Question
Need Help with A and B
Thanks in advance
price land_fcv age time pop_sqml gr_fl_ar Patio_Floor sedi_per_lake imp_fcv 245373.9 49096 5 10.66 4.17669 1710 0.106583 270.852 106186 305659.7 46497 36 10.73 4.17669 1652 0.098253 270.852 100628 260180.9 70629 8 11.42 4.17669 1967 0.098946 270.852 121079 243258.6 51534 27 11.44 4.17669 2352 0.089078 270.852 134085 269699.7 63992 17 11.79 4.17669 2037 0.097475 270.852 162465 301429.1 52793 11 12.11 4.17669 2472 0.092511 270.852 161584 138551.6 29921 26 18.13 203.668 960 0.117647 270.852 56544 185088 32404 40 17.36 203.668 1080 0.108911 270.852 80407 134321 50000 35 16.45 203.668 989 0.133216 270.852 77686 180328.6 29050 20 16.04 203.668 1320 0.10143 270.852 85571 169223.4 14800 29 20.05 203.668 1179 0.116854 270.852 74387 278160.9 46000 1 27.07 4.17669 2224 0.095935 40.83888 96717 185088 40500 17 11.4 203.668 1208 0.11437 270.852 91304 186674.5 40500 17 11.82 203.668 1208 0.11437 270.852 87569 181915.1 40500 17 11.71 203.668 1208 0.11437 270.852 81670 182972.8 62500 17 11.38 203.668 1208 0.11437 270.852 79853 343734.9 62500 10 11.87 203.668 3017 0.08907 270.852 223109 391752.1 27500 2 11.79 203.668 2555 0.084558 270.852 211511 332100.8 71000 5 29.22 4.17669 2137 0.102478 40.83888 205954 460869.3 5472 8 27.31 4.17669 2840 0.094099 40.83888 189398 222105.7 22553 16 14.96 4.17669 1478 0.10152 340.4167 139692 154310.5 20690 29 14.86 4.17669 1232 0.104651 340.4167 83611 132205.8 21261 31 14.52 4.17669 1232 0.104651 340.4167 66594 354311.4 54969 9 14.9 4.17669 1726 0.105236 340.4167 175794 135590.2 19000 31 6.53 222.533 1389 0.11246 340.4167 62691 134849.9 19000 31 6.5 222.533 1283 0.115782 340.4167 68674 145955.1 50000 39 6.98 222.533 1158 0.110599 340.4167 65503 195664.5 50000 13 7.09 222.533 1632 0.099338 340.4167 88900 261238.6 59375 10 18.73 59.1291 1914 0.099718 340.4167 156766 273930.3 59375 10 18.82 59.1291 1747 0.101337 340.4167 109027 344792.6 59375 9 17.75 4.17669 2063 0.100697 340.4167 160713 315707.3 66250 8 18.69 59.1291 2156 0.097152 340.4167 133659 333052.7 59375 9 19.04 59.1291 2016 0.099598 340.4167 168272 284506.8 59375 9 19.36 59.1291 2548 0.087393 340.4167 138439 327870.3 59375 9 19.49 59.1291 1876 0.10024 340.4167 133970 280276.2 69044 16 14.91 4.17669 1778 0.099747 340.4167 103570 409837.8 60000 8 6.53 222.533 2701 0.090266 19.51661 190565 242200.9 60000 5 5.74 222.533 2101 0.109746 19.51661 136186 169223.4 42000 1 5.7 222.533 1465 0.102878 19.51661 87630 216817.4 40000 8 5.56 222.533 2016 0.097179 19.51661 120646 449499.6 74888 9 19.29 59.1291 2007 0.097978 340.4167 198247 406664.9 69190 12 21.02 59.1291 2243 0.102082 340.4167 205632 391329 88872 9 21.11 59.1291 1870 0.131444 340.4167 170003 395559.6 88872 12 22.19 59.1291 2095 0.103168 340.4167 246569 433634.9 80178 7 20.37 59.1291 2258 0.099322 340.4167 168868 362772.6 80178 4 20.83 59.1291 2196 0.094059 340.4167 181785 317293.8 80178 10 20.47 59.1291 1786 0.125795 340.4167 126688 525650.1 104880 12 21.85 59.1291 3032 0.088942 340.4167 328893 793234.5 71225 10 19.88 59.1291 5167 0.070349 340.4167 441161 Yoo et al. (2014) recently studied the impacts of a variety of factors influencing house prices in Prescott, Arizona. Prescott metropolitan area in Central Arizona includes five recreational lakes -Granite Basin Lake, Watson Lake, Willow Creek Reservoir, Lynx Lake and Upper Goldwater Lake. The five lakes in the study area provide a range of benefits recreational opportunity, scenic beauty, clear water, etc to the residents of Prescott, and hence easier access to those lakes is expected to increase nearby residential property prices. Higher level of sedimentation in the lake or rivers leads to physical disruption of water quality and creates high levels of turbidity by limiting penetration of sunlight into the water column. Therefore, higher level of sedimentation is expected to decrease nearby residential property values. Using a regression model(s), you will investigate a variety of environmental, structural, and socio-economic factors that affect residential property values using this dataset (Prescott _Parcel.xlsx) Description of variables included in the dataset is shown below Variable Price Description Residential property sales in dollar (Year: 2003) Land fcv Land full cash value in dollar (reflection of the market value of your property and consists of land and improvements) The age of property Traveling time to the nearest lake in minute Time Pop sqmlNumber of population/mile in 2000 (measured on a Census tract level) Gr fl ar The area of ground floor (sq) Patio-Floor The ratio of patio area to total area (Total area=ground floor area+patio area) sedi_per_lake Tons of sediment loads/lake acre in the nearest lake from each residential property Imp fcv Improved full cash value Please address the following; Explain your answers A - B - What are the research questions you want to investigate using this dataset? Based on a multiple linear regression model, which variables are significant, and which variables are not? Did the signs of each variable come out as expected?
Explanation / Answer
Answer:
a).
The problem is to identify the environmental, structural and socio economic factors that affect residential property values (price).
b).
Regression Analysis
R²
0.915
Adjusted R²
0.898
n
49
R
0.957
k
8
Std. Error
39906.781
Dep. Var.
price
ANOVA table
Source
SS
df
MS
F
p-value
Regression
685,372,001,444.6720
8
85,671,500,180.5840
53.80
5.38E-19
Residual
63,702,045,263.5306
40
1,592,551,131.5883
Total
749,074,046,708.2020
48
Regression output
confidence interval
variables
coefficients
std. error
t (df=40)
p-value
95% lower
95% upper
Intercept
-106,691.6578
107,737.0734
-0.990
.3280
-324,436.4055
111,053.0898
land_fcv
0.2094
0.3825
0.547
.5872
-0.5638
0.9825
age
-706.3103
765.3319
-0.923
.3616
-2,253.1037
840.4831
time
2,291.8411
1,294.0452
1.771
.0842
-323.5218
4,907.2039
pop_sqml
-56.1268
85.0952
-0.660
.5133
-228.1106
115.8571
gr_fl_ar
69.1724
23.9132
2.893
.0062
20.8421
117.5028
Patio_Floor
846,087.1653
878,713.0414
0.963
.3414
-929,858.1379
2,622,032.4685
sedi_per_lake
56.4783
67.0032
0.843
.4043
-78.9401
191.8968
imp_fcv
0.9096
0.2178
4.177
.0002
0.4695
1.3498
Regression Equation
price
=
-106692 + 0.209 land_fcv - 706 age + 2292 time - 56.1 pop_sqml + 69.2 gr_fl_ar
+ 846087 Patio_Floor + 56.5 sedi_per_lake + 0.910 imp_fcv
The significant variables are gr_fl_ar (area of ground floor) and imp_fcv ( improved full cash value). The p values are < 0.05 level.
The signs are come out as expected.
Regression Analysis
R²
0.915
Adjusted R²
0.898
n
49
R
0.957
k
8
Std. Error
39906.781
Dep. Var.
price
ANOVA table
Source
SS
df
MS
F
p-value
Regression
685,372,001,444.6720
8
85,671,500,180.5840
53.80
5.38E-19
Residual
63,702,045,263.5306
40
1,592,551,131.5883
Total
749,074,046,708.2020
48
Regression output
confidence interval
variables
coefficients
std. error
t (df=40)
p-value
95% lower
95% upper
Intercept
-106,691.6578
107,737.0734
-0.990
.3280
-324,436.4055
111,053.0898
land_fcv
0.2094
0.3825
0.547
.5872
-0.5638
0.9825
age
-706.3103
765.3319
-0.923
.3616
-2,253.1037
840.4831
time
2,291.8411
1,294.0452
1.771
.0842
-323.5218
4,907.2039
pop_sqml
-56.1268
85.0952
-0.660
.5133
-228.1106
115.8571
gr_fl_ar
69.1724
23.9132
2.893
.0062
20.8421
117.5028
Patio_Floor
846,087.1653
878,713.0414
0.963
.3414
-929,858.1379
2,622,032.4685
sedi_per_lake
56.4783
67.0032
0.843
.4043
-78.9401
191.8968
imp_fcv
0.9096
0.2178
4.177
.0002
0.4695
1.3498
