La Quinta is a moderately priced chain of motels in the USA. Its market is frequent business travelers. Thechain recently launched a campaign to increase maket share by building new motels. Operating margin is theratio of the sum of profit, depeciation and interest expenses divided by total revenue. Thus operating marginis measured in percent units and the higher the operating margin the bigger the success of the motel. Let Ybe the operating margin of a La Quinta motel. Let x1 be the number (in thousands) of total motel and hotel rooms within three miles. Let x2 be the office space (in thousand square meters) in the surrounding community. Let x3 be the median household income in the surrounding community (in thousands dollars). Let x4 be the distance (in miles) from the downtown core. The management acquired data on 40 randomly selected La Quinta motels. The sample measurements, x1, x2, x3, x4 and y are given below. A multiple regression model with Y as the dependent variable and x1, x2, x3, x4 as the independent variables was applied to these data. Which of the following is the estimated regression equation of the reduced model?ý=18.059 – 4.852 xị+0.019 x,(1)(2)(3)(5)ỳ=18.059 +0.019 xy +0.664 xyỳ=18.059 – 4.852 x +0.664 xyỳ 18.059-4.852 x₁ -0.366x4ỳ 18.059 +0.019x₂ -0.366 x4 Motel1234567891011121314151617181920X43.503 32.077.22.72.115 57.6 68.0 4.32.84621.562.1 1.12.848 69.1 65.5 7.540.33.12442.4 61.4 4.0 32.42.443 51.7 57.8 5.1 45.42.65561.9 70.9 6.6 46.02.687 45.2 62.1 6.1 57,440.4 57.5 7.63.71427.32.691 48.267.9 4.445.53.83881.3 67.5 2.942.92.75139.6 67.4 7.7 47.62.386 50.8 69.3 3.1 35.93.23460.371.1 7.254.42.81321.663.8 9.344.02.793 59.9 66.17.655.42.676 27.962.6 3.8 40.83.517 47.962.8 2.1 41.93.01367.174.5 9.952.63.473 67.2 58.1 1.444.2y55.543.741.0MotelX221 2.389 29.0223.389 33.970.22.623 3.597 62.8 65.4 9.42.72455.557.71.025 2.429 46.3 61.2 8.826 2.826 36.2 65.927 3.59147.428 3.285 32.9293.56730 3.082312.172323.91033 3.44834353637 2.62238 2.64039 2,21040 3.0802464.341.6X43.2y58.049.643.443.248.28.5 49.039.353.529.851.261.2 6.063.4 1.363.68.359.267.88.618.461.7 7.945.138.862.71.8 43.570.7 66.3 5.3 52.73.422 43.068.3 7.431.93.670 22.3 60.9 8.040.257.66.2 41.13.098 60.342.661.03.549.635.0 65.7 5.851.436.8 74.3 4.058.536.368.17.047.5

Given: x1 x2 x3 x4 y 3.503 32 77.2 2.7 55.5 2.115 57.6 68 4.3 43.7 2.846 21.5 62.1 1.1 41…

Answered: Which of the following is the estimated…

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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Question

La Quinta is a moderately priced chain of motels in the USA. Its market is frequent business travelers. The
chain recently launched a campaign to increase maket share by building new motels. Operating margin is the
ratio of the sum of profit, depeciation and interest expenses divided by total revenue. Thus operating margin
is measured in percent units and the higher the operating margin the bigger the success of the motel. Let Y
be the operating margin of a La Quinta motel. Let x1 be the number (in thousands) of total motel and hotel rooms within three miles. Let x2 be the office space (in thousand square meters) in the surrounding community. Let x3 be the median household income in the surrounding community (in thousands dollars). Let x4 be the distance (in miles) from the downtown core. The management acquired data on 40 randomly selected La Quinta motels. The sample measurements, x1, x2, x3, x4 and y are given below. A multiple regression model with Y as the dependent variable and x1, x2, x3, x4 as the independent variables was applied to these data.

Which of the following is the estimated regression equation of the reduced model?
ý=18.059 – 4.852 xị+0.019 x,
(1)
(2)
(3)
(5)
ỳ=18.059 +0.019 xy +0.664 xy
ỳ=18.059 – 4.852 x +0.664 xy
ỳ 18.059-4.852 x₁ -0.366x4
ỳ 18.059 +0.019x₂ -0.366 x4

Motel
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
X4
3.503 32.0
77.2
2.7
2.115 57.6 68.0 4.3
2.846
21.5
62.1 1.1
2.848 69.1 65.5 7.5
40.3
3.124
42.4 61.4 4.0 32.4
2.443 51.7 57.8 5.1 45.4
2.655
61.9 70.9 6.6 46.0
2.687 45.2 62.1 6.1 57,4
40.4 57.5 7.6
3.714
27.3
2.691 48.2
67.9 4.4
45.5
3.838
81.3 67.5 2.9
42.9
2.751
39.6 67.4 7.7 47.6
2.386 50.8 69.3 3.1 35.9
3.234
60.3
71.1 7.2
54.4
2.813
21.6
63.8 9.3
44.0
2.793 59.9 66.1
7.6
55.4
2.676 27.9
62.6 3.8 40.8
3.517 47.9
62.8 2.1 41.9
3.013
67.1
74.5 9.9
52.6
3.473 67.2 58.1 1.4
44.2
y
55.5
43.7
41.0
Motel
X2
21 2.389 29.0
22
3.389 33.9
70.2
2.6
23 3.597 62.8 65.4 9.4
2.724
55.5
57.7
1.0
25 2.429 46.3 61.2 8.8
26 2.826 36.2 65.9
27 3.591
47.4
28 3.285 32.9
29
3.567
30 3.082
31
2.172
32
3.910
33 3.448
34
35
36
37 2.622
38 2.640
39 2,210
40 3.080
24
64.3
41.6
X4
3.2
y
58.0
49.6
43.4
43.2
48.2
8.5 49.0
39.3
53.5
29.8
51.2
61.2 6.0
63.4 1.3
63.6
8.3
59.2
67.8
8.6
18.4
61.7 7.9
45.1
38.8
62.7
1.8 43.5
70.7 66.3 5.3 52.7
3.422 43.0
68.3 7.4
31.9
3.670 22.3 60.9 8.0
40.2
57.6
6.2 41.1
3.098 60.3
42.6
61.0
3.5
49.6
35.0 65.7 5.8
51.4
36.8 74.3 4.0
58.5
36.3
68.1
7.0
47.5

Definition Definition Middle value of a data set. The median divides a data set into two halves, and it also called the 50th percentile. The median is much less affected by outliers and skewed data than the mean. If the number of elements in a dataset is odd, then the middlemost element of the data arranged in ascending or descending order is the median. If the number of elements in the dataset is even, the average of the two central elements of the arranged data is the median of the set. For example, if a dataset has five items—12, 13, 21, 27, 31—the median is the third item in ascending order, or 21. If a dataset has six items—12, 13, 21, 27, 31, 33—the median is the average of the third (21) and fourth (27) items. It is calculated as follows: (21 + 27) / 2 = 24.

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