Question

In models B through D, what seems to be the relationship between the burglary rate and the percent of the 18-64 population who are young adults (18-24)?

Select one:

a. It is difficult to describe the relationship; the young adult variables were all significant at 5% in models B, C, and D, but the signs and sizes of the coefficients were very different between models.

b. Conclusions about the relationship between young adults and the burglary rate are difficult to draw since the unemployment rate variable is consistently positive and significant, which reduces the reliability of the estimates for the young adult variables.

c. The burglary rate seems to increase as the proportion of young adults increases (models B, C, and D), though the effect is only significant (at the 10% level) for young adult males (model C).

d. We can be confident that the relationship between the burglary rate and proportion of young adults is negative, given the signs of the young adult coefficients in all models and the high adjusted R-square values.

MODULE B

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.428911
R Square	0.183965
Adjusted R Square	0.147696
Standard Error	185.2789
Observations	48
ANOVA
	df	SS	MS	F	Significance F
Regression	2	348248.8263	174124.4	5.072335	0.010315
Residual	45	1544771.532	34328.26
Total	47	1893020.358
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	-480.503	498.0290621	-0.96481	0.339797	-1483.58	522.5791	-1483.58	522.5791
%Unemploy	60.64388	19.15148576	3.166537	0.002769	22.07081	99.21696	22.07081	99.21696
%young	4186.85	2696.892719	1.552472	0.127555	-1244.97	9618.671	-1244.97	9618.671

MODULE C

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.444877
R Square	0.197916
Adjusted R Square	0.162267
Standard Error	183.6883
Observations	48
ANOVA
	df	SS	MS	F	Significance F
Regression	2	374658.3	187329.2	5.551912	0.006998
Residual	45	1518362	33741.38
Total	47	1893020
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	-603.329	499.929	-1.20683	0.233803	-1610.24	403.5793	-1610.24	403.5793
%Unemploy	61.16653	18.73611	3.264634	0.002098	23.43007	98.90299	23.43007	98.90299
%youngmale	4794.899	2665.975	1.798553	0.078799	-574.651	10164.45	-574.651	10164.45

MODULE D

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.413764
R Square	0.1712
Adjusted R Square	0.134365
Standard Error	186.7223
Observations	48
ANOVA
	df	SS	MS	F	Significance F
Regression	2	324085.9	162042.9	4.647697	0.014626
Residual	45	1568934	34865.21
Total	47	1893020
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	-338.182	484.4083	-0.69813	0.488686	-1313.83	637.4666	-1313.83	637.4666
%Unemploy	59.26618	19.44323	3.048165	0.003847	20.1055	98.42685	20.1055	98.42685
%youngfemale	3454.179	2664.948	1.296153	0.201531	-1913.3	8821.659	-1913.3	8821.659

Answer 1

Option C is correct

The burglary rate seems to increase as the proportion of young adults increases (models B, C, and D), though the effect is only significant (at the 10% level) for young adult males (model C).

Explanation: The coefficient for % yound adult and P-values for each model are,

	Coefficient for %young adult	P-value		Significance level = 0.10	Significance
Model B	4186.85	0.127555	>	0.1	Not Significant
Model C	4794.899	0.078799	<	0.1	Significant
Model D	3454.179	0.201531	>	0.1	Not Significant

The only coefficient for % young male adult is significant at 10 % significant level

All the coefficients are positive hence burglary will increase for increase in % young adult.