2) What are the important variables that predict Crime rate? How did you identif
ID: 3207061 • Letter: 2
Question
2) What are the important variables that predict Crime rate? How did you identify them to be important/significant variables?
3) is the model a good model for predicting the crime rate? If yes, why? If no, why not?
4) Next, perform stepwise regression i.e, rerun the regression analysis as many times as necessary till you are left with only significant variables. Please use separate worksheets every time you delete a variable and run the analysis. On what basis did you delete variables one by one?
5) What are the final significant variables you are left with by doing question 4) In other words what factors are important in predicting Crime rate after you re-run analysis in question 4?
AREA NON-SUB % > 66 DOCS HOSP BEDS HS GRAD LABOR INCOME SER CRIMES 1.384 78.1 12.3 2.7300522 7.422818792 50.1 0.435059124 72.1 75.55491637 3.553 37.4 10.7 2.028368794 7.036086775 50.6 0.431017939 33.216 41.32290363 3.916 29.9 8.8 1.464988558 5.53020595 52.2 0.450045767 32.906 67.38352403 2.48 31.5 10.5 2.671904463 5.264299183 66.1 0.475958517 26.573 80.18918919 1.218 0 8.8 1.954985119 8.235491071 62.9 0.451376488 21.524 47.45796131 8.36 46.3 8.2 1.514029181 5.367377478 53.6 0.494276094 18.35 72.25028058 4.935 21.8 11 1.710504202 7.458823529 47.8 0.445882353 16.12 57.76428571 1.008 16.6 10.3 2.034535297 8.483494159 55.9 0.475114271 15.953 54.16251905 4.326 23.6 7.3 1.672489083 5.445414847 50.4 0.473362445 12.107 58.12336245 4.651 38.8 7.7 2.277628032 5.739218329 67.4 0.491374663 10.375 78.74730458 4.226 38.1 9.8 2.302032235 3.778556412 67.8 0.490399439 10.918 64.04975473 2.045 37.2 21.4 1.412318841 6.422463768 50.7 0.393623188 7.989 64.67898551 1.59 30.1 10.9 1.748667174 7.607006855 50.4 0.430845392 8.411 51.5575019 3.65 34.6 11.1 2.103479037 5.552185549 62.9 0.481088314 7.792 68.970562 3.434 28.9 8.3 1.984930032 3.460710441 65.1 0.45489774 5.909 77.94402583 3.358 35.1 11.3 2.048447205 6.847204969 44.9 0.446086957 4.941 53.15031056 3.491 48.5 9.7 1.945383615 7.308192458 59.6 0.471131339 4.798 57.88426528 4.08 59.6 9.9 2.065976714 9.697283312 47.3 0.492755498 4.6 43.90168176 0.596 100 6 1.742738589 3.899031812 66 0.442461964 5.181 64.98478562 2.419 27.8 9.9 1.931993818 4.435857805 57.8 0.443276662 3.86 47.64914992 1.951 28.4 14.5 1.106518283 7.699523052 47.9 0.43163752 3.667 23.63751987 1.49 33.1 11.9 1.325320513 6.118589744 47.4 0.481089744 4.144 30.59294872 0.047 41.9 11.9 1.320921986 5.943262411 36.3 0.459042553 3.915 51.69680851 1.182 32.4 7.4 1.007782101 4.892996109 52.4 0.421789883 3.627 68.4844358 0.476 8.9 10.9 1.599593496 5.646341463 60.1 0.443902439 3.603 50.3800813 2.766 67.9 7.7 1.432489451 8.170886076 56.3 0.47257384 2.598 63.22151899 5.966 39.5 9.6 1.561440678 4.040254237 52.7 0.522457627 3.007 80.94279661 1.863 50.4 7.7 1.44017094 6.386752137 63.8 0.416239316 2.747 53.75854701 9.24 67 10.3 2.468131868 5.158241758 63.1 0.403516484 2.598 91.53626374 1.63 41.9 10.7 1.61247216 9.788418708 50 0.440979955 2.445 39.18930958 1.624 13.4 11 1.939393939 6.848484848 55.4 0.484382284 2.885 39.59207459 2.109 41.2 10.3 1.290322581 6.300248139 45.2 0.454342432 2.308 40.29776675 8.152 22.3 9.1 1.115702479 3.454545455 51.7 0.456749311 2.257 78.10192837 0.655 75.2 6.6 1.167582418 10.65659341 51.6 0.447802198 2.088 42.92032967 1.803 35.3 10.4 1.334254144 5.903314917 53.7 0.466574586 2.666 45.31767956 1.198 55.1 8 3.741214058 12.38658147 71.2 0.550479233 2.038 59.66773163 1.412 39.2 11.3 1.40192926 5.906752412 49.4 0.495819936 2.098 82.68167203 2.071 19.9 11.3 1.535947712 8.27124183 58.9 0.43496732 1.782 36.47385621 0.862 26.3 13.4 1.400662252 6.387417219 43.3 0.481788079 2.01 25.49337748 1.526 71.7 7.7 1.363036304 5.399339934 47.1 0.415181518 1.692 66.1320132 1.758 33.2 11.6 0.996632997 8.929292929 45.3 0.385185185 1.641 41.97643098 2.71 63.7 6.2 1.239583333 4.434027778 72.8 0.385069444 1.639 63.10069444 3.324 49.7 8.4 1.356363636 3.378181818 62.5 0.438181818 1.918 53.73090909 7.397 47.3 12.1 1.329588015 7.647940075 56.2 0.425842697 1.654 45.96629213 1.148 45.3 11.1 1.512733447 9.830220713 54 0.470288625 3.51 49.63837012 1.509 37.6 12 1.690513219 7.620528771 51.4 0.497045101 3.982 45.19129082 2.013 61.7 9.7 1.07480315 5.842519685 50.9 0.42007874 1.412 56.87401575 1.011 37.8 10.5 1.13304721 4.137339056 70.7 0.4 1.337 60.16309013 0.813 13.4 10.9 1.599137931 18.77155172 58 0.418103448 1.589 36.32758621 0.654 28.8 3.9 0.606060606 5.61038961 55.1 0.28961039 1.148 68.76190476Explanation / Answer
Answer:
2) What are the important variables that predict Crime rate? How did you identify them to be important/significant variables?
important variables: AREA, . HOSP BEDS
both variables are significant, p values for both variables are < 0.05 level.
3) is the model a good model for predicting the crime rate? If yes, why? If no, why not?
The model is significant, F=5.42, P=0.0001.
R square value is 0.514, 51.4% of crime rate is explained by the model.
Regression Analysis
R²
0.514
Adjusted R²
0.419
n
50
R
0.717
k
8
Std. Error
11.886
Dep. Var.
SER CRIMES
ANOVA table
Source
SS
df
MS
F
p-value
Regression
6,126.7512
8
765.8439
5.42
.0001
Residual
5,792.8441
41
141.2889
Total
11,919.5953
49
Regression output
confidence interval
variables
coefficients
std. error
t (df=41)
p-value
95% lower
95% upper
Intercept
60.5831
32.0356
1.891
.0657
-4.1142
125.2804
AREA
2.1204
0.8600
2.466
.0180
0.3835
3.8572
NON-SUB
0.1151
0.0937
1.228
.2264
-0.0741
0.3043
% > 66
-0.8788
0.7528
-1.167
.2498
-2.3990
0.6415
DOCS
6.2809
5.4390
1.155
.2549
-4.7033
17.2651
HOSP BEDS
-2.1005
0.7373
-2.849
.0068
-3.5896
-0.6114
HS GRAD
0.2769
0.2845
0.973
.3360
-0.2976
0.8514
LABOR
-41.6172
53.3533
-0.780
.4399
-149.3665
66.1320
INCOME
0.1793
0.1703
1.053
.2986
-0.1646
0.5232
4) Next, perform stepwise regression i.e, rerun the regression analysis as many times as necessary till you are left with only significant variables. Please use separate worksheets every time you delete a variable and run the analysis. On what basis did you delete variables one by one?
Basis of p values. Include the variable is its p value <0.05 and delete if its p value >0.05.
Regression Analysis -- Stepwise Selection displaying the best model of each size
50
observations
SER CRIMES
is the dependent variable
p-values for the coefficients
Nvar
AREA
NON-SUB
% > 66
DOCS
HOSP BEDS
HS GRAD
LABOR
INCOME
s
Adj R²
R²
Cp
p-value
1
.0006
13.921
.203
.220
19.833
.0006
2
.0059
.0001
12.967
.309
.337
11.936
.0001
3
.0113
.0077
.0158
12.438
.364
.403
8.366
2.53E-05
4
.0265
.0471
.0125
.0015
12.034
.405
.453
6.122
1.41E-05
5
.0116
.0895
.0083
.0130
.0582
11.788
.429
.487
5.274
1.28E-05
6
.0114
.1575
.3356
.0110
.0435
.0478
11.795
.428
.498
6.341
2.62E-05
7
.0197
.1888
.2700
.3948
.0080
.1919
.1792
11.831
.425
.507
7.608
.0001
8
.0180
.2264
.2498
.2549
.0068
.3360
.4399
.2986
11.886
.419
.514
9.000
.0001
5) What are the final significant variables you are left with by doing question
AREA, HOSP BEDS, HS GRAD
Regression Analysis
R²
0.403
Adjusted R²
0.364
n
50
R
0.635
k
3
Std. Error
12.438
Dep. Var.
SER CRIMES
ANOVA table
Source
SS
df
MS
F
p-value
Regression
4,803.4030
3
1,601.1343
10.35
2.53E-05
Residual
7,116.1922
46
154.6998
Total
11,919.5953
49
Regression output
confidence interval
variables
coefficients
std. error
t (df=46)
p-value
95% lower
95% upper
Intercept
32.6757
14.1295
2.313
.0253
4.2345
61.1170
AREA
2.3205
0.8797
2.638
.0113
0.5499
4.0912
HOSP BEDS
-1.9916
0.7151
-2.785
.0077
-3.4310
-0.5523
HS GRAD
0.5581
0.2227
2.506
.0158
0.1099
1.0064
Regression Analysis
R²
0.514
Adjusted R²
0.419
n
50
R
0.717
k
8
Std. Error
11.886
Dep. Var.
SER CRIMES
ANOVA table
Source
SS
df
MS
F
p-value
Regression
6,126.7512
8
765.8439
5.42
.0001
Residual
5,792.8441
41
141.2889
Total
11,919.5953
49
Regression output
confidence interval
variables
coefficients
std. error
t (df=41)
p-value
95% lower
95% upper
Intercept
60.5831
32.0356
1.891
.0657
-4.1142
125.2804
AREA
2.1204
0.8600
2.466
.0180
0.3835
3.8572
NON-SUB
0.1151
0.0937
1.228
.2264
-0.0741
0.3043
% > 66
-0.8788
0.7528
-1.167
.2498
-2.3990
0.6415
DOCS
6.2809
5.4390
1.155
.2549
-4.7033
17.2651
HOSP BEDS
-2.1005
0.7373
-2.849
.0068
-3.5896
-0.6114
HS GRAD
0.2769
0.2845
0.973
.3360
-0.2976
0.8514
LABOR
-41.6172
53.3533
-0.780
.4399
-149.3665
66.1320
INCOME
0.1793
0.1703
1.053
.2986
-0.1646
0.5232
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