crime.sav (3.91 KB)
outlierCheck.sps (2.53 KB)

get file = "DirectoryOfYourComputer\crime.sav".

descriptives
  /var=crime murder pctmetro pctwhite pcths poverty single.

		Descriptive Statistics
			N	Minimum	Maximum	Mean	Std. Deviation
violent crime rate	51	82	2922	612.84	441.100
murder rate		51	1.60	78.50	8.7275	10.71758
pct metropolitan	51	24.00	100.00	67.3902	21.95713
pct white		51	31.80	98.50	84.1157	13.25839
pct hs graduates	51	64.30	86.60	76.2235	5.59209
pct poverty		51	8.00	26.40	14.2588	4.58424
pct single parent	51	8.40	22.10	11.3255	2.12149
Valid N (listwise)	51				

graph
  /scatterplot(matrix)=crime murder pctmetro pctwhite pcths poverty single .

scatterplot for all variables [JPG image (141.43 KB)]

GRAPH /SCATTERPLOT(BIVAR)=pctmetro WITH crime BY state(name) .

scatterplot of pcmetro by crime by state [JPG image (24.93 KB)]

GRAPH /SCATTERPLOT(BIVAR)=poverty WITH crime BY state(name) .

scatterplot of poverty by state [JPG image (23.89 KB)]

GRAPH /SCATTERPLOT(BIVAR)=single WITH crime BY state(name) .

scatterplot of single by state [JPG image (26.6 KB)]

regression
  /dependent crime
  /method=enter pctmetro poverty single.

		Model Summary
Model	R	R Square	Adjusted R Square	Std. Error of the Estimate
1	.916a	.840	.830	182.068
a. Predictors: (Constant), pct single parent, pct metropolitan, pct poverty

			ANOVA(b)
Model			Sum of Squares	df	Mean Square	F	Sig.
1	Regression	8170480.211	3	2723493.404	82.160	.000a
	Residual	1557994.534	47	33148.820		
	Total		9728474.745	50			
a. Predictors: (Constant), pct single parent, pct metropolitan, pct poverty
b. Dependent Variable: violent crime rate

			Coefficients(a)
		Unstandardized Coefficients		Standardized Coefficients
Model				B		Std. Error	Beta	t	Sig.
1	(Constant)		-1666.436	147.852			-11.271	.000
	pct metropolitan	7.829		1.255		.390	6.240	.000
	pct poverty		17.680		6.941		.184	2.547	.014
	pct single parent	132.408		15.503		.637	8.541	.000
a. Dependent Variable: violent crime rate

regression
  /dependent crime
  /method=enter pctmetro poverty single
  /residuals=histogram.

		Model Summary(b)
Model	R	R Square	Adjusted R Square	Std. Error of the Estimate
1	.916a	.840	.830	182.068
a. Predictors: (Constant), pct single parent, pct metropolitan, pct poverty
b. Dependent Variable: violent crime rate

			ANOVA(b)
Model			Sum of Squares	df	Mean Square	F	Sig.
1	Regression	8170480.211	3	2723493.404	82.160	.000a
	Residual	1557994.534	47	33148.820		
	Total		9728474.745	50			
a. Predictors: (Constant), pct single parent, pct metropolitan, pct poverty
b. Dependent Variable: violent crime rate

			Coefficients(a)
		Unstandardized Coefficients		Standardized Coefficients
Model				B		Std. Error	Beta	t	Sig.
1	(Constant)		-1666.436	147.852		-11.271	.000
	pct metropolitan	7.829		1.255		.390	6.240	.000
	pct poverty		17.680		6.941		.184	2.547	.014
	pct single parent	132.408		15.503		.637	8.541	.000
a. Dependent Variable: violent crime rate

		Residuals Statistics(a)
			Minimum		Maximum		Mean	Std.Deviation	N
Predicted Value	-30.51		2509.43		612.84	404.240		51
Residual		-523.013	426.111		.000	176.522		51
Std. Predicted Value	-1.592		4.692		.000	1.000		51
Std. Residual		-2.873		2.340		.000	.970		51
a. Dependent Variable: violent crime rate

histogram [JPG image (26.38 KB)]

regression
  /dependent crime
  /method=enter pctmetro poverty single
  /residuals=histogram(sdresid).

histogram sdresid [JPG image (25.2 KB)]

regression
  /dependent crime
  /method=enter pctmetro poverty single
  /residuals=histogram(sdresid) id(state) outliers(sdresid).

		Residuals Statistics(a)
					Minimum		Maximum		Mean	Std. Deviation	N
Predicted Value				-30.51		2509.43		612.84	404.240		51
Std. Predicted Value			-1.592		4.692		.000	1.000		51
Standard Error of Predicted Value	25.788		133.343		47.561	18.563		51
Adjusted Predicted Value		-39.26		2032.11		605.66	369.075		51
Residual				-523.013	426.111		.000	176.522		51
Std. Residual				-2.873		2.340		.000	.970		51
Stud. Residual				-3.194		3.328		.015	1.072		51
Deleted Residual			-646.503	889.885		7.183	223.668		51
Stud. Deleted Residual		-3.571		3.766		.018	1.133		51
Mahal. Distance			.023		25.839		2.941	4.014		51
Cook's Distance			.000		3.203		.089	.454		51
Centered Leverage Value		.000		.517		.059	.080		51
a. Dependent Variable: violent crime rate

regression
  /dependent crime
  /method=enter pctmetro poverty single
  /residuals=histogram(sdresid) id(state) outliers(sdresid)
  /casewise=plot(sdresid) outliers(2)  .

		Casewise Diagnostics(a)
Case Number	state	Stud. Deleted 	violent crime 	Predicted 	Residual
			Residual	rate		Value
9		fl	2.620		1206		779.89		426.111
25		ms	-3.571		434		957.01		-523.013
51		dc	3.766		2922		2509.43		412.566
a. Dependent Variable: violent crime rate

regression
  /dependent crime
  /method=enter pctmetro poverty single
  /residuals=histogram(sdresid lever) id(state) outliers(sdresid lever)
  /casewise=plot(sdresid) outliers(2).

		Outlier Statistics(a)
				Case 	state	Statistic
				Number
Stud. Deleted Residual	1	51	dc 	3.766
			2	25	ms 	-3.571
			3	9	fl 	2.620
			4	18	la 	-1.839
			5	39	ri 	-1.686
			6	12	ia 	1.590
			7	47	wa 	-1.304
			8	13	id 	1.293
			9	14	il 	1.152
			10	35	oh 	-1.148
Centered Leverage Value	1	51	dc 	.517
			2	1	ak 	.241
			3	25	ms 	.171
			4	49	wv 	.161
			5	18	la 	.146
			6	46	vt 	.117
			7	9	fl 	.083
			8	26	mt 	.080
			9	31	nj 	.075
			10	17	ky 	.072
a. Dependent Variable: violent crime rate

histogram sdresid [JPG image (25.2 KB)]

histogram leverage [JPG image (20.5 KB)]

regression
  /dependent crime
  /method=enter pctmetro poverty single
  /residuals=histogram(sdresid lever) id(state) outliers(sdresid, lever)
  /casewise=plot(sdresid)  outliers(2)
  /scatterplot(*lever, *sdresid).

histogram sdresid [JPG image (26.07 KB)]

regression
  /dependent crime
  /method=enter pctmetro poverty single
  /residuals=histogram(sdresid lever) id(state) outliers(sdresid, lever, cook)
  /casewise=plot(sdresid)  outliers(2) cook dffit
  /scatterplot(*lever, *sdresid).

		Casewise Diagnostics(a)
Case Number	state	Stud. 		violent 	Cook's		DFFIT
			Deleted		crime		Distance	
			Residual	rate
9	fl		2.620		1206		.174		48.507
25	ms		-3.571		434		.602		-123.490
51	dc		3.766		2922		3.203		477.319
a. Dependent Variable: violent crime rate

		Outlier Statistics(a)
		Case Number	state	Statis	Sig. F
Stud.  		1	51	dc 	3.766	
Deleted		2	25	ms 	-3.571	
Residual	3	9	fl 	2.620	
		4	18	la 	-1.839	
		5	39	ri 	-1.686	
		6	12	ia 	1.590	
		7	47	wa 	-1.304	
		8	13	id 	1.293	
		9	14	il 	1.152	
		10	35	oh 	-1.148	
Cook's 		1	51	dc 	3.203	.021
Distance	2	25	ms 	.602	.663
		3	9	fl 	.174	.951
		4	18	la 	.159	.958
		5	39	ri 	.041	.997
		6	12	ia 	.041	.997
		7	13	id 	.037	.997
		8	20	md 	.020	.999
		9	6	co 	.018	.999
		10	49	wv 	.016	.999
Centered  	1	51	dc 	.517	
Leverage	2	1	ak 	.241	
Value		3	25	ms 	.171	
		4	49	wv 	.161	
		5	18	la 	.146	
		6	46	vt 	.117	
		7	9	fl 	.083	
		8	26	mt 	.080	
		9	31	nj 	.075	
		10	17	ky 	.072	
a. Dependent Variable: violent crime rate

regression
  /dependent crime
  /method=enter pctmetro poverty single
  /residuals=histogram(sdresid lever) id(state) outliers(sdresid, lever, cook)
  /casewise=plot(sdresid)  outliers(2) cook dffit
  /scatterplot(*lever, *sdresid)
  /save sdbeta(sdfb).

list
  /variables state sdfb1 sdfb2 sdfb3
  /cases from 1 to 10.

state       sdfb1       sdfb2       sdfb3

ak        -.10618     -.13134      .14518
al         .01243      .05529     -.02751
ar        -.06875      .17535     -.10526
az        -.09476     -.03088      .00124
ca         .01264      .00880     -.00364
co        -.03705      .19393     -.13846
ct        -.12016      .07446      .03017
de         .00558     -.01143      .00519
fl         .64175      .59593     -.56060
ga         .03171      .06426     -.09120


Number of cases read:  10    Number of cases listed:  10

VARIABLE LABLES sdfb1 "Sdfbeta pctmetro"
                              /sdfb2 "Sdfbeta poverty"
                              /sdfb3 "Sdfbeta single" .

GRAPH
  /SCATTERPLOT(OVERLAY)=sid sid sid  WITH sdfb1 sdfb2 sdfb3 (PAIR) BY state(name)
  /MISSING=LISTWISE .

dbfBeta value [JPG image (33.11 KB)]

Note
Measure	Value
leverage	>(2k+2)/n
abs(rstu)	> 2
Cook's D	> 4/n
abs(DFBETA)	> 2/sqrt(n)

PRED

Unstandardized predicted values.

RESID

Unstandardized residuals.

DRESID

Deleted residuals.

ADJPRED

Adjusted predicted values.

ZPRED

Standardized predicted values.

ZRESID

Standardized residuals.

SRESID

Studentized residuals.

SDRESID

Studentized deleted residuals.

SEPRED

Standard errors of the predicted values.

MAHAL

Mahalanobis distances.

COOK

Cook’s distances.

LEVER

Centered leverage values.

DFBETA

Change in the regression coefficient that results from the deletion of the ith case. A DFBETA value is computed for each case for each regression coefficient generated by a model.

SDBETA

Standardized DFBETA. An SDBETA value is computed for each case for each regression coefficient generated by a model.

DFFIT

Change in the predicted value when the ith case is deleted.

SDFIT

Standardized DFFIT.

COVRATIO

Ratio of the determinant of the covariance matrix with the ith case deleted to the determinant of the covariance matrix with all cases included.

MCIN

Lower and upper bounds for the prediction interval of the mean predicted response. A lowerbound LMCIN and an upperbound UMCIN are generated. The default confidence interval is 95%. The confidence interval can be reset with the CIN subcommand. (See Dillon & Goldstein

ICIN

Lower and upper bounds for the prediction interval for a single observation. A lowerbound LICIN and an upperbound UICIN are generated. The default confidence interval is 95%. The confidence interval can be reset with the CIN subcommand. (See Dillon & Goldstein

regression
  /dependent crime
  /method=enter pctmetro poverty single
  /residuals=histogram(sdresid lever) id(state) outliers(sdresid, lever, cook)
  /casewise=plot(sdresid)  outliers(2) cook dffit
  /scatterplot(*lever, *sdresid)
  /partialplot.  

[JPG image (28.2 KB)]

[JPG image (28.53 KB)]

[JPG image (27.35 KB)]

regression
  /dependent crime
  /method=enter pctmetro poverty single.

			Coefficients(a)
		Unstandardized Coefficients		Standardized Coefficients
Model		B	Std. Error	Beta	t	Sig.
1	(Constant)	-1666.436	147.852		-11.271	.000
	pct metropolitan	7.829	1.255	.390	6.240	.000
	pct poverty	17.680	6.941	.184	2.547	.014
	pct single parent	132.408	15.503	.637	8.541	.000
a. Dependent Variable: violent crime rate

compute filtvar = (state NE "dc").
filter by filtvar.
regression
  /dependent crime
  /method=enter pctmetro poverty single . 

			Coefficients(a)
		Unstandardized Coefficients		Standardized Coefficients
Model		B	Std. Error	Beta	t	Sig.
1	(Constant)	-1197.538	180.487		-6.635	.000
	pct metropolitan	7.712	1.109	.565	6.953	.000
	pct poverty	18.283	6.136	.265	2.980	.005
	pct single parent	89.401	17.836	.446	5.012	.000
a. Dependent Variable: violent crime rate

descriptives /var= ALL .

Descriptive Statistics
	N	Minimum	Maximum	Mean	Std. Deviation
api 2000	400	369	940	647.62	142.249
english language learners	400	0	91	31.45	24.839
avg class size k-3	398	14	25	19.16	1.369
avg parent ed	381	1.00	4.62	2.6685	.76379
pct free meals	400	0	100	60.32	31.912
Valid N (listwise)	379

graph
  /scatterplot(matrix)=api00 ell acs_k3 avg_ed meals .

[JPG image (167.94 KB)]

This graph does not give any suspicious cases.

GRAPH /SCATTERPLOT(BIVAR)=ell with api00 .
GRAPH /SCATTERPLOT(BIVAR)=acs_k3 with api00  .
GRAPH /SCATTERPLOT(BIVAR)=avg_ed with api00 .
GRAPH /SCATTERPLOT(BIVAR)=meals with api00  .

ell [JPG image (129.45 KB)]	acsk3 [JPG image (77.27 KB)]
ave_ed [JPG image (117.17 KB)]	meals [JPG image (119.43 KB)]

We speculate that the second IV (average class size) is not quite related to DV (api00). And, there seems no particular suspicious data.

REGRESSION
  /DEPENDENT api00
  /METHOD=ENTER ell acs_k3 avg_ed meals 
   /residuals=histogram(sdresid lever) id(snum) outliers(sdresid, lever, cook)
  /casewise=plot(sdresid)  outliers(2) cook dffit
  /scatterplot(*lever, *sdresid)
  /save sdbeta(sdfb) 
   /partialplot.  

Model Summary
Model	R	R Square	Adjusted R Square	Std. Error of the Estimate
1	.912a	.833	.831	58.633
a. Predictors: (Constant), pct free meals, avg class size k-3, english language learners, avg parent ed

ANOVA(b)
Model		Sum of Squares	df	Mean Square	F	Sig.
1	Regression	6393719.254	4	1598429.813	464.956	.000a
	Residual	1285740.498	374	3437.809
	Total	7679459.752	378
a. Predictors: (Constant), pct free meals, avg class size k-3, english language learners, avg parent ed
b. Dependent Variable: api 2000

Coefficients(a)
		Unstandardized Coefficients		Standardized Coefficients
Model		B	Std. Error	Beta	t	Sig.
1	(Constant)	709.639	56.240		12.618	.000
	english language learners	-.843	.196	-.147	-4.307	.000
	avg class size k-3	3.388	2.333	.032	1.452	.147
	avg parent ed	29.072	6.924	.156	4.199	.000
	pct free meals	-2.937	.195	-.655	-15.081	.000
a. Dependent Variable: api 2000

Casewise Diagnostics(a)
Case Number	school number	Stud. Deleted Residual	api 2000	Cook's Distance	DFFIT
93	1497	2.170	604	.010	1.292
97	1539	2.230	700	.006	.826
100	1515	2.222	667	.005	.661
105	1516	2.128	597	.010	1.380
135	1633	2.072	584	.044	6.085
188	1731	2.121	719	.015	2.126
203	1621	2.034	717	.006	.831
226	211	-3.241	386	.015	-1.325
227	182	-2.653	411	.005	-.581
228	167	2.903	774	.010	.987
232	210	-2.369	432	.018	-2.263
234	165	-2.734	449	.019	-1.997
252	3700	2.036	717	.013	1.878
259	3537	-2.425	694	.012	-1.436
271	3758	3.012	690	.022	2.108
272	3794	2.083	610	.010	1.400
274	3759	-2.290	585	.069	-8.646
304	4507	2.011	751	.013	1.917
327	4737	2.470	808	.012	1.447
334	4744	2.160	700	.005	.645
346	5362	-2.138	487	.010	-1.359
a. Dependent Variable: api 2000

Residuals Statistics(a)
	Minimum	Maximum	Mean	Std. Deviation	N
Predicted Value	449.17	910.04	647.64	130.056	379
Std. Predicted Value	-1.526	2.018	.000	1.000	379
Standard Error of Predicted Value	3.218	14.681	6.496	1.780	379
Adjusted Predicted Value	449.44	909.36	647.65	130.056	379
Residual	-187.020	173.697	.000	58.322	379
Std. Residual	-3.190	2.962	.000	.995	379
Stud. Residual	-3.201	2.980	.000	1.002	379
Deleted Residual	-188.345	175.805	-.016	59.138	379
Stud. Deleted Residual	-3.241	3.012	.000	1.005	379
Mahal. Distance	.141	22.702	3.989	3.030	379
Cook's Distance	.000	.069	.003	.006	379
Centered Leverage Value	.000	.060	.011	.008	379
a. Dependent Variable: api 2000

Outlier Statistics(a)
		Case Number	school number	Statistic	Sig. F
Stud. Deleted Residual	1	226	211	-3.241
	2	271	3758	3.012
	3	228	167	2.903
	4	234	165	-2.734
	5	227	182	-2.653
	6	327	4737	2.470
	7	259	3537	-2.425
	8	232	210	-2.369
	9	274	3759	-2.290
	10	97	1539	2.230
Cook's Distance	1	274	3759	.069	.997
	2	135	1633	.044	.999
	3	26	4299	.030	1.000
	4	193	1952	.025	1.000
	5	271	3758	.022	1.000
	6	234	165	.019	1.000
	7	232	210	.018	1.000
	8	200	1872	.018	1.000
	9	108	1606	.018	1.000
	10	388	4878	.017	1.000
Centered Leverage Value	1	274	3759	.060
	2	37	4308	.058
	3	209	1795	.050
	4	135	1633	.046
	5	26	4299	.040
	6	69	3000	.037
	7	372	6068	.036
	8	30	4317	.035
	9	147	1709	.035
	10	193	1952	.033
a. Dependent Variable: api 2000

sdresidual check [JPG image (29.53 KB)]

leverage check [JPG image (22.84 KB)]

"plot spred by sresid [JPG image (62.22 KB)]

REGRESSION
  /DESCRIPTIVES MEAN STDDEV CORR SIG N
  /MISSING LISTWISE
  /STATISTICS COEFF OUTS R ANOVA COLLIN TOL CHANGE ZPP
  /CRITERIA=PIN(.05) POUT(.10)
  /NOORIGIN 
  /DEPENDENT api00
  /METHOD=ENTER meals ell acs_k3 avg_ed
  /residuals=histogram(sdresid lever) id(snum) outliers(sdresid, lever, cook) Durbin
  /casewise=plot(sdresid)  outliers(2) cook dffit
  /SCATTERPLOT=(*ZRESID ,*ZPRED)
  /SAVE PRED ZPRED MAHAL COOK LEVER RESID ZRESID SDRESID DFBETA.

USE ALL.
COMPUTE filterVar=(abs(SDR)_1 < 2).
FILTER BY filterVar.
EXECUTE.

REGRESSION
  /DESCRIPTIVES MEAN STDDEV CORR SIG N
  /MISSING LISTWISE
  /STATISTICS COEFF OUTS R ANOVA CHANGE ZPP
  /CRITERIA=PIN(.05) POUT(.10)
  /NOORIGIN 
  /DEPENDENT api00
  /METHOD=ENTER ell avg_ed acs_k3 meals
  /SCATTERPLOT=(*ZRESID ,*ZPRED) .