ABC Company, a discount clothing retailer, would like to compare the sales per square foot in its different locations, taking into account the substantial differences in income and population. The management is planning to use this information to guide their location selections for new store openings.

The table below , includes Retail Sales data at 87 locations. This data set has been randomly split into two sections: The Training dataset contains 67 observations, representing the bulk of the locations, and the Holdoutdataset includes 20 observations to use to test and validate models that are constructed with the Trainingdataset.

For each of the locations in the dataset, we have values of the following variables: Variable	Coding & explanation
STORE ID .	Each store has a unique identifier number
SALES	Sales per square foot (in dollars/sq-ft)
INCOME	The median household income in the surrounding community (in dollars)
POPULATION	The size of the surrounding population (in thousands)
MARKET	The market type which can take 3 possible values: Rural, Urban and Suburban

1. Using the Trainingdataset, run a regression with Sales as the dependent variable and Population as the only explanatory variable. Print out regression output on a single page, and answer the following:

a) Is the sign on the slope coefficients for Population as you expected? Please provide a brief justification for your conclusions.

b) Provide a brief interpretation of the value of the Population coefficient in your model.

c) What percent of the variation in Sales is explained by your model?

d) Using the Holdoutdataset, measure the RMSPR for the regression model.

2. Build the best model you can to predict the sales per square foot at any ABC location. You may use any of the variables listed above and/or create new ones. Once you have settled on your model, print the regression output and provide a 1-2 page discussion of your regression model that covers the following topics:

a) How did you choose the explanatory variables in your regression?

b) If you created new variables, explain what they are.

c) Explain how you validated your model, and justify why your model is better than the one you created in Question 1 and any other models you created.

Store ID	Sales ($/SF)	Income	Population (000)	Market		Random
1	393.4	65000	710	Urban		0.9421167
2	488.8	93000	947	Suburban	0.8753115
3	471.4	67000	831	Rural		0.325584
4	532.9	75000	470	Urban		0.809741
5	588.3	72000	829	Urban		0.8358955
6	409.9	60000	774	Rural		0.5073342
7	561.1	69000	684	Urban		0.6258087
8	564.2	52000	592	Urban		0.3979399
9	213.8	63000	222	Rural		0.6684851
10	417.5	76000	1034	Suburban	0.6246485
11	290.9	65000	395	Rural		0.4298419
12	468.4	86000	713	Suburban	0.0520569
13	319.8	66000	260	Rural		0.4669508
14	209.4	62000	410	Rural		0.8547977
15	476.2	87000	850	Suburban	0.8999421
16	283.5	64000	635	Suburban	0.8277788
17	353.2	52000	551	Urban		0.9272327
18	441.5	78000	326	Urban		0.023217
19	481.2	78000	463	Urban		0.7893981
20	572.6	64000	760	Urban		0.7812228
21	355.8	73000	798	Suburban	0.5811773
22	376	63000	612	Rural		0.3660083
23	428	70000	926	Suburban	0.1530077
24	310.5	65000	438	Rural		0.7012616
25	555.2	73000	992	Suburban	0.1562667
26	455.9	74000	786	Suburban	0.5304186
27	489.1	68000	712	Urban		0.1864392
28	454	92000	424	Suburban	0.0726347
29	469.3	86000	1224	Suburban	0.3940539
30	349.2	56000	646	Rural		0.8580489
31	475.7	80000	953	Suburban	0.5251337
32	162.8	50000	560	Rural		0.8733175
33	458.2	69000	548	Rural		0.0416188
34	495.8	84000	796	Suburban	0.7544696
35	612.8	73000	872	Urban		0.7337205
36	466.6	78000	923	Suburban	0.1718359
37	401.7	71000	626	Suburban	0.2691121
38	375.1	66000	323	Rural		0.5256277
39	490.1	67000	559	Urban		0.608761
40	646.4	78000	531	Urban		0.8947365
41	607.6	72000	499	Urban		0.0783688
42	476.4	56000	947	Rural		0.4114759
43	305.1	54000	705	Rural		0.0819157
44	587.4	71000	1077	Urban		0.0897385
45	491.1	59000	610	Urban		0.132568
46	483.5	59000	663	Urban		0.7551134
47	379.3	86000	849	Suburban	0.2820937
48	437.9	95000	884	Suburban	0.4860746
49	508.9	67000	672	Urban		0.4371968
50	573.8	76000	769	Urban		0.2634168
51	376.8	85000	828	Suburban	0.2548404
52	518.1	63000	628	Rural		0.9827471
53	467.9	78000	421	Urban		0.5087367
54	582	76000	569	Urban		0.8624967
55	550.5	64000	452	Urban		0.4769442
56	544.3	89000	503	Urban		0.2909594
57	467.1	61000	581	Urban		0.7059228
58	126.9	55000	321	Rural		0.64167
59	382	84000	740	Suburban	0.0885328
60	403.3	61000	685	Urban		0.3819721
61	407.5	63000	945	Rural		0.3342186
62	512	71000	1075	Suburban	0.3314819
63	691.7	76000	699	Urban		0.6074417
64	569.4	73000	650	Urban		0.7365464
65	425.6	70000	552	Rural		0.1462433
66	481	84000	514	Urban		0.8343099
67	465.5	90000	641	Suburban	0.9501743
68	442	74000	862	Suburban	0.6062411
69	272.7	59000	434	Rural		0.0514388
70	630.2	79000	531	Urban		0.1486485
71	416.7	73000	985	Suburban	0.8221382
72	527.5	71000	597	Urban		0.9333084
73	341.4	77000	729	Suburban	0.8096481
74	325.7	58000	611	Rural		0.982407
75	461.1	79000	793	Suburban	0.1957593
76	352.7	75000	827	Suburban	0.2156417
77	325.9	74000	270	Rural		0.2121122
78	458.3	64000	452	Rural		0.50538
79	362.9	80000	578	Suburban	0.5865473
80	442.9	66000	738	Rural		0.4057885
81	641.9	88000	755	Urban		0.3748682
82	287.2	56000	401	Rural		0.5828727
83	313.1	62000	433	Rural		0.6306487
84	468.4	72000	656	Rural		0.7036573
85	616.5	69000	726	Urban		0.3942697
86	276.6	65000	658	Rural		0.2217373
87	580.2	71000	482	Urban		0.7480467