Data Set ObservationCost (y)Sq Ft (x)11375.45932.5721101.84748.5131117.36802.8941264.47863.7051153.78820.8161284.78880.1871347.72889.9981153.94757.0091227.91832.3210940.92636.79111451.17964.54121227.46787.09131223.59729.62141299.92824.61151033.04707.14161332.67847.91171167.35793.93181424.591067.78191212.05963.8520730.11600.31211318.49894.13221004.32710.19231165.73824.49241304.73866.44251322.26924.77261171.99822.70271573.411007.63281282.09801.91291568.79882.75301405.95916.47311294.61858.52321350.73938.10331304.96882.32341153.32771.5935829.62669.46361529.051035.86371260.27789.55381234.43860.34391409.90906.32401392.18861.36411248.01759.53421283.53803.23431031.28837.51441441.41997.90451237.03763.92461433.17928.47471322.78880.86481284.61826.61491230.46744.30501248.76821.59511187.13841.33521037.57703.06531284.05869.22541242.33767.77551303.09840.58561381.18883.62571155.09759.53581196.53821.17591334.62885.01601022.29666.41611291.58953.60621657.561092.45631512.67945.94641217.62818.42651497.53892.86661176.65746.40671515.651037.79681401.71944.07691366.58928.73701168.73762.41711399.46881.99721163.06794.17731275.13818.86741366.03793.00751215.29747.43761222.21759.13771163.03829.0178967.75680.11791391.40910.76801248.27838.22811218.37919.92821165.00876.96831452.76899.4384977.72701.69851330.79747.9786986.75805.30871337.33860.97881445.37962.87891156.88821.00901505.67976.16911267.93897.54921538.10967.41931301.73862.69941013.54784.3295811.32701.86961270.94865.55971513.36931.86981250.23820.74991200.31795.921001298.48819.14 An agent for a residential real estate company has the business objective of developing more accurate estimates ofthe monthly rental cost of apartments. Toward that goal, the agent would like to use the size of the apartment asdefined by square footage to predict monthly rental cost. The agent selects a sample of 100 one-bedroomapartments and collects the data given in the worksheet labeled "Problem 6" in the spreadsheetFinal_SU2020_Data_Sets.xlsx.Construct a scatter plot of the data. Comment on the relationship between square footage (x) and monthlycost (y).Fit the simple linear regression model y = Bo + B1x + €, where y denotes cost, x denotes square footageand e~N(0, 02). Using the data and the method of ordinary least squares, determine the estimates for Boand B1, say bo and b .Compute the coefficient of determination and interpret this measure.Construct a 95% confidence interval on the slope of the linear regression model. Is there evidence that themodel slope is not equal to zero? Explain.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?Predict the mean monthly rent for an apartment that has 850 square feet.7.1.2.3.4.6.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.5.

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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 in the worksheet labeled "Problem 6" in the spreadsheet Final_SU2020_Data_Sets.xlsx. Construct a scatter plot of the data. Comment on the relationship between square footage (x) and monthly cost (y). Fit the simple linear regression model y = Bo + B1x + €, where y denotes cost, x denotes square footage and e~N(0, 02). Using the data and the method of ordinary least squares, determine the estimates for Bo and B1, say bo and b . Compute the coefficient of determination and interpret this measure. 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. 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? Predict the mean monthly rent for an apartment that has 850 square feet. 7. 1. 2. 3. 4. 6. 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. 5.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Data Set


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

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 in the worksheet labeled "Problem 6" in the spreadsheet
Final_SU2020_Data_Sets.xlsx.
Construct a scatter plot of the data. Comment on the relationship between square footage (x) and monthly
cost (y).
Fit the simple linear regression model y = Bo + B1x + €, where y denotes cost, x denotes square footage
and e~N(0, 02). Using the data and the method of ordinary least squares, determine the estimates for Bo
and B1, say bo and b .
Compute the coefficient of determination and interpret this measure.
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.
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?
Predict the mean monthly rent for an apartment that has 850 square feet.
7.
1.
2.
3.
4.
6.
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.
5.

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