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Table 5 Multivariate regression

From: The modifiable areal unit problem (MAUP) in the relationship between exposure to NO2 and respiratory health

 

Natural Neighbourhood (n = 95)

Aggregated (n = 95)

Census Tract (n = 184)

 

Multivariate OLS

Multivariate OLS

Multivariate OLS

R-squared

0.4306

0.3947

0.4341

Adjusted R-squared

0.3848

0.3678

0.4150

Sum squared residual

32783700.0000

576190000000.0000

252486000.0000

Sigma-square

376824.0000

841798.0000

1426470.0000

S.E. of regression

613.8600

917.4960

1194.3500

Sigma-square ML

345091.0000

797493.0000

1372210.0000

S.E of regression ML

587.4450

893.0250

1171.4100

F-statistic

9.3999

14.6759

22.6379

Prob(F-statistic)

0.0000

0.0000

0.0000

Log likelihood

-740.4980

-780.2880

-1561.2200

Akaike

1497.0000

1570.5800

3136.4400

Schwarz criterion

1517.4300

1583.3400

3158.9500

Variables

n.a.

n.a.

n.a.

 

Intercept 5327.4610 (0.0001)

Intercept 738.3682 (0.0192)

Intercept -1013.495 (0.0905)

 

Mean NO2 concentration -18.0183 (0.6855)

Mean NO2 concentration 36.4373 (0.5349)

Mean NO2 concentration 30.9425 (0.5706)

 

Educational Attainment 78.4534 (0.0002)

% Occupied private dwellings in need of major repairs 179.7687 (0.0007)

% Occupied private dwellings in need of major repairs 177.3213 (< 0.0001)

 

Participation Rate -53.0824 (0.0003)

% Occupied private dwellings built before 1946 -29.6505 (0.0118)

% Occupied private dwellings built before 1946 -20.91902 (0.0163)

 

% Management occupations -84.1282 (0.004)

Educational Attainment 73.4928 (0.0111)

Educational Attainment 113.1868 (< 0.0001)

 

% Walk - mode of transportation to work 40.1355 (< 0.0001)

 

Average income 0.0151 (0.0442)

 

% Occupied private dwellings of type apartment -16.7916 (0.0015)

 

% Retail trade industry 73.8654 (0.0161)

 

% Lone-parent families -34.7820 (0.0157)

  

Jarque-Bera

0.9239 (0.6300)

44.1697 (< 0.0001)

1173.241 (< 0.0001)

Breusch-Pagan Test

3.0898 (0.8765)

8.5867 (0.0723)

149.1566 (< 0.0001)

Koenker-Bassett test

3.1269 (0.8730)

3.8557 (0.4258)

21.8956 (0.0012)

Moran's I (error)

0.0498 (0.2527)

0.1892 (0.0006)

0.1091 (0.0051)

Lagrange Multiplier (lag)

0.1953 (0.6584)

7.8384 (0.0051)

2.7432 (0.0976)

Robust LM (lag)

3.4593 (0.0628)

0.6030 (0.4374)

0.2288 (0.6324)

Lagrange Multiplier (error)

0.4047 (0.0554)

7.8074 (0.0052)

5.5355 (0.0186)

Robust LM (error)

3.6687 (0.0628)

0.5720 (0.4494)

3.0211 (0.0821)

  1. Results of the multivariate regressions (OLS) for the three spatial structures under study. p-values are in parentheses.