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.

1. Construct a scatter plot of the data. Comment on the relationship between square footage (x) and monthly cost (y).

2. Fit the simple linear regression model ? = ?₀ + ?₁? + ?, where ? denotes cost, ? denotes square footage and ?~?(0, ?!). Using the data and the method of ordinary least squares, determine the estimates for ?₀ and ?₁, say ?₀ and ?₁.

3. Compute the coefficient of determination and interpret this measure.

4. Construct a 95% confidence interval on the slope of the linear regression model. Is there evidence that the

   model slope is not equal to zero? Explain.

5. Plot the standardized residuals versus ?, 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

Not mention which software use ... I solved using Excel

IN excel input data and and select data analysis tool for run a regrssion equation.

Select regression option from drop down menu in data analysis tool and selct input range of Y , X , label , confidence interval percentage and for plot also click on the plot which you want.Here used normal probability plot and standardized residuals versus ? and then click OK.

Result you get in this form.

coefficient of determination is 0.700781 i.e 70.08%

which means 70.08% variablity in dependent variable i.e Y(cost) is explained indpendent variable i.e  X(Sq. ft area)

95% confidence interval on the slope of the linear regression model is (1.300759 , 1.692894)

- lower confidence interval value is 1.300759

-Upper confidence interval is 1.692894

Monthly rent for an apartment that has 850 square feet.

Y=-0.2926+1.496826*X

X= 850 , solving  Y=-0.2926+1.496826*850

Y=1272.01 rent for 850 suare feet apartment

Normal Probaility plot is

standardized residuals versus ?

plots suggest about the model assumptions is data set follows assumption of normal distribution and no problem of autocorrealtion.