####################################################################

> names(prestige)
[1] "education"      "income"         "percent.female" "occ.prestige"  
[5] "occ.code"       "occ.type"      
> motif()
> pairs(prestige[,1:4])
> 

#####################################################################

> fit.ed _ lm(occ.prestige ~ education,data=prestige)
> fit.ed
Call:
lm(formula = occ.prestige ~ education, data = prestige)

Coefficients:
 (Intercept) education 
   -10.73198  5.360878

Degrees of freedom: 102 total; 100 residual
Residual standard error: 9.103291 
> 
> par(mfrow=c(2,2))
> 
> plot(prestige$education,prestige$occ.prestige)
> abline(fit.ed)
> 
> plot(fitted(fit.ed),prestige$occ.prestige)
> abline(0,1)
> 
> plot(prestige$education,residuals(fit.ed))
> abline(0,0)
> 
> plot(fitted(fit.ed),residuals(fit.ed))
> abline(0,0)
> 
> par(mfrow=c(2,3))
> plot(fit.ed)
> 

##########################################################

> fit.in _ lm(occ.prestige ~ income, data=prestige)
> fit.in
Call:
lm(formula = occ.prestige ~ income, data = prestige)

Coefficients:
 (Intercept)      income 
    27.14118 0.002896799

Degrees of freedom: 102 total; 100 residual
Residual standard error: 12.08974 
> 
> par(mfrow=c(2,2))
> 
> plot(prestige$income,prestige$occ.prestige)
> abline(fit.in)
> 
> plot(fitted(fit.in),prestige$occ.prestige)
> abline(0,1)
> 
> plot(prestige$income,residuals(fit.in))
> abline(0,0)
> 
> plot(fitted(fit.in),residuals(fit.in))
> abline(0,0)
> 
> par(mfrow=c(2,3))
> plot(fit.in)
> 

################################################################

> fit.pf _ lm(occ.prestige ~ percent.female, data=prestige)
> fit.pf
Call:
lm(formula = occ.prestige ~ percent.female, data = prestige)

Coefficients:
 (Intercept) percent.female 
      48.693    -0.06417284

Degrees of freedom: 102 total; 100 residual
Residual standard error: 17.16881 
> 
> 
> par(mfrow=c(2,2))
> 
> plot(prestige$percent.female,prestige$occ.prestige)
> abline(fit.pf)
> 
> plot(fitted(fit.pf),prestige$occ.prestige)
> abline(0,1)
> 
> plot(prestige$percent.female,residuals(fit.in))
> abline(0,0)
> 
> plot(fitted(fit.pf),residuals(fit.pf))
> abline(0,0)
> 
> par(mfrow=c(2,3))
> plot(fit.pf)
> 

#######################################################################

> summary(fit.ed)

Call: lm(formula = occ.prestige ~ education, data = prestige)
Residuals:
    Min     1Q Median    3Q   Max 
 -26.04 -6.523 0.6611 6.743 18.16

Coefficients:
               Value Std. Error  t value Pr(>|t|) 
(Intercept) -10.7320   3.6771    -2.9186   0.0043
  education   5.3609   0.3320    16.1478   0.0000

Residual standard error: 9.103 on 100 degrees of freedom
Multiple R-Squared: 0.7228 
F-statistic: 260.8 on 1 and 100 degrees of freedom, the p-value is 0 

Correlation of Coefficients:
          (Intercept) 
education -0.9695    
> 
> 
> summary(fit.in)

Call: lm(formula = occ.prestige ~ income, data = prestige)
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    
> 
> 
> summary(fit.pf)

Call: lm(formula = occ.prestige ~ percent.female, data = prestige)
Residuals:
    Min     1Q Median    3Q   Max 
 -33.44 -12.39 -4.126 13.03 39.18

Coefficients:
                  Value Std. Error  t value Pr(>|t|) 
   (Intercept)  48.6930   2.3076    21.1011   0.0000
percent.female  -0.0642   0.0538    -1.1917   0.2362

Residual standard error: 17.17 on 100 degrees of freedom
Multiple R-Squared: 0.014 
F-statistic: 1.42 on 1 and 100 degrees of freedom, the p-value is 0.2362 

Correlation of Coefficients:
               (Intercept) 
percent.female -0.6762    
> 

#######################################################################

> 
> fit.all3 _ lm(occ.prestige ~ education + income + percent.female,data=prestige)
> fit.all3
Call:
lm(formula = occ.prestige ~ education + income + percent.female, data = 
	prestige)

Coefficients:
 (Intercept) education     income percent.female 
   -6.794334  4.186637 0.00131356   -0.008905157

Degrees of freedom: 102 total; 98 residual
Residual standard error: 7.846467 
> 
> par(mfrow=c(2,3))
> plot(fit.all3)
> 

######################################################################

> summary(fit.all3)

Call: lm(formula = occ.prestige ~ education + income + percent.female, data = 
	prestige)
Residuals:
    Min     1Q  Median    3Q  Max 
 -19.82 -5.333 -0.1364 5.159 17.5

Coefficients:
                  Value Std. Error  t value Pr(>|t|) 
   (Intercept)  -6.7943   3.2391    -2.0976   0.0385
     education   4.1866   0.3887    10.7708   0.0000
        income   0.0013   0.0003     4.7288   0.0000
percent.female  -0.0089   0.0304    -0.2929   0.7702

Residual standard error: 7.846 on 98 degrees of freedom
Multiple R-Squared: 0.7982 
F-statistic: 129.2 on 3 and 98 degrees of freedom, the p-value is 0 

Correlation of Coefficients:
               (Intercept) education  income 
     education -0.7774                      
        income  0.1280     -0.6752          
percent.female -0.0563     -0.4321    0.5852
>