id Price ($ thousands) SqFt Baths Bedrooms Garage Age of Property Lot Size Property Condition Basement Outdoor Amenities School Quality Crime Rate Proximity to Amenities Transportation Accessibility Property Tax Rate 153000 920 1 0 33 3280 Poor Yes None 1.83 3.5 No 1.86 2 163150 750 1 2 о 38 2772 Poor No None 9 2.34 3.9 Yes 1.04 3 164900 900 1 2 0 13 3530 Excellent Yes None 6 2.98 3.9 No 2.11 4 170175 1500 1 2 о 31 5561 Fair Yes Deck 7 2.49 4.8 No 1.84 5 176900 1030 2 2 0 47 3247 Excellent No None 3 2.82 4.3 No 1.96 G 187700 1090 1 2 0 36 3898 Poor No Garden 8 2.68 4 No 1.5 7 295000 1280 2 2 1 45 4617 Excellent Yes None 9 2.66 5 No 2.22 8 251650 1355 1 2 1 24 4674 Good No Garden 8 2.69 3.81 No 2.32 9 472990 1690 3 3 1 15 6315 Fair Yes Deck 8 1.2 4 No 1.5 10 473000 1765 3 3 1 29 6944 Fair Yes Deck 9 1.74 4.2 Not 1.88 11 773650 2780 3.5 4 2 8 10913 Fair Yes Deck 8 1 1.6 No 1.63 12 674000 1910 3 3 2 5 6591 Poar Yes Garden 6 1 2.8 No 1.95 13 885000 1920 4 4 2 29 5977 Fair No Deck 7 1 1.8 No 2.19 14 780000 1930 4 4 2 47 7691 Good Yes Garden 8 1 2.1 Yes 2.3 15 385900 950 1.5 3 1 4 3647 Poor Yes Deck 6 1.94 4 No 1.34 16 284650 850 1 2 1 12 2656 Fair No None 5 1.94 3.7 No 1.09 17 189500 950 2 1 0 45 3725 Fair No None 7 2.93 4.1 Yes 1.93 18 392800 1025 2 2 1 2 3967 Excellent No Garden 6 1.65 3.6 No 1.66 19 299600 1560 15 2 1 27 5489 Excellent No Pool 7 1.77 3.8 Yes 1.97 20 115350 980 1.5 1 0 31 3519 Fair No Deck 7 3.06 4 Yes 1.19 21 120170 750 15 1 0 36 2549 Good No None 6 1.9 5 No 1.63 22 164900 840 1 1 0 35 2566 Poor No None 6 2.7 5 Yes 1.5 23 574900 2180 25 3 1 26 7271 Good Yes Garden 6 1 3.3 No 2.27 24 970000 3400 3.5 4 3 43 12930 Fair Yes Garden 9 1 1.6 Not 2.94 25 810000 2790 3 4 2 27 8383 Good Yes Garden 8 1 1.9 No 2.79 26 840000 2860 3 4 2 5 9534 Excellent No Deck 9 1 1.8 Yes 2.8 27 185500 1350 1 1 0 20 4588 Good Yes None 6 2.59 5 Yes 2.02 28 289600 1100 15 2 0 11 3891 Fair No Pool 6 1.07 4.5 No 1.93 29 389800 1250 2 3 1 10 4900 Fair Yes None 8 1.38 3.3 No 2.29 30 689500 1870 3 3 1 40 6258 Good Yes Garden 9 1.22 2.8 No 1.9 31 889100 2850 3.5 4 2 38 9539 Good Yes Garden 7 1 1.9 Yes 2.15 32 283700 985 15 2 о 6 3681 Good No None 6 2.2 4.3 No 1.09 33 160450 980 1 1 0 8 3383 Poor Yes None 8 1.79 4.7 No 2.08 34 195989 1100 1.5 1 0 23 3547 Fair No Garden 8 2.64 4.9 No 1.12 35 999900 3250 4 4 2 47 11220 Good No Garden 8 1 1.2 Yes 2.21 36 225340 1150 2 2 0 26 3612 Good No None 7 2.27 4.3 No 1.22 37 125750 950 1.5 1 0 46 3018 Good No Deck 6 3.19 3.7 No 2.14 38 124700 890 2 0 43 3114 Fair No None 3 2.24 4 No 2.18 39 200500 1200 2 2 1 12 4103 Fair Yes Deck 9 2.08 4.8 Yes 1.72 40 128500 980 1 1 0 26 3837 Poor Yes None 8 1.33 4.1 No 2.1 41 174360 1100 15 1 1 13 3699 Excellent No Garden 7 2.88 4 No 1.37 42 179800 1210 2 1 0 40 4333 Poor Yes Deck 7 2.56 4.4 Yes 2.15 43 205450 1350 25 2 1 18 4904 Fair Yes Garden 7 1.47 4.7 No 1.69 44 779800 2600 3 4 2 25 7834 Excellent Yes Garden 9 1 1.9 No 1.99 45 128800 985 15 1 0 33 3609 Fair No None 8 2.13 2.8 Yes 1.11 46 522200 2345 3 3 1 47 7452 Fair No Pool 6 1.66 2.8 Yes 1.77 47 1173200 3250 3.5 2 40 12873 Poor No Deck 9 1 1.7 No 1.59 48 1824200 3875 4 5 3 43 12201 Good Yes Garden 8 1 1 Yes 2.91 49 2475200 4560 5 6 3 12 15571 Good No Garden 8 1 1 No 3.78 50 3126200 5870 5.5 7 4 44 18111 Fair Yes Pool 9 1 1 No 2
id Price ($ thousands) SqFt Baths Bedrooms Garage Age of Property Lot Size Property Condition Basement Outdoor Amenities School Quality Crime Rate Proximity to Amenities Transportation Accessibility Property Tax Rate 153000 920 1 0 33 3280 Poor Yes None 1.83 3.5 No 1.86 2 163150 750 1 2 о 38 2772 Poor No None 9 2.34 3.9 Yes 1.04 3 164900 900 1 2 0 13 3530 Excellent Yes None 6 2.98 3.9 No 2.11 4 170175 1500 1 2 о 31 5561 Fair Yes Deck 7 2.49 4.8 No 1.84 5 176900 1030 2 2 0 47 3247 Excellent No None 3 2.82 4.3 No 1.96 G 187700 1090 1 2 0 36 3898 Poor No Garden 8 2.68 4 No 1.5 7 295000 1280 2 2 1 45 4617 Excellent Yes None 9 2.66 5 No 2.22 8 251650 1355 1 2 1 24 4674 Good No Garden 8 2.69 3.81 No 2.32 9 472990 1690 3 3 1 15 6315 Fair Yes Deck 8 1.2 4 No 1.5 10 473000 1765 3 3 1 29 6944 Fair Yes Deck 9 1.74 4.2 Not 1.88 11 773650 2780 3.5 4 2 8 10913 Fair Yes Deck 8 1 1.6 No 1.63 12 674000 1910 3 3 2 5 6591 Poar Yes Garden 6 1 2.8 No 1.95 13 885000 1920 4 4 2 29 5977 Fair No Deck 7 1 1.8 No 2.19 14 780000 1930 4 4 2 47 7691 Good Yes Garden 8 1 2.1 Yes 2.3 15 385900 950 1.5 3 1 4 3647 Poor Yes Deck 6 1.94 4 No 1.34 16 284650 850 1 2 1 12 2656 Fair No None 5 1.94 3.7 No 1.09 17 189500 950 2 1 0 45 3725 Fair No None 7 2.93 4.1 Yes 1.93 18 392800 1025 2 2 1 2 3967 Excellent No Garden 6 1.65 3.6 No 1.66 19 299600 1560 15 2 1 27 5489 Excellent No Pool 7 1.77 3.8 Yes 1.97 20 115350 980 1.5 1 0 31 3519 Fair No Deck 7 3.06 4 Yes 1.19 21 120170 750 15 1 0 36 2549 Good No None 6 1.9 5 No 1.63 22 164900 840 1 1 0 35 2566 Poor No None 6 2.7 5 Yes 1.5 23 574900 2180 25 3 1 26 7271 Good Yes Garden 6 1 3.3 No 2.27 24 970000 3400 3.5 4 3 43 12930 Fair Yes Garden 9 1 1.6 Not 2.94 25 810000 2790 3 4 2 27 8383 Good Yes Garden 8 1 1.9 No 2.79 26 840000 2860 3 4 2 5 9534 Excellent No Deck 9 1 1.8 Yes 2.8 27 185500 1350 1 1 0 20 4588 Good Yes None 6 2.59 5 Yes 2.02 28 289600 1100 15 2 0 11 3891 Fair No Pool 6 1.07 4.5 No 1.93 29 389800 1250 2 3 1 10 4900 Fair Yes None 8 1.38 3.3 No 2.29 30 689500 1870 3 3 1 40 6258 Good Yes Garden 9 1.22 2.8 No 1.9 31 889100 2850 3.5 4 2 38 9539 Good Yes Garden 7 1 1.9 Yes 2.15 32 283700 985 15 2 о 6 3681 Good No None 6 2.2 4.3 No 1.09 33 160450 980 1 1 0 8 3383 Poor Yes None 8 1.79 4.7 No 2.08 34 195989 1100 1.5 1 0 23 3547 Fair No Garden 8 2.64 4.9 No 1.12 35 999900 3250 4 4 2 47 11220 Good No Garden 8 1 1.2 Yes 2.21 36 225340 1150 2 2 0 26 3612 Good No None 7 2.27 4.3 No 1.22 37 125750 950 1.5 1 0 46 3018 Good No Deck 6 3.19 3.7 No 2.14 38 124700 890 2 0 43 3114 Fair No None 3 2.24 4 No 2.18 39 200500 1200 2 2 1 12 4103 Fair Yes Deck 9 2.08 4.8 Yes 1.72 40 128500 980 1 1 0 26 3837 Poor Yes None 8 1.33 4.1 No 2.1 41 174360 1100 15 1 1 13 3699 Excellent No Garden 7 2.88 4 No 1.37 42 179800 1210 2 1 0 40 4333 Poor Yes Deck 7 2.56 4.4 Yes 2.15 43 205450 1350 25 2 1 18 4904 Fair Yes Garden 7 1.47 4.7 No 1.69 44 779800 2600 3 4 2 25 7834 Excellent Yes Garden 9 1 1.9 No 1.99 45 128800 985 15 1 0 33 3609 Fair No None 8 2.13 2.8 Yes 1.11 46 522200 2345 3 3 1 47 7452 Fair No Pool 6 1.66 2.8 Yes 1.77 47 1173200 3250 3.5 2 40 12873 Poor No Deck 9 1 1.7 No 1.59 48 1824200 3875 4 5 3 43 12201 Good Yes Garden 8 1 1 Yes 2.91 49 2475200 4560 5 6 3 12 15571 Good No Garden 8 1 1 No 3.78 50 3126200 5870 5.5 7 4 44 18111 Fair Yes Pool 9 1 1 No 2
Chapter15: Property Transactions: Nontaxable Exchanges
Section: Chapter Questions
Problem 4RP
Related questions
Question
You must use Excel to perform the regression analysis. Provide the answers under the space provided for each question. You must provide the Excel output for the question along with the answers. Round off the values on the output to three-five decimal places if appropriate.Examine the interaction effect between Bedrooms and Square Footage (SqFt) on house price in a multiple regression model. Include an interaction term for Bedroom × SqFt in the regression model alongside the individual terms for Bathrooms and SqFt.
12) Provide the Excel output below here: (2p)
13) Analyze the p-value of the interaction term to determine if the interaction significantly contributes to predicting house price. (α = 0.05) (3p)
14) Interpret the coefficient of the interaction term to understand how the effect of Bedroom on house price may change depending on the Square Footage of the home. (3p)
15) Why does the main effect of Square Footage (SqFt) become insignificant when the interaction term (SqFt × Bedrooms) is included in the model? Briefly explain the reason for this change. (3p)
16) Write the corresponding regression equation substituting each coefficient and independent variables along with the interaction term. What is the predicted price for homes with 5 bedrooms and a square footage of 3000 square feet? (4p)
arger lots with outdoor amenities (e.g., pool, deck, garden) could have added value, as these features are often more attractive on spacious properties.
Examine the interaction effect between Lot Size and Outdoor Amenities (deck or garden) on house price in a multiple regression model. Include an interaction term for Lot Size × Outdoor Amenities in the regression model, along with the individual terms for Lot Size and Outdoor Amenities.
17) Provide the Excel output below here: (2p)
18) Analyze the p-value of the interaction term to determine if the interaction significantly contributes to predicting house price. (α = 0.05) (3p)
19) Interpret the coefficient of the interaction term to understand how the presence of outdoor amenities may add value to properties with larger lot sizes. (3p)
20) Why does the main effect of Outdoor Amenities become insignificant when the interaction term (Lot Size × D_Deck of Garden) is included in the model? Briefly explain the reason for this change. (3p)
21) Write the corresponding regression equation substituting each coefficient and independent variables along with the interaction term. What is the predicted price for homes with a lot size of 5,000 square feet that include a garden? (3p)
Transcribed Image Text:id
Price ($ thousands)
SqFt
Baths Bedrooms Garage Age of Property Lot Size Property Condition Basement
Outdoor Amenities School Quality Crime Rate Proximity to Amenities
Transportation Accessibility
Property Tax Rate
153000
920
1
0
33
3280
Poor
Yes
None
1.83
3.5
No
1.86
2
163150
750
1
2
о
38
2772
Poor
No
None
9
2.34
3.9
Yes
1.04
3
164900
900
1
2
0
13
3530
Excellent
Yes
None
6
2.98
3.9
No
2.11
4
170175
1500
1
2
о
31
5561
Fair
Yes
Deck
7
2.49
4.8
No
1.84
5
176900
1030
2
2
0
47
3247
Excellent
No
None
3
2.82
4.3
No
1.96
G
187700
1090
1
2
0
36
3898
Poor
No
Garden
8
2.68
4
No
1.5
7
295000
1280
2
2
1
45
4617
Excellent
Yes
None
9
2.66
5
No
2.22
8
251650
1355
1
2
1
24
4674
Good
No
Garden
8
2.69
3.81
No
2.32
9
472990
1690
3
3
1
15
6315
Fair
Yes
Deck
8
1.2
4
No
1.5
10
473000
1765
3
3
1
29
6944
Fair
Yes
Deck
9
1.74
4.2
Not
1.88
11
773650
2780
3.5
4
2
8
10913
Fair
Yes
Deck
8
1
1.6
No
1.63
12
674000
1910
3
3
2
5
6591
Poar
Yes
Garden
6
1
2.8
No
1.95
13
885000
1920
4
4
2
29
5977
Fair
No
Deck
7
1
1.8
No
2.19
14
780000
1930
4
4
2
47
7691
Good
Yes
Garden
8
1
2.1
Yes
2.3
15
385900
950
1.5
3
1
4
3647
Poor
Yes
Deck
6
1.94
4
No
1.34
16
284650
850
1
2
1
12
2656
Fair
No
None
5
1.94
3.7
No
1.09
17
189500
950
2
1
0
45
3725
Fair
No
None
7
2.93
4.1
Yes
1.93
18
392800
1025
2
2
1
2
3967
Excellent
No
Garden
6
1.65
3.6
No
1.66
19
299600
1560
15
2
1
27
5489
Excellent
No
Pool
7
1.77
3.8
Yes
1.97
20
115350
980
1.5
1
0
31
3519
Fair
No
Deck
7
3.06
4
Yes
1.19
21
120170
750
15
1
0
36
2549
Good
No
None
6
1.9
5
No
1.63
22
164900
840
1
1
0
35
2566
Poor
No
None
6
2.7
5
Yes
1.5
23
574900
2180
25
3
1
26
7271
Good
Yes
Garden
6
1
3.3
No
2.27
24
970000
3400
3.5
4
3
43
12930
Fair
Yes
Garden
9
1
1.6
Not
2.94
25
810000
2790
3
4
2
27
8383
Good
Yes
Garden
8
1
1.9
No
2.79
26
840000
2860
3
4
2
5
9534
Excellent
No
Deck
9
1
1.8
Yes
2.8
27
185500
1350
1
1
0
20
4588
Good
Yes
None
6
2.59
5
Yes
2.02
28
289600
1100
15
2
0
11
3891
Fair
No
Pool
6
1.07
4.5
No
1.93
29
389800
1250
2
3
1
10
4900
Fair
Yes
None
8
1.38
3.3
No
2.29
30
689500
1870
3
3
1
40
6258
Good
Yes
Garden
9
1.22
2.8
No
1.9
31
889100
2850
3.5
4
2
38
9539
Good
Yes
Garden
7
1
1.9
Yes
2.15
32
283700
985
15
2
о
6
3681
Good
No
None
6
2.2
4.3
No
1.09
33
160450
980
1
1
0
8
3383
Poor
Yes
None
8
1.79
4.7
No
2.08
34
195989
1100
1.5
1
0
23
3547
Fair
No
Garden
8
2.64
4.9
No
1.12
35
999900
3250
4
4
2
47
11220
Good
No
Garden
8
1
1.2
Yes
2.21
36
225340
1150
2
2
0
26
3612
Good
No
None
7
2.27
4.3
No
1.22
37
125750
950
1.5
1
0
46
3018
Good
No
Deck
6
3.19
3.7
No
2.14
38
124700
890
2
0
43
3114
Fair
No
None
3
2.24
4
No
2.18
39
200500
1200
2
2
1
12
4103
Fair
Yes
Deck
9
2.08
4.8
Yes
1.72
40
128500
980
1
1
0
26
3837
Poor
Yes
None
8
1.33
4.1
No
2.1
41
174360
1100
15
1
1
13
3699
Excellent
No
Garden
7
2.88
4
No
1.37
42
179800
1210
2
1
0
40
4333
Poor
Yes
Deck
7
2.56
4.4
Yes
2.15
43
205450
1350
25
2
1
18
4904
Fair
Yes
Garden
7
1.47
4.7
No
1.69
44
779800
2600
3
4
2
25
7834
Excellent
Yes
Garden
9
1
1.9
No
1.99
45
128800
985
15
1
0
33
3609
Fair
No
None
8
2.13
2.8
Yes
1.11
46
522200
2345
3
3
1
47
7452
Fair
No
Pool
6
1.66
2.8
Yes
1.77
47
1173200
3250
3.5
2
40
12873
Poor
No
Deck
9
1
1.7
No
1.59
48
1824200
3875
4
5
3
43
12201
Good
Yes
Garden
8
1
1
Yes
2.91
49
2475200
4560
5
6
3
12
15571
Good
No
Garden
8
1
1
No
3.78
50
3126200
5870
5.5
7
4
44
18111
Fair
Yes
Pool
9
1
1
No
2
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