#######################################
#
# SOME INITIAL SIMPLE LINEAR REGRESSION STUFF
#
#######################################


 > attach(prestige)
 > motif()
 > plot(income,occ.prestige)



 > myfit <- lm(occ.prestige ~ income, data=prestige)
 > summary(myfit)

Call: lm(formula = occ.prestige ~ income)
Residuals:
    Min     1Q Median    3Q   Max 
 -33.01 -8.378 -2.378 8.432 32.08

Coefficients:
              Value Std. Error t value Pr(>|t|) 
(Intercept) 27.1412  2.2677    11.9686  0.0000 
     income  0.0029  0.0003    10.2243  0.0000 

Residual standard error: 12.09 on 100 degrees of freedom
Multiple R-Squared: 0.5111 
F-statistic: 104.5 on 1 and 100 degrees of freedom, the p-value is 0 

Correlation of Coefficients:
       (Intercept) 
income -0.8493    

 > anova(myfit)
Analysis of Variance Table

Response: occ.prestige

Terms added sequentially (first to last)
           Df Sum of Sq  Mean Sq  F Value Pr(F) 
   income   1  15279.26 15279.26 104.5367     0
Residuals 100  14616.17   146.16               



 > lines(income,fitted(myfit))
Lines out of bounds X= 25879 Y= 102.1074
Lines out of bounds X= 9271 Y= 53.9974
Lines out of bounds X= 25308 Y= 100.4534
Lines out of bounds X= 14558 Y= 69.3128

 > plot(income,residuals(myfit))
 > plot(fitted(myfit),residuals(myfit))         


 > par(mfrow=c(2,3))
 > plot(myfit)
 > summary(myfit)

Call: lm(formula = occ.prestige ~ income)
Residuals:
    Min     1Q Median    3Q   Max 
 -33.01 -8.378 -2.378 8.432 32.08

Coefficients:
              Value Std. Error t value Pr(>|t|) 
(Intercept) 27.1412  2.2677    11.9686  0.0000 
     income  0.0029  0.0003    10.2243  0.0000 

Residual standard error: 12.09 on 100 degrees of freedom
Multiple R-Squared: 0.5111 
F-statistic: 104.5 on 1 and 100 degrees of freedom, the p-value is 0 

Correlation of Coefficients:
       (Intercept) 
income -0.8493    
 > q()