How much of the variance in homicide rate is explained by the hardship index, to

ID: 3320456 • Letter: H

Question

How much of the variance in homicide rate is explained by the hardship index, to two decimal places?

COMMUNITY AREA NAME Average Adjusted Rate 2006 - 2010 HOMICIDE Percent Elevated 1999 Percent Non White HARDSHIP INDEX BUSINESS LICENSES GROCERY STORES Edison Park 0 0 0.128725239 8 304 1 Mount Greenwood 0 0.7 0.118559099 16 210 3 Lincoln Park 0.7 6.4 0.221957188 6 1441 6 Forest Glen 0.7 3.6 0.486439828 33 379 2 North Park 0.9 0 0.186913834 11 221 2 North Center 1 5.8 0.176381994 2 2351 11 Loop 1.1 4 0.206480322 5 2148 9 Lake View 1.1 13.1 0.371696383 3 6972 4 Near North Side 2.1 6.4 0.277754708 1 4986 17 Lincoln Square 2.4 7.2 0.397187323 17 1079 4 Albany Park 3.3 7.7 0.489250646 14 469 3 Portage Park 3.5 5.7 0.473266675 19 981 11 Dunning 3.8 4.8 0.48280853 35 951 10 West Elsdon 3.9 9.7 0.707257031 53 1123 12 Edgewater 4 4.5 0.797976895 82 787 4 Avondale 4.4 1.6 0.210836507 21 524 4 Beverly 4.4 1.8 0.241288059 28 513 9 Near South Side 4.6 8.5 0.581155073 7 573 2 Hyde Park 4.7 3.3 0.40881179 12 351 1 Armour Square 4.8 24.8 0.57909887 46 1033 18 Bridgeport 5 0 0.801292407 24 313 1 West Ridge 5.3 21.8 0.805032058 69 554 3 Uptown 5.4 1.4 0.333616649 25 618 3 Irving Park 5.4 8.6 0.693362555 42 956 6 Norwood Park 5.4 7.6 0.655820571 43 559 2 O'Hare 5.6 13.4 0.478255159 20 890 15 Jefferson Park 5.8 5.9 0.57348481 34 809 7 Belmont Cragin 6.1 6.4 0.826583508 70 1091 23 Rogers Park 6.4 5.2 0.605764581 44 128 3 Hegewisch 6.9 10.5 0.619076669 39 873 13 Logan Square 7.7 5.8 0.529468136 32 219 4 West Town 7.7 12.8 0.58302533 23 1206 15 Clearing 8.4 6 0.400354344 10 2611 14 Garfield Ridge 8.6 2.1 0.383647413 29 410 1 East Side 9.1 6.6 0.825793762 61 351 4 West Lawn 9.4 7.7 0.837733906 64 296 3 McKinley Park 10.1 35 0.810968212 56 560 4 Brighton Park 10.7 5.8 0.620753133 50 522 1 Lower West Side 10.9 4 0.85982421 37 373 3 South Lawndale 11.5 11.9 0.876220905 71 1230 6 Gage Park 11.6 9.9 0.9054532 84 720 9 Montclaire 11.7 14.4 0.882766794 76 1019 11 Hermosa 11.8 9.5 0.968810916 78 64 Ashburn 11.9 15.3 0.563147363 15 2141 9 Archer Heights 12.6 10.5 0.952511262 93 591 6 Near West Side 12.8 14.6 0.955992363 96 1119 22 Oakland 13.4 12.2 0.985369077 38 183 2 Douglas 18.4 5 0.760197869 67 408 4 Calumet Heights 18.7 10.8 0.877184224 47 205 2 Kenwood 18.7 16 0.842302065 26 155 4 Avalon Park 22.1 16.1 0.942591156 51 133 2 Chicago Lawn 24.1 8.7 0.630036789 30 294 7 Morgan Park 26.6 14.4 0.98696604 41 316 3 Pullman 27.8 19.7 0.985689037 55 469 7 New City 28.3 39.5 0.609655172 97 216 1 South Shore 28.5 17.2 0.959124876 80 568 12 Woodlawn 30.1 22.5 0.953962421 91 735 17 Humboldt park 30.9 25.9 0.954959242 85 826 16 South Deering 31.7 13.4 0.929178088 58 215 5 Grand Boulevard 31.8 18.6 0.961687583 57 217 4 Riverdale 34.3 9.2 0.966815571 65 55 4 Austin 34.8 11.3 0.987472265 48 300 2 Washington Height 36.1 34.2 0.977154543 73 962 14 East Garfield Park 37.8 22 0.995278615 74 617 11 South Chicago 39.9 37.8 0.945847491 83 595 3 Roseland 41.5 20.2 0.964224548 75 311 5 Auburn Gresham 41.6 24 0.990329811 52 351 7 Englewood 42.4 17.5 0.996038372 60 563 6 West Pullman 42.5 30.5 0.981468398 87 528 4 North Lawndale 43.5 2.4 0.989835042 62 271 5 Chatham 43.5 5.6 0.994134531 98 56 2 West Garfield Park 47.2 38.9 0.992638689 94 308 8 Fuller Park 51.7 34.4 0.982488193 92 589 7 West Englewood 51.9 3 0.988413682 89 347 11 Washington Park 52.7 25.1 0.99135876 66 466 7 Greater Grand Crossing 53.8 12.8 0.996017447 88 219 3 Burnside 78.2 21.8 0.991037891 79 175

Explanation / Answer

Solution:

Here, we have to find the variance in homicide rate is explained by the hardship index.

That is we have to find the coefficient of determination or the value of R square.

For the given scenario, the correlation coefficient R is given as 0.6586, and value of R square or coefficient of determination is given as 0.4338. This means about 43.38% of the variation in the dependent variable or response variable homicide rate is explained by the independent variable or explanatory variable hardship index.

Regression output for more reference is given as below:

SUMMARY OUTPUT

Regression Statistics

Multiple R

0.658646459

R Square

0.433815157

Adjusted R Square

0.426266026

Standard Error

13.18977352

Observations

ANOVA

Significance F

Regression

9997.293062

57.4655737

7.46729E-11

Residual

13047.75941

173.9701254

Total

23045.05247

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Intercept

-1.612616944

3.012475015

-0.53531297

0.59401724

-7.613774818

4.388540931

HARDSHIP INDEX

0.399756428

0.052734105

7.580605101

7.4673E-11

0.294704705

0.504808152