An agent for a property management company would like to be able to predict the monthly rental cost for apartments based on the size of the apartment as defined by square footage. A sample of the rent of 25 apartments in a college rental neighborhood was selected, and the information collected revealed the following: Apartment Size (Sq. Ft.) Monthly Rent ($) 1 850 950 2 1,450 1,600 3 1,085 1,200 4 1,232 1,500 5 718 950 6 1,485 1,700 7 1,136 1,650 8 726 935 9 700 875 10 956 1,150 11 1,100 1,400 12 1,285 1,650 13 1,985 2,300 14 1,369 1,800 15 1,175 1,400 16 1,225 1,450 17 1,245 1,100 18 1,259 1,700 19 1,150 1,200 20 896 1,150 21 1,361 1,600 22 1,040 1,650 23 755 1,200 24 1,000 800 25 1,200 1,750 i) Determine a 95% interval estimate for the average rent of apartments with 1000 square feet. Determine ŷ1000 and interpret the interval estimate for the average rent completely…this has been done by Minitab, follow the notes. j) Predict the rent of an apartment with 1650 square feet. What is the S.D. of this estimate? ie: determine ŷ1650 and SE(ŷ1650)…SE is the same here as it was in part b. k) Determine the correlation coefficient ‘r’ and interpret its meaning.

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Description: An agent for a property management company would like to be able to predict the monthly rental cost for apartments based on the size of the apartment as defined by square footage. A sample of the rent of 25 apartments in a college rental neighborhood

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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An agent for a property management company would like to be able to predict the monthly rental cost for apartments based on the size of the apartment as defined by square footage. A sample of the rent of 25 apartments in a college rental neighborhood was selected, and the information collected revealed the following:

Apartment	Size (Sq. Ft.)	Monthly Rent ($)
1	850	950
2	1,450	1,600
3	1,085	1,200
4	1,232	1,500
5	718	950
6	1,485	1,700
7	1,136	1,650
8	726	935
9	700	875
10	956	1,150
11	1,100	1,400
12	1,285	1,650
13	1,985	2,300
14	1,369	1,800
15	1,175	1,400
16	1,225	1,450
17	1,245	1,100
18	1,259	1,700
19	1,150	1,200
20	896	1,150
21	1,361	1,600
22	1,040	1,650
23	755	1,200
24	1,000	800
25	1,200	1,750

i) Determine a 95% interval estimate for the average rent of apartments with 1000 square feet. Determine ŷ₁₀₀₀ and interpret the interval estimate for the average rent completely…this has been done by Minitab, follow the notes.

j) Predict the rent of an apartment with 1650 square feet. What is the S.D. of this estimate? ie: determine ŷ₁₆₅₀and SE(ŷ₁₆₅₀)…SE is the same here as it was in part b.

k) Determine the correlation coefficient ‘r’ and interpret its meaning.

Regr ssion Analysis: Rent versus Size
The regression equation is
Rent = 177 + 1.07 Size
Predictor
Coef SE Coef
Constant
Size
161.0 1.10 0.283
1.0651 0.1376 7.74 0.000
177.1
S = 194.595 R-Sq = 72.3% R-Sq (adj) = 71.1%
Analysis of Variance
Source
DF
SS
Regression
Residual Error 23 870949
Total
MS
1 2268777 2268777 59.91 0.000
37867
24 3139726
Predicted Values for New Observations
New
Obs
Fit
SE Fit
95% CI
(1153.0, 1331.5)
95% PI
1
1242.3
43.1
(829.9, 1654.6)
a)
State the regression model and completely interpret th

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