilrock Sales Corp	6361	7557	60	75
132	Lowe Co Motion Inc.	3509	6616	16	80
133	Daley Plastering	7675	5536	83	86
134	Walter Drake Inc	8011	2665	85	68
135	Philips Business Solutions	8417	2808	88	88
136	Bacik Karpinski Associates Inc	7190	8807	77	41
137	Jeff Munchick Sales	5499	5077	49	23
138	GEO-THERMAL SALES; INC	6720	7404	70	99
139	Sprinkler Supply Company	9686	1178	99	96
140	Rol-Tru Putting Greens	9432	2599	95	25
141	Energy Mgmt Systems	5050	6596	45	69
142	B & D Sales	7529	1033	82	55
143	Tech-Tran Corp.	6877	1271	72	52
144	Judy Rees	6459	1996	61	32
145	Jenskates	4048	3723	28	68
146	Custom Filter Supply; Inc	2110	4898	3	57
147	Fiduciary Trust Co. Intl	4429	9501	36	73
148	The Office Supply Store; Inc.	8898	8190	93	53
149	Char Sakamoto Ishii Lum Ching	6274	7326	58	85
150	Otto Wolff U.S. Sales Corp	7162	4839	76	74
151	Bailey Slipper Shop	3883	7446	26	44
152	Megaidea; Inc	5962	2154	55	49
153	Jeff Branch Motor Sales	8845	6854	92	99
154	Aeropostale Inc	4735	1110	42	31
155	High Tides	3134	5581	13	33
156	Foley's Department Store	6100	1948	55	51
157	Gornet Technologies	3615	1225	18	69
158	Brinton Vet Supply	6308	8620	59	20
159	The Jones Shop	1004	7848	-10	81
160	WOODSTOCK QUILT CO.; INC	8427	7816	89	79
161	KWB SALES	4228	2742	32	52
162	Efficient Lighting Sales Co.	7381	7066	81	37
163	Filene'S	3913	1176	27	71
164	Gemini Technical Sales	5827	1504	53	75
165	Walter Long	3714	1584	21	97
166	Cloutier Property Management	9566	6887	97	78
167	ATMCo	7180	2327	76	67
168	Mark Maggiacoma	9973	8707	101	79
169	Global Granite	7608	8684	83	39
170	NuHS	5337	2539	48	26
171	JTC Express Office Supply	6751	6204	71	81
172	Inductive Technologies; LLC	7701	9342	83	41
173	Florida Villa Vacations Inc	1917	9450	-2	77
174	Misty Mountain Sales	5012	2294	44	29
175	Outpost	6640	4570	67	72
176	Dollar All	7879	5010	83	71
177	Clinical Laboratory Standard	7546	1229	83	20
178	AdultPaths.com	9627	3445	97	79
179	Ship Supply Of Florida; Inc.	4039	1385	27	68
180	M Hoffman Enterprises Inc.	3068	2896	11	45
181	Worldscale Association	9070	7770	94	34
182	Dream Weavers Network	9401	7552	95	53
183	Mr. Trademark Inc.	3754	4761	24	90
184	Jefferson Financial	3730	5878	21	78
185	P J P Sales	7900	6278	84	81
186	Mylon C. Jacobs Supply	2911	4628	11	86
187	Terry Smith	1569	2078	-3	60
188	Smith Supply	3337	5390	14	24
189	Complete Police Supply Limited	2342	5262	4	94
190	Design Build Concepts	8181	7472	86	34
191	Bon Voyage Travel	8702	3493	91	66
192	Diverse Technologies Corporation	9537	3047	97	59
193	Magic Dollar	3503	2386	16	65
194	Syracuse Castings Sales	8596	4174	91	81
195	McCormick Sales And Service	6196	2909	56	49
196	Zecharya Sales & Services;Inc	9167	1727	94	45
197	Marinette Co. Abstract & Land	6257	3575	57	78
198	BoKip Sales	4183	1880	30	85
199	Mark's Sales	7135	6928	76	39
200	Pete Reilly Consultants	4992	5412	43	55

Answer 1

Step 1

Analyze – descriptive statistics – frequencies

Step 2

Statistics
	2015 Profit	2016 Profit	Two Year avg. change in daily no. of visits	Two Year Average Number of Employees
N	Valid	200	200	200	200
Missing	0	0	0	0
Mean	5609.14	5177.85	49.72	59.91
Median	5802.00	5101.00	51.00	62.00
Std. Deviation	2524.385	2682.574	33.177	22.625
Range	9673	9457	111	80
Minimum	300	500	-10	20
Maximum	9973	9957	101	100
Percentiles	25	3606.00	2740.50	19.00	40.00
50	5802.00	5101.00	51.00	62.00
75	7592.50	7384.50	82.00	78.75

Step 3

Coefficient of variation= ( Std. Deviation/ Mean)*100

We find the variability in 2016 profit is higher compared to 2015

Compute the percent change in profit from 2015 to 2016 for each business. Then use the z-score to determine which businesses were outliers with respect to percent change in profit.

Percent change in profit = (2016 profit – 2015 profit )/ 2015 profit

Z score= ( Percent change in profit – mean (percent change in profit ) )/ S.D (percent change in profit )

In spss ,

Go to

Analyze – descriptive statistics –descriptive

Then make sure,’ save standardized values as variables’, is ticked

The click ok

Z-score is got in data view

Findings

Outliers-

Those that are beyond 3 stdanadrd deviations are selectred as outliers

Here it is.

68-Sears Grand

102-Taylor Supply

159- The Jones Shop

Compute the sample correlation coefficient, showing the relationship between percent change in profit and each of the other two variables (2015-2016 Two-Year Change in Daily Average Customer Visits and Two-Year Average Number of Employees). Explain what the correlation coefficients tell us about the three pairs of relationships. Use tables, charts, or graphs to support your conclusions.

Correlation

To looks for

• Statistical significance-a correlation is statistically significant if its “Sig. (2-tailed)” < 0.05.
• Correlation coefficient

Step 1

Spss

Analyze—correlate- bivariate

Step 2

Correlations
	Zscore: Percent change in profit	Two Year avg. change in daily no. of visits
Zscore: Percent change in profit	Pearson Correlation	1	-.351**
Sig. (2-tailed)		.000
N	200	200
Two Year avg. change in daily no. of visits	Pearson Correlation	-.351**	1
Sig. (2-tailed)	.000
N	200	200
**. Correlation is significant at the 0.01 level (2-tailed).

Correlations
	Zscore: Percent change in profit	Two Year Average Number of Employees
Zscore: Percent change in profit	Pearson Correlation	1	.078
Sig. (2-tailed)		.272
N	200	200
Two Year Average Number of Employees	Pearson Correlation	.078	1
Sig. (2-tailed)	.272
N	200	200

Step 3

Percent change in profit and Two Year avg. change in daily no. of visits

• Statistically significant(0.000<0.05)
• Coefficient   =   - 0.351

Percent change in profit and Two Year Average Number of Employees

• Not Statistically significant(0.272 > 0.05)

• Coefficient   =   0.272