Question

The printout on the next page shows a multivariate regression of CLEANPCT on POOR, WORKERS, POPDENS, and SUMMONS based on 59 sanitation districts in New York City. The variables have the following meaning for each district: CLEANPCT: Percent of streets rated clean by the Sanitation Department POOR: Poverty stats [1 if median household income <$10,000 and 0 if median household income >=$10,000] WORKERS: Number of sanitation field employees in the district POPDENS: Number of residents per acre SUMMONS: Number of summonses issued during the year Write the sample regression equation. Estimate the percentage of streets that are rated clean for a district that has: - A median income of $18,000 - 50 residents per acre - 100 field employees - 3,000 summonses issued during the year Which variables have coefficients that are significant at the 0.05 level? What percentage of variation in CLEANPCT is explained by variation in the other four variables? Is your equation significant at the 5% level? Explain in one sentence why you believe this to be true. Controlling for WORKERS, SUMMONS, and POOR, what is the impact of POPDENS on the percentage of streets that are rated clean? Controlling for WORKERS, POPDENS, and SUMMONS, what is the difference in cleanliness between a district that has a median household income below $10,000 and one that has a median household income above $10,000? Regression Variables Entered/Removed (b) Model Variables Entered Variables Removed Method 1 Summonses Issued, Sanitation Dept. Field Employees, Population Density, Poverty Status (a) . Enter a All requested variables entered. b Dependent Variable: % of Streets Rated Clean Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate 1 0.857 (a) 0.734 -0.714 9.020 a Predictors: (Constant), Summonses Issued, Sanitation Dept. Field Employees, Population Density, Poverty Status ANOVA (b) Model Sum of Squares df Mean Square F Sig. 1 Regression 12099.787 4 3024.947 37.176 0.000 (a) Residual 4393.898 54 81.368 Total 16493.685 58 a Predictors: (Constant), Summonses Issued, Sanitation Dept. Field Employees, Population Density, Poverty Status b Dependent Variable: % of Streets Rated Clean Coefficients (a) Model Unstandardized Coefficients Standardized Coefficients t Sig. B Std. Error Beta 1 (Constant) 79.629 5.306 15.008 0.000 Poverty Status -18.370 3.117 -0.478 -5.893 0.000 Sanitation Dept. Field Employees 0.03302 0.041 0.063 0.802 0.426 Population Density -0.133 0.036 -0.303 -3.718 0.000 Summonses Issued -0.003108 0.001 -0.341 -4.023 0.000 a Dependent Variable: % of Streets Rated Clean

The printout on the next page shows a multivariate regression of CLEANPCT on POOR, WORKERS, POPDENS, and SUMMONS based on 59 sanitation districts in New York City. The variables have the following meaning for each district:

CLEANPCT: Percent of streets rated clean by the Sanitation Department
POOR: Poverty stats [1 if median household income <$10,000 and 0 if median household income >=$10,000]
WORKERS: Number of sanitation field employees in the district
POPDENS: Number of residents per acre
SUMMONS: Number of summonses issued during the year

Write the sample regression equation.

Estimate the percentage of streets that are rated clean for a district that has:
- A median income of $18,000
- 50 residents per acre
- 100 field employees
- 3,000 summonses issued during the year

Which variables have coefficients that are significant at the 0.05 level?

What percentage of variation in CLEANPCT is explained by variation in the other four variables?

Is your equation significant at the 5% level? Explain in one sentence why you believe this to be true.

Controlling for WORKERS, SUMMONS, and POOR, what is the impact of POPDENS on the percentage of streets that are rated clean?

Controlling for WORKERS, POPDENS, and SUMMONS, what is the difference in cleanliness between a district that has a median household income below $10,000 and one that has a median household income above $10,000?

Regression

Variables Entered/Removed (b)
Model
Variables Entered
Variables Removed
Method
1
Summonses Issued, Sanitation Dept. Field Employees, Population Density, Poverty Status (a)
.
Enter
a All requested variables entered.
b Dependent Variable: % of Streets Rated Clean

Model Summary
Model
R
R Square
Adjusted R Square
Std. Error of the Estimate
1
0.857 (a)
0.734
-0.714
9.020
a Predictors: (Constant), Summonses Issued, Sanitation Dept. Field Employees, Population Density, Poverty Status

ANOVA (b)
Model
Sum of Squares
df
Mean Square
F
Sig.
1
Regression
12099.787
4
3024.947
37.176
0.000 (a)
Residual
4393.898
54
81.368
Total
16493.685
58
a Predictors: (Constant), Summonses Issued, Sanitation Dept. Field Employees, Population Density, Poverty Status
b Dependent Variable: % of Streets Rated Clean

Coefficients (a)
Model
Unstandardized Coefficients
Standardized Coefficients
t
Sig.
B
Std. Error
Beta
1
(Constant)
79.629
5.306
15.008
0.000
Poverty Status
-18.370
3.117
-0.478
-5.893
0.000
Sanitation Dept. Field Employees
0.03302
0.041
0.063
0.802
0.426
Population Density
-0.133
0.036
-0.303
-3.718
0.000
Summonses Issued
-0.003108
0.001
-0.341
-4.023
0.000
a Dependent Variable: % of Streets Rated Clean

Added by Jennifer B.

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