Question

In: Operations Management

In Florida, real estate agents refer to homes having a swimming pool as pool homes. In...

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

Solutions

Expert Solution

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

  • The mean selling price of homes with pools is significantly high
  • We have taken averages for calculation. Averages can be misleading due to extreme outliers. This decrease s reliability
  • Also selling prices of homes could be higher because of increased number of bathrooms or greater size. These have not been taken into account in calculation. Hence they may show a greater value for pools and their recoup %


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