Results: Lynch1.sas

The SGPLOT Procedure

The SGPlot Procedure

Hovland and Sears Lynching data

Lynchings and Cotton Prices over Time

The MEANS Procedure

Summary statistics

Variable	Label	N	Mean	Std Dev	Minimum	Maximum
Ayres Cotton1 Cotton2 Blynch Totlynch olynch	Ayres' composite economic index Per-acre value of cotton Farm value of cotton Negro lynchings Total lynchings Non-Black lynchings	48 48 48 48 48 48	0.6020833 22.6325000 714.6041667 69.5208333 96.8125000 27.2916667	7.5534264 11.0907833 475.4278136 35.4904779 60.1291717 34.8491939	-23.9000000 10.9400000 251.0000000 7.0000000 10.0000000 0	13.7000000 62.0000000 2020.00 155.0000000 255.0000000 158.0000000

Hovland and Sears Lynching data

Lynchings and Cotton Prices over Time

The CORR Procedure

Variables Information

7 Variables:	Year Ayres Cotton1 Cotton2 Blynch Totlynch olynch

Simple Statistics

Simple Statistics
Variable	N	Mean	Std Dev	Sum	Minimum	Maximum	Label
Year	48	1907	14.00000	91512	1883	1930
Ayres	48	0.60208	7.55343	28.90000	-23.90000	13.70000	Ayres' composite economic index
Cotton1	48	22.63250	11.09078	1086	10.94000	62.00000	Per-acre value of cotton
Cotton2	48	714.60417	475.42781	34301	251.00000	2020	Farm value of cotton
Blynch	48	69.52083	35.49048	3337	7.00000	155.00000	Negro lynchings
Totlynch	48	96.81250	60.12917	4647	10.00000	255.00000	Total lynchings
olynch	48	27.29167	34.84919	1310	0	158.00000	Non-Black lynchings

Pearson Correlations

Pearson Correlation Coefficients, N = 48 Prob > \|r\| under H0: Rho=0
	Year	Ayres	Cotton1	Cotton2	Blynch	Totlynch	olynch
Year	1.00000	0.03896 0.7926	0.67572 <.0001	0.82050 <.0001	-0.70983 <.0001	-0.88317 <.0001	-0.80093 <.0001
Ayres Ayres' composite economic index	0.03896 0.7926	1.00000	0.28021 0.0537	0.26851 0.0650	-0.15649 0.2881	-0.18221 0.2151	-0.15502 0.2928
Cotton1 Per-acre value of cotton	0.67572 <.0001	0.28021 0.0537	1.00000	0.96025 <.0001	-0.52926 0.0001	-0.59990 <.0001	-0.49607 0.0003
Cotton2 Farm value of cotton	0.82050 <.0001	0.26851 0.0650	0.96025 <.0001	1.00000	-0.65317 <.0001	-0.73861 <.0001	-0.60922 <.0001
Blynch Negro lynchings	-0.70983 <.0001	-0.15649 0.2881	-0.52926 0.0001	-0.65317 <.0001	1.00000	0.85769 <.0001	0.46146 0.0010
Totlynch Total lynchings	-0.88317 <.0001	-0.18221 0.2151	-0.59990 <.0001	-0.73861 <.0001	0.85769 <.0001	1.00000	0.85194 <.0001
olynch Non-Black lynchings	-0.80093 <.0001	-0.15502 0.2928	-0.49607 0.0003	-0.60922 <.0001	0.46146 0.0010	0.85194 <.0001	1.00000

Hovland and Sears Lynching data

Naive regression, but request Durbin-Watson statistic

Lower Durbin-Watson critical value = 1.5

The REG Procedure

Model: MODEL1

Dependent Variable: Totlynch Total lynchings

The REG Procedure

MODEL1

Fit

Totlynch

Number of Observations

Number of Observations Read	48
Number of Observations Used	48

Analysis of Variance

Analysis of Variance
Source	DF	Sum of Squares	Mean Square	F Value	Pr > F
Model	2	132644	66322	80.04	<.0001
Error	45	37286	828.57106
Corrected Total	47	169929

Fit Statistics

Root MSE	28.78491	R-Square	0.7806
Dependent Mean	96.81250	Adj R-Sq	0.7708
Coeff Var	29.73264

Parameter Estimates

Parameter Estimates
Variable	Label	DF	Parameter Estimate	Standard Error	t Value	Pr > \|t\|
Intercept	Intercept	1	7045.12587	991.20413	7.11	<.0001
Year		1	-3.64251	0.52464	-6.94	<.0001
Cotton2	Farm value of cotton	1	-0.00541	0.01545	-0.35	0.7280

Hovland and Sears Lynching data

Naive regression, but request Durbin-Watson statistic

Lower Durbin-Watson critical value = 1.5

The REG Procedure

Model: MODEL1

Dependent Variable: Totlynch Total lynchings

Miscellaneous Statistics

Totlynch

Durbin Watson Statistic

Durbin-Watson D	1.014
Number of Observations	48
1st Order Autocorrelation	0.453

Hovland and Sears Lynching data

Autocorrelations and partial autocorrelations

The ARIMA Procedure

Identification 1

Descriptive Statistics

Name of Variable = epsilonhat
Mean of Working Series	4.66E-14
Standard Deviation	27.87087
Number of Observations	48

Autocorrelation Check for White Noise

Autocorrelation Check for White Noise
To Lag	Chi-Square	DF	Pr > ChiSq	Autocorrelations
6	19.58	6	0.0033	0.453	0.201	0.224	0.021	-0.149	-0.231
12	27.20	12	0.0072	-0.096	-0.072	-0.160	-0.164	-0.153	-0.172

Series Correlation Panel

Trend and Correlation Analysis for epsilonhat

Hovland and Sears Lynching data

Fit AR(1) with proc mixed

The Mixed Procedure

The MIXED Procedure

Model Information

Model Information
Data Set	WORK.DIXIE
Dependent Variable	Totlynch
Covariance Structure	Autoregressive
Subject Effect	one
Estimation Method	REML
Residual Variance Method	Profile
Fixed Effects SE Method	Model-Based
Degrees of Freedom Method	Between-Within

Dimensions

Dimensions
Covariance Parameters	2
Columns in X	3
Columns in Z	0
Subjects	1
Max Obs per Subject	48

Number of Observations

Number of Observations
Number of Observations Read	48
Number of Observations Used	48
Number of Observations Not Used	0

Iteration History

Iteration History
Iteration	Evaluations	-2 Res Log Like	Criterion
0	1	458.15063689
1	2	443.76191861	0.00000009
2	1	443.76190247	0.00000000

Convergence Status

Convergence criteria met.

Covariance Parameter Estimates

Covariance Parameter Estimates
Cov Parm	Subject	Estimate
AR(1)	one	0.5615
Residual		941.90

Fit Statistics

Fit Statistics
-2 Res Log Likelihood	443.8
AIC (Smaller is Better)	447.8
AICC (Smaller is Better)	448.0
BIC (Smaller is Better)	451.4

Null Model Likelihood Ratio Test

Null Model Likelihood Ratio Test
DF	Chi-Square	Pr > ChiSq
1	14.39	0.0001

Solution for Fixed Effects

Solution for Fixed Effects
Effect	Estimate	Standard Error	DF	t Value	Pr > \|t\|
Intercept	6525.64	1323.55	0	4.93	.
Year	-3.3695	0.6979	45	-4.83	<.0001
Cotton2	-0.00854	0.01669	45	-0.51	0.6114

Type 3 Tests of Fixed Effects

Type 3 Tests of Fixed Effects
Effect	Num DF	Den DF	F Value	Pr > F
Year	1	45	23.31	<.0001
Cotton2	1	45	0.26	0.6114

Hovland and Sears Lynching data

Reduced model is AR(1)

The Mixed Procedure

The MIXED Procedure

Model Information

Model Information
Data Set	WORK.DIXIE
Dependent Variable	Totlynch
Covariance Structure	Autoregressive
Subject Effect	one
Estimation Method	ML
Residual Variance Method	Profile
Fixed Effects SE Method	Model-Based
Degrees of Freedom Method	Between-Within

Dimensions

Dimensions
Covariance Parameters	2
Columns in X	3
Columns in Z	0
Subjects	1
Max Obs per Subject	48

Number of Observations

Number of Observations
Number of Observations Read	48
Number of Observations Used	48
Number of Observations Not Used	0

Iteration History

Iteration History
Iteration	Evaluations	-2 Log Like	Criterion
0	1	455.66597488
1	2	443.68131815	0.00000000

Convergence Status

Convergence criteria met.

Covariance Parameter Estimates

Covariance Parameter Estimates
Cov Parm	Subject	Estimate
AR(1)	one	0.4858
Residual		787.66

Fit Statistics

Fit Statistics
-2 Log Likelihood	443.7
AIC (Smaller is Better)	453.7
AICC (Smaller is Better)	455.1
BIC (Smaller is Better)	463.0

Null Model Likelihood Ratio Test

Null Model Likelihood Ratio Test
DF	Chi-Square	Pr > ChiSq
1	11.98	0.0005

Solution for Fixed Effects

Solution for Fixed Effects
Effect	Estimate	Standard Error	DF	t Value	Pr > \|t\|
Intercept	6619.93	1181.69	0	5.60	.
Year	-3.4188	0.6237	45	-5.48	<.0001
Cotton2	-0.00837	0.01595	45	-0.52	0.6024

Type 3 Tests of Fixed Effects

Type 3 Tests of Fixed Effects
Effect	Num DF	Den DF	F Value	Pr > F
Year	1	45	30.05	<.0001
Cotton2	1	45	0.28	0.6024

Hovland and Sears Lynching data

Full model is Autoregressive Moving Average: ARMA(1,1)

The Mixed Procedure

The MIXED Procedure

Model Information

Model Information
Data Set	WORK.DIXIE
Dependent Variable	Totlynch
Covariance Structure	Autoregressive Moving Average
Subject Effect	one
Estimation Method	ML
Residual Variance Method	Profile
Fixed Effects SE Method	Model-Based
Degrees of Freedom Method	Between-Within

Dimensions

Dimensions
Covariance Parameters	3
Columns in X	3
Columns in Z	0
Subjects	1
Max Obs per Subject	48

Number of Observations

Number of Observations
Number of Observations Read	48
Number of Observations Used	48
Number of Observations Not Used	0

Iteration History

Iteration History
Iteration	Evaluations	-2 Log Like	Criterion
0	1	455.66597488
1	2	441.53825241	0.00021139
2	1	441.50228689	0.00000202
3	1	441.50192160	0.00000000

Convergence Status

Convergence criteria met.

Covariance Parameter Estimates

Covariance Parameter Estimates
Cov Parm	Subject	Estimate
Rho	one	-0.1016
Gamma	one	0.4205
Residual		799.64

Fit Statistics

Fit Statistics
-2 Log Likelihood	441.5
AIC (Smaller is Better)	453.5
AICC (Smaller is Better)	455.6
BIC (Smaller is Better)	464.7

Null Model Likelihood Ratio Test

Null Model Likelihood Ratio Test
DF	Chi-Square	Pr > ChiSq
2	14.16	0.0008

Solution for Fixed Effects

Solution for Fixed Effects
Effect	Estimate	Standard Error	DF	t Value	Pr > \|t\|
Intercept	6715.57	1071.90	0	6.27	.
Year	-3.4690	0.5665	45	-6.12	<.0001
Cotton2	-0.00796	0.01568	45	-0.51	0.6142

Type 3 Tests of Fixed Effects

Type 3 Tests of Fixed Effects
Effect	Num DF	Den DF	F Value	Pr > F
Year	1	45	37.50	<.0001
Cotton2	1	45	0.26	0.6142

Hovland and Sears Lynching data

Difference between -2 Log Likelihood values is chi-squared

The IML Procedure

Chisquare_df_pvalue

Chisquare	df	pvalue
2.2	1	0.1380107