In: Operations Management
In Florida, real estate agents refer to homes having a swimming pool as pool homes. In this case, Sunshine Pools Inc. markets and installs pools throughout the state of Florida. The company wishes to estimate the percentage of a pool's cost that can be recouped by a buyer when he or she sells the home. For instance, if a homeowner buys a pool for which the current purchase price is $30,000 and then sells the home in the current real estate market for $20,000 more than the homeowner would get if the home did not have a pool, the homeowner has recouped (20,000/30,000) × 100% = 66.67% of the pool's cost.
To make this estimate, the company randomly selects 80 homes from all of the homes sold in a Florida city (over the last six months) having a size between 2,000 and 3,500 square feet. For each sampled home, the following data are collected: Price - selling price (in thousands of dollars); Size - square footage; Bathrooms - the number of bathrooms; Rating - a niceness rating (expressed as an integer from 1 to 7 and assigned by a real estate agent); and Pool - whether or not the home has a pool (1 = yes, 0 = no). The data are given in the file FloridaPoolHome-Spring2018.
4. Compute the mean selling prices of the homes having a pool and the homes that do not have a pool. Assuming that the average current purchase price of the pools in the sample is $32,500, estimate the percentage of a pool's cost that can be recouped when the home is sold. What concerns do you have about the reliability of the estimate?
Data Set:
Home | Price | Size | Bathrooms | Rating | Pool |
1 | 260.9 | 2666 | 2.5 | 7 | 0 |
2 | 337.3 | 3418 | 3.5 | 6 | 1 |
3 | 268.4 | 2945 | 2.0 | 5 | 1 |
4 | 242.2 | 2942 | 2.5 | 3 | 1 |
5 | 255.2 | 2798 | 3.0 | 3 | 1 |
6 | 205.7 | 2210 | 2.5 | 2 | 0 |
7 | 249.5 | 2209 | 2.0 | 7 | 0 |
8 | 193.6 | 2465 | 2.5 | 1 | 0 |
9 | 242.7 | 2955 | 2.0 | 4 | 1 |
10 | 244.5 | 2722 | 2.5 | 5 | 0 |
11 | 184.2 | 2590 | 2.5 | 1 | 0 |
12 | 325.7 | 3138 | 3.5 | 7 | 1 |
13 | 266.1 | 2713 | 2.0 | 7 | 0 |
14 | 166.0 | 2284 | 2.5 | 2 | 0 |
15 | 330.7 | 3140 | 3.5 | 6 | 1 |
16 | 289.1 | 3205 | 2.5 | 3 | 1 |
17 | 268.8 | 2721 | 2.5 | 6 | 1 |
18 | 276.7 | 3245 | 2.5 | 2 | 1 |
19 | 222.4 | 2464 | 3.0 | 3 | 1 |
20 | 241.5 | 2993 | 2.5 | 1 | 0 |
21 | 307.9 | 2647 | 3.5 | 6 | 1 |
22 | 223.5 | 2670 | 2.5 | 4 | 0 |
23 | 231.1 | 2895 | 2.5 | 3 | 0 |
24 | 216.5 | 2643 | 2.5 | 3 | 0 |
25 | 205.5 | 2915 | 2.0 | 1 | 0 |
26 | 258.3 | 2800 | 3.5 | 2 | 1 |
27 | 227.6 | 2557 | 2.5 | 3 | 1 |
28 | 255.4 | 2805 | 2.0 | 3 | 1 |
29 | 235.7 | 2878 | 2.5 | 4 | 0 |
30 | 285.1 | 2795 | 3.0 | 7 | 1 |
31 | 284.8 | 2748 | 2.5 | 7 | 1 |
32 | 193.7 | 2256 | 2.5 | 2 | 0 |
33 | 247.5 | 2659 | 2.5 | 2 | 1 |
34 | 274.8 | 3241 | 3.5 | 4 | 1 |
35 | 264.4 | 3166 | 3.0 | 3 | 1 |
36 | 204.1 | 2466 | 2.0 | 4 | 0 |
37 | 273.9 | 2945 | 2.5 | 5 | 1 |
38 | 238.5 | 2727 | 3.0 | 1 | 1 |
39 | 274.4 | 3141 | 4.0 | 4 | 1 |
40 | 259.6 | 2552 | 2.0 | 7 | 1 |
41 | 285.6 | 2761 | 3.0 | 6 | 1 |
42 | 216.1 | 2880 | 2.5 | 2 | 0 |
43 | 261.3 | 3426 | 3.0 | 1 | 1 |
44 | 236.4 | 2895 | 2.5 | 2 | 1 |
45 | 267.5 | 2726 | 3.0 | 7 | 0 |
46 | 220.2 | 2930 | 2.5 | 2 | 0 |
47 | 300.1 | 3013 | 2.5 | 6 | 1 |
48 | 260.0 | 2675 | 2.0 | 6 | 0 |
49 | 277.5 | 2874 | 3.5 | 6 | 1 |
50 | 274.9 | 2765 | 2.5 | 4 | 1 |
51 | 259.8 | 3020 | 3.5 | 2 | 1 |
52 | 235.0 | 2887 | 2.5 | 1 | 1 |
53 | 191.4 | 2032 | 2.0 | 3 | 0 |
54 | 228.5 | 2698 | 2.5 | 4 | 0 |
55 | 266.6 | 2847 | 3.0 | 2 | 1 |
56 | 233.0 | 2639 | 3.0 | 3 | 0 |
57 | 343.4 | 3431 | 4.0 | 5 | 1 |
58 | 334.0 | 3485 | 3.5 | 5 | 1 |
59 | 289.7 | 2991 | 2.5 | 6 | 1 |
60 | 228.4 | 2482 | 2.5 | 2 | 0 |
61 | 233.4 | 2712 | 2.5 | 1 | 1 |
62 | 275.7 | 3103 | 2.5 | 2 | 1 |
63 | 290.8 | 3124 | 2.5 | 3 | 1 |
64 | 230.8 | 2906 | 2.5 | 2 | 0 |
65 | 310.1 | 3398 | 4.0 | 4 | 1 |
66 | 247.9 | 3028 | 3.0 | 4 | 0 |
67 | 249.9 | 2761 | 2.0 | 5 | 0 |
68 | 220.5 | 2842 | 3.0 | 3 | 0 |
69 | 226.2 | 2666 | 2.5 | 6 | 0 |
70 | 313.7 | 2744 | 2.5 | 7 | 1 |
71 | 210.1 | 2508 | 2.5 | 4 | 0 |
72 | 244.9 | 2480 | 2.5 | 5 | 0 |
73 | 235.8 | 2986 | 2.5 | 4 | 0 |
74 | 263.2 | 2753 | 2.5 | 7 | 0 |
75 | 280.2 | 2522 | 2.5 | 6 | 1 |
76 | 290.8 | 2808 | 2.5 | 7 | 1 |
77 | 235.4 | 2616 | 2.5 | 3 | 0 |
78 | 190.3 | 2603 | 2.5 | 2 | 0 |
79 | 234.4 | 2804 | 2.5 | 4 | 0 |
80 | 238.7 | 2851 | 2.5 | 5 | 0 |
We calculate the average selling price of homes with pools and without pools separately
SUMIF and COUNTIF functions have been used to find Summation- price of (homes with pools) and number of homes with pools-count. Same method for homes without pools
Average selling price homes with pools (In thousands of dollars)= $ 276100
Average selling price homes without pools (In thousands of dollars)=$ 226900
We want to calculate how much amount that we have invested in the pool, can be recovered
The amount invested in the pool is $32500(purchase price of pool, home not included)
Percentage recovered
= (selling price of pool /amount invested in pool ) *100
=(selling price of pool /$32500) *100
Selling price of pool =Selling price of home with pool (home+pool) - selling price of home(home)
== 276100-226900
=$ 49200
Percentage recovered(% Recouped)
= (selling price of pool /amount invested in pool ) *100
=($ 49200/$32500) *100
= 151.38 %
Reliability of the estimate