Question

An agent for a residential real estate company has the business objective of developing more accurate estimates of the monthly rental cost of apartments. Toward that goal, the agent would like to use the size of the apartment as defined by square footage to predict monthly rental cost. The agent selects a sample of 100 one-bedroom apartments and collects the data given . 5. Plot the standardized residuals versus x , as well as a normal probability plot of the standardized residuals. What do these plots suggest about the model assumptions? 6. Predict the mean monthly rent for an apartment that has 850 square feet 7. Construct a 95% confidence interval on the mean monthly rent for an apartment that has 850 square feet 8. Construct a 95% prediction interval on monthly rent for an apartment that has 850 square feet.

Observation	Cost (y)	Sq Ft (x)
1	1375.45	932.57
2	1101.84	748.51
3	1117.36	802.89
4	1264.47	863.70
5	1153.78	820.81
6	1284.78	880.18
7	1347.72	889.99
8	1153.94	757.00
9	1227.91	832.32
10	940.92	636.79
11	1451.17	964.54
12	1227.46	787.09
13	1223.59	729.62
14	1299.92	824.61
15	1033.04	707.14
16	1332.67	847.91
17	1167.35	793.93
18	1424.59	1067.78
19	1212.05	963.85
20	730.11	600.31
21	1318.49	894.13
22	1004.32	710.19
23	1165.73	824.49
24	1304.73	866.44
25	1322.26	924.77
26	1171.99	822.70
27	1573.41	1007.63
28	1282.09	801.91
29	1568.79	882.75
30	1405.95	916.47
31	1294.61	858.52
32	1350.73	938.10
33	1304.96	882.32
34	1153.32	771.59
35	829.62	669.46
36	1529.05	1035.86
37	1260.27	789.55
38	1234.43	860.34
39	1409.90	906.32
40	1392.18	861.36
41	1248.01	759.53
42	1283.53	803.23
43	1031.28	837.51
44	1441.41	997.90
45	1237.03	763.92
46	1433.17	928.47
47	1322.78	880.86
48	1284.61	826.61
49	1230.46	744.30
50	1248.76	821.59
51	1187.13	841.33
52	1037.57	703.06
53	1284.05	869.22
54	1242.33	767.77
55	1303.09	840.58
56	1381.18	883.62
57	1155.09	759.53
58	1196.53	821.17
59	1334.62	885.01
60	1022.29	666.41
61	1291.58	953.60
62	1657.56	1092.45
63	1512.67	945.94
64	1217.62	818.42
65	1497.53	892.86
66	1176.65	746.40
67	1515.65	1037.79
68	1401.71	944.07
69	1366.58	928.73
70	1168.73	762.41
71	1399.46	881.99
72	1163.06	794.17
73	1275.13	818.86
74	1366.03	793.00
75	1215.29	747.43
76	1222.21	759.13
77	1163.03	829.01
78	967.75	680.11
79	1391.40	910.76
80	1248.27	838.22
81	1218.37	919.92
82	1165.00	876.96
83	1452.76	899.43
84	977.72	701.69
85	1330.79	747.97
86	986.75	805.30
87	1337.33	860.97
88	1445.37	962.87
89	1156.88	821.00
90	1505.67	976.16
91	1267.93	897.54
92	1538.10	967.41
93	1301.73	862.69
94	1013.54	784.32
95	811.32	701.86
96	1270.94	865.55
97	1513.36	931.86
98	1250.23	820.74
99	1200.31	795.92
100	1298.48	819.14

Answer 1

5. Plot the standardized residuals versus x , as well as a normal probability plot of the standardized residuals. What do these plots suggest about the model assumptions?

The standardized residuals versus x plot is:

The normal probability plot of the standardized residuals is:

The plots suggest that the equal variance and the normality condition are met.

6. Predict the mean monthly rent for an apartment that has 850 square feet

The mean monthly rent for an apartment that has 850 square feet is 1,272.00987.

Predicted

1,272.00987

7. Construct a 95% confidence interval on the mean monthly rent for an apartment that has 850 square feet

The 95% confidence interval on the mean monthly rent for an apartment that has 850 square feet is between 1,253.65245 and 1,290.36729.

95% Confidence Interval
lower	upper
1,253.65245	1,290.36729

8. Construct a 95% prediction interval on monthly rent for an apartment that has 850 square feet.

The 95% prediction interval on monthly rent for an apartment that has 850 square feet is between 1,088.07203 and 1,455.94770.

95% Prediction Interval
lower	upper
1,088.07203	1,455.94770