> #let's do the hsb ancova
> hsbancdat = read.table(file="D:\\drr09\\stat209\\hsbancova", header = T)
> summary(hsbancdat)
     school       Intercept        csesslp       sector    meanses         
> attach(hsbancdat)
> tapply(Intercept, sector, summary)
$C   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
   7.336  13.200  14.470  14.200  15.900  19.720 
$P  Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
   4.240   9.719  11.710  11.390  13.200  18.110 
> tapply(csesslp, sector, summary)
$C    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  -2.0150  0.5698  1.5230  1.4680  2.4600  5.2580 
$P   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  -1.014   1.695   2.922   2.772   3.824   6.266 

> #initial differences on covariate?
> tapply(meanses, sector, summary)
$C   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
-0.7619 -0.1039  0.2388  0.1601  0.4346  0.8250 
$P   Min.  1st Qu.   Median     Mean  3rd Qu.     Max. 
-1.19400 -0.40090 -0.09058 -0.13550  0.11370  0.68200 
> #Cath higher on school-level SES

> # do the ancova on school-level outcomes (level, slope)
> hsbancdat$gr = 2 - as.numeric(sector) # code Cath = 1, Pub = 0 on sector
> intancova = lm(Intercept ~ gr + meanses)
> summary(intancova)
Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  12.1195     0.2026  59.807  < 2e-16 ***
gr            1.2219     0.3169   3.855 0.000168 ***
meanses       5.3874     0.3810  14.140  < 2e-16 ***
---
Residual standard error: 1.859 on 157 degrees of freedom
Multiple R-squared: 0.6489,     Adjusted R-squared: 0.6444 
F-statistic: 145.1 on 2 and 157 DF,  p-value: < 2.2e-16 

> # compare with hlm/lme coeffs gr vs 1.226 (.306) df 157 t = 4.00
> # compare with hlm/lme coeffs meanses vs 5.33 (.369) df 157 t = 14.4

> slpancova = lm(csesslp ~ gr + meanses)
> summary(slpancova)
Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)   2.8886     0.1600  18.049  < 2e-16 ***
gr           -1.5580     0.2503  -6.224 4.22e-09 ***
meanses       0.8612     0.3009   2.862  0.00478 ** 
---
Residual standard error: 1.468 on 157 degrees of freedom
Multiple R-squared: 0.1999,     Adjusted R-squared: 0.1897 
F-statistic: 19.61 on 2 and 157 DF,  p-value: 2.492e-08 

> # compare with hlm/lme coeffs gr vs -1.64 (.239) t = -6.85
> # compare with hlm/lme coeffs meanses vs 1.03 (.299) df 157 t = 3.48

> # look at comparing regressions; neither outcome refutes parallel regressions
> intcnrl = lm(Intercept ~ gr + meanses + I(gr*meanses))
Coefficients:
                Estimate Std. Error t value Pr(>|t|)    
(Intercept)      12.1825     0.2075  58.714  < 2e-16 ***
gr                1.2487     0.3168   3.942 0.000122 ***
meanses           5.8524     0.5139  11.388  < 2e-16 ***
I(gr * meanses)  -1.0261     0.7634  -1.344 0.180855    
---
> slpcnrl = lm(csesslp ~ gr + meanses + I(gr*meanses))
Coefficients:
                Estimate Std. Error t value Pr(>|t|)    
(Intercept)       2.9122     0.1646  17.692  < 2e-16 ***
gr               -1.5480     0.2513  -6.160 5.92e-09 ***
meanses           1.0351     0.4077   2.539   0.0121 *  
I(gr * meanses)  -0.3837     0.6056  -0.634   0.5272    
---