Results: lynch.sas

Hovland and Sears Lynching data

The CORR Procedure

The Corr Procedure

Variables Information


6 Variables:	year cotton1 cotton2 Blynch Totlynch olynch

Simple Statistics


Simple Statistics
Variable	N	Mean	Std Dev	Sum	Minimum	Maximum	Label
year	49	1906	14.28869	93394	1882	1930
cotton1	49	22.54735	10.99082	1105	10.94000	62.00000	Per-acre value of cotton
cotton2	49	706.34694	473.98684	34611	251.00000	2020	Farm value of cotton
Blynch	49	69.10204	35.24098	3386	7.00000	155.00000	Negro lynchings
Totlynch	49	97.16327	59.55017	4761	10.00000	255.00000	Total lynchings
olynch	49	28.06122	34.90249	1375	0	158.00000	Non-Black lynchings

Pearson Correlations


Pearson Correlation Coefficients, N = 49 Prob > \|r\| under H0: Rho=0
	year	cotton1	cotton2	Blynch	Totlynch	olynch
year	1.00000	0.66746 <.0001	0.81944 <.0001	-0.66545 <.0001	-0.86563 <.0001	-0.80503 <.0001
cotton1 Per-acre value of cotton	0.66746 <.0001	1.00000	0.95829 <.0001	-0.52214 0.0001	-0.60074 <.0001	-0.49777 0.0003
cotton2 Farm value of cotton	0.81944 <.0001	0.95829 <.0001	1.00000	-0.63590 <.0001	-0.73750 <.0001	-0.61625 <.0001
Blynch Negro lynchings	-0.66545 <.0001	-0.52214 0.0001	-0.63590 <.0001	1.00000	0.85056 <.0001	0.44151 0.0015
Totlynch Total lynchings	-0.86563 <.0001	-0.60074 <.0001	-0.73750 <.0001	0.85056 <.0001	1.00000	0.84738 <.0001
olynch Non-Black lynchings	-0.80503 <.0001	-0.49777 0.0003	-0.61625 <.0001	0.44151 0.0015	0.84738 <.0001	1.00000

Hovland and Sears Lynching data

Naive regression

The REG Procedure

Model: MODEL1

Dependent Variable: Blynch Negro lynchings

The Reg Procedure

MODEL1

Fit

Blynch

Number of Observations


Number of Observations Read	49
Number of Observations Used	49

Analysis of Variance


Analysis of Variance
Source	DF	Sum of Squares	Mean Square	F Value	Pr > F
Model	1	16252	16252	17.62	0.0001
Error	47	43360	922.56301
Corrected Total	48	59612

Fit Statistics


Root MSE	30.37372	R-Square	0.2726
Dependent Mean	69.10204	Adj R-Sq	0.2572
Coeff Var	43.95488

Parameter Estimates


Parameter Estimates
Variable	Label	DF	Parameter Estimate	Standard Error	t Value	Pr > \|t\|
Intercept	Intercept	1	106.85043	9.98579	10.70	<.0001
cotton1	Per-acre value of cotton	1	-1.67418	0.39888	-4.20	0.0001

Hovland and Sears Lynching data

Naive regression, but request Durbin-Watson statistic

The REG Procedure

Model: MODEL1

Dependent Variable: Blynch Negro lynchings

The Reg Procedure

MODEL1

Fit

Blynch

Number of Observations


Number of Observations Read	49
Number of Observations Used	49

Analysis of Variance


Analysis of Variance
Source	DF	Sum of Squares	Mean Square	F Value	Pr > F
Model	2	29660	14830	22.78	<.0001
Error	46	29952	651.13433
Corrected Total	48	59612

Fit Statistics


Root MSE	25.51733	R-Square	0.4976
Dependent Mean	69.10204	Adj R-Sq	0.4757
Coeff Var	36.92703

Parameter Estimates


Parameter Estimates
Variable	Label	DF	Parameter Estimate	Standard Error	t Value	Pr > \|t\|
Intercept	Intercept	1	79.03202	10.39033	7.61	<.0001
cotton1	Per-acre value of cotton	1	3.42479	1.17256	2.92	0.0054
cotton2	Farm value of cotton	1	-0.12338	0.02719	-4.54	<.0001

Hovland and Sears Lynching data

Naive regression, but request Durbin-Watson statistic

The REG Procedure

Model: MODEL1

Dependent Variable: Blynch Negro lynchings

Miscellaneous Statistics

Blynch

Durbin Watson Statistic


Durbin-Watson D	0.549
Number of Observations	49
1st Order Autocorrelation	0.659

The SGPlot Procedure

Hovland and Sears Lynching data

Durbin-Watson test with proc autoreg

The AUTOREG Procedure

The Autoreg Procedure

Model 1

Dependent Variable


Dependent Variable	Blynch
	Negro lynchings

Hovland and Sears Lynching data

Durbin-Watson test with proc autoreg

The AUTOREG Procedure

Ordinary Least Squares Estimates

Fit Summary


Ordinary Least Squares Estimates
SSE	29952.1792	DFE	46
MSE	651.13433	Root MSE	25.51733
SBC	465.092753	AIC	459.417292
MAE	18.6215958	AICC	459.950626
MAPE	37.588333	HQC	461.570554
Durbin-Watson	0.5485	Total R-Square	0.4976

Durbin-Watson Statistics


Durbin-Watson Statistics
Order	DW	Pr < DW	Pr > DW
1	0.5485	<.0001	1.0000

NOTE: Pr<DW is the p-value for testing positive autocorrelation, and Pr>DW is the p-value for testing negative autocorrelation.

Parameter Estimates


Parameter Estimates
Variable	DF	Estimate	Standard Error	t Value	Approx Pr > \|t\|	Variable Label
Intercept	1	79.0320	10.3903	7.61	<.0001
cotton1	1	3.4248	1.1726	2.92	0.0054	Per-acre value of cotton
cotton2	1	-0.1234	0.0272	-4.54	<.0001	Farm value of cotton

Hovland and Sears Lynching data

Durbin-Watson test with proc autoreg

The AUTOREG Procedure

Fit Diagnostics Plots

Fit Diagnostics for Blynch

Hovland and Sears Lynching data

First-order autoregressive model with proc autoreg

The AUTOREG Procedure

The Autoreg Procedure

Model 1

Dependent Variable


Dependent Variable	Blynch
	Negro lynchings

Hovland and Sears Lynching data

First-order autoregressive model with proc autoreg

The AUTOREG Procedure

Ordinary Least Squares Estimates

Fit Summary


Ordinary Least Squares Estimates
SSE	29952.1792	DFE	46
MSE	651.13433	Root MSE	25.51733
SBC	465.092753	AIC	459.417292
MAE	18.6215958	AICC	459.950626
MAPE	37.588333	HQC	461.570554
Durbin-Watson	0.5485	Total R-Square	0.4976

Parameter Estimates


Parameter Estimates
Variable	DF	Estimate	Standard Error	t Value	Approx Pr > \|t\|	Variable Label
Intercept	1	79.0320	10.3903	7.61	<.0001
cotton1	1	3.4248	1.1726	2.92	0.0054	Per-acre value of cotton
cotton2	1	-0.1234	0.0272	-4.54	<.0001	Farm value of cotton

Test BOTH


Test BOTH
Source	DF	Mean Square	F Value	Pr > F
Numerator	2	14830	22.78	<.0001
Denominator	46	651.134331

Autoregressive Error Analysis

Estimates of Autocorrelations

Preliminary MSE


Preliminary MSE	345.5

Estimates of Autoregressive Parameters


Estimates of Autoregressive Parameters
Lag	Coefficient	Standard Error	t Value
1	-0.659323	0.112081	-5.88

Final Model Estimation

Convergence Status


Algorithm converged.

Hovland and Sears Lynching data

First-order autoregressive model with proc autoreg

The AUTOREG Procedure

Fit Summary


Maximum Likelihood Estimates
SSE	12851.2228	DFE	45
MSE	285.58273	Root MSE	16.89919
SBC	428.790325	AIC	421.223044
MAE	11.8879272	AICC	422.132135
MAPE	21.9010442	HQC	424.09406
Log Likelihood	-206.61152	Transformed Regression R-Square	0.0450
Durbin-Watson	1.9913	Total R-Square	0.7844
		Observations	49

Parameter Estimates


Parameter Estimates
Variable	DF	Estimate	Standard Error	t Value	Approx Pr > \|t\|	Variable Label
Intercept	1	62.0293	16.5484	3.75	0.0005
cotton1	1	1.5055	1.1485	1.31	0.1966	Per-acre value of cotton
cotton2	1	-0.0477	0.0332	-1.44	0.1580	Farm value of cotton
AR1	1	-0.8477	0.0800	-10.59	<.0001

Test BOTH


Test BOTH
Source	DF	Mean Square	F Value	Pr > F
Numerator	2	297.852513	1.04	0.3608
Denominator	45	285.582729

Parameter Estimates with AR Parameters Assumed Given


Autoregressive parameters assumed given
Variable	DF	Estimate	Standard Error	t Value	Approx Pr > \|t\|	Variable Label
Intercept	1	62.0293	16.3826	3.79	0.0005
cotton1	1	1.5055	1.1439	1.32	0.1948	Per-acre value of cotton
cotton2	1	-0.0477	0.0330	-1.45	0.1551	Farm value of cotton

Hovland and Sears Lynching data

First-order autoregressive model with proc autoreg

The AUTOREG Procedure

Fit Diagnostics Plots

Fit Diagnostics for Blynch

Hovland and Sears Lynching data

Sixth-order autoregressive model with cotton1 and cotton2

The AUTOREG Procedure

The Autoreg Procedure

Model 1

Dependent Variable


Dependent Variable	Blynch
	Negro lynchings

Hovland and Sears Lynching data

Sixth-order autoregressive model with cotton1 and cotton2

The AUTOREG Procedure

Ordinary Least Squares Estimates

Fit Summary


Ordinary Least Squares Estimates
SSE	29952.1792	DFE	46
MSE	651.13433	Root MSE	25.51733
SBC	465.092753	AIC	459.417292
MAE	18.6215958	AICC	459.950626
MAPE	37.588333	HQC	461.570554
Durbin-Watson	0.5485	Total R-Square	0.4976

Parameter Estimates


Parameter Estimates
Variable	DF	Estimate	Standard Error	t Value	Approx Pr > \|t\|	Variable Label
Intercept	1	79.0320	10.3903	7.61	<.0001
cotton1	1	3.4248	1.1726	2.92	0.0054	Per-acre value of cotton
cotton2	1	-0.1234	0.0272	-4.54	<.0001	Farm value of cotton

Test BOTH


Test BOTH
Source	DF	Mean Square	F Value	Pr > F
Numerator	2	14830	22.78	<.0001
Denominator	46	651.134331

Autoregressive Error Analysis

Autocorrelations


Estimates of Autocorrelations
Lag	Covariance	Correlation	-1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1
0	611.3	1.000000	\| \|********************\|
1	403.0	0.659323	\| \|************* \|
2	243.5	0.398384	\| \|******** \|
3	150.4	0.245970	\| \|***** \|
4	71.3292	0.116690	\| \|** \|
5	29.9049	0.048923	\| \|* \|
6	42.4207	0.069398	\| \|* \|

Estimates of Autocorrelations

Preliminary MSE


Preliminary MSE	339.7

Estimates of Autoregressive Parameters


Estimates of Autoregressive Parameters
Lag	Coefficient	Standard Error	t Value
1	-0.703467	0.157441	-4.47
2	0.074086	0.192562	0.38
3	-0.056168	0.192657	-0.29
4	0.063519	0.192657	0.33
5	0.056217	0.192562	0.29
6	-0.092181	0.157441	-0.59

Final Model Estimation

Convergence Status


Algorithm converged.

Hovland and Sears Lynching data

Sixth-order autoregressive model with cotton1 and cotton2

The AUTOREG Procedure

Fit Summary


Maximum Likelihood Estimates
SSE	12320.2193	DFE	40
MSE	308.00548	Root MSE	17.55008
SBC	446.386252	AIC	429.359869
MAE	11.4603716	AICC	433.975254
MAPE	21.1354075	HQC	435.819655
Log Likelihood	-205.67993	Transformed Regression R-Square	0.0425
Durbin-Watson	1.9423	Total R-Square	0.7933
		Observations	49

Parameter Estimates


Parameter Estimates
Variable	DF	Estimate	Standard Error	t Value	Approx Pr > \|t\|	Variable Label
Intercept	1	61.0118	19.8858	3.07	0.0039
cotton1	1	1.2995	1.1697	1.11	0.2732	Per-acre value of cotton
cotton2	1	-0.0435	0.0345	-1.26	0.2144	Farm value of cotton
AR1	1	-0.8340	0.1583	-5.27	<.0001
AR2	1	0.0519	0.2059	0.25	0.8021
AR3	1	-0.1594	0.2065	-0.77	0.4448
AR4	1	0.0780	0.2056	0.38	0.7064
AR5	1	0.1147	0.2072	0.55	0.5828
AR6	1	-0.1294	0.1602	-0.81	0.4239

Test BOTH


Test BOTH
Source	DF	Mean Square	F Value	Pr > F
Numerator	2	256.087220	0.83	0.4428
Denominator	40	308.005482

Parameter Estimates with AR Parameters Assumed Given


Autoregressive parameters assumed given
Variable	DF	Estimate	Standard Error	t Value	Approx Pr > \|t\|	Variable Label
Intercept	1	61.0118	19.3018	3.16	0.0030
cotton1	1	1.2995	1.1476	1.13	0.2642	Per-acre value of cotton
cotton2	1	-0.0435	0.0335	-1.30	0.2015	Farm value of cotton

Hovland and Sears Lynching data

First-order autoregressive model with just cotton1

The AUTOREG Procedure

The Autoreg Procedure

Model 1

Dependent Variable


Dependent Variable	Blynch
	Negro lynchings

Hovland and Sears Lynching data

First-order autoregressive model with just cotton1

The AUTOREG Procedure

Ordinary Least Squares Estimates

Fit Summary


Ordinary Least Squares Estimates
SSE	43360.4613	DFE	47
MSE	922.56301	Root MSE	30.37372
SBC	479.328283	AIC	475.544642
MAE	22.5785652	AICC	475.805512
MAPE	66.4416427	HQC	476.98015
Durbin-Watson	0.4768	Total R-Square	0.2726

Parameter Estimates


Parameter Estimates
Variable	DF	Estimate	Standard Error	t Value	Approx Pr > \|t\|	Variable Label
Intercept	1	106.8504	9.9858	10.70	<.0001
cotton1	1	-1.6742	0.3989	-4.20	0.0001	Per-acre value of cotton

Autoregressive Error Analysis

Estimates of Autocorrelations

Preliminary MSE


Preliminary MSE	438.2

Estimates of Autoregressive Parameters


Estimates of Autoregressive Parameters
Lag	Coefficient	Standard Error	t Value
1	-0.710513	0.103753	-6.85

Final Model Estimation

Convergence Status


Algorithm converged.

Hovland and Sears Lynching data

First-order autoregressive model with just cotton1

The AUTOREG Procedure

Fit Summary


Maximum Likelihood Estimates
SSE	13305.1176	DFE	46
MSE	289.24169	Root MSE	17.00711
SBC	426.841702	AIC	421.166241
MAE	12.2923217	AICC	421.699574
MAPE	24.4269583	HQC	423.319503
Log Likelihood	-207.58312	Transformed Regression R-Square	0.0001
Durbin-Watson	2.0084	Total R-Square	0.7768
		Observations	49

Parameter Estimates


Parameter Estimates
Variable	DF	Estimate	Standard Error	t Value	Approx Pr > \|t\|	Variable Label
Intercept	1	61.4594	20.0259	3.07	0.0036
cotton1	1	-0.0229	0.3657	-0.06	0.9504	Per-acre value of cotton
AR1	1	-0.8827	0.0699	-12.62	<.0001

Parameter Estimates with AR Parameters Assumed Given


Autoregressive parameters assumed given
Variable	DF	Estimate	Standard Error	t Value	Approx Pr > \|t\|	Variable Label
Intercept	1	61.4594	19.7074	3.12	0.0031
cotton1	1	-0.0229	0.3655	-0.06	0.9504	Per-acre value of cotton

Hovland and Sears Lynching data

First-order autoregressive model with just cotton1

The AUTOREG Procedure

Fit Diagnostics Plots

Fit Diagnostics for Blynch