Splus handout #1

S-PLUS : Copyright (c) 1988, 1996 MathSoft, Inc.
S : Copyright AT&T.
Version 3.4 Release 1 for Sun SPARC, SunOS 5.3 : 1996 
Working data will be in /home/fac/d/jah/.Data 
Warning: Cannot open audit file
> #ANALYSIS OF BOILING POINT DATA
> #X=boiling point (degrees F)
> #Y=log(barometric pressure) (inches of mercury)
> #17 locations in the Alps and in Scotland
> #_________________________________________________________________________
> 
> bp<-read.table("alr.3",header=T)
> bp$pressure<-bp$pressure*100
> bp
    boil pressure 
 1 194.5   131.79
 2 194.3   131.79
 3 197.9   135.02
 4 198.4   135.55
 5 199.4   136.46
 6 199.9   136.83
 7 200.9   137.82
 8 201.1   138.00
 9 201.4   138.06
10 201.3   138.05
11 203.6   140.04
12 204.6   142.44
13 209.5   145.47
14 208.6   144.34
15 210.7   146.30
16 211.9   147.54
17 212.2   147.80
> motif()
> par(mfrow=c(2,2))
> plot(bp$boil,bp$pressure,xlab="boiling point, degrees F",
+ ylab="log(pressure)*100") 
> title("Boiling point versus log pressure")
> #_________________________________________________________________________
> bp.lm<-lm(pressure~boil,bp)
> bp.lm
Call:
lm(formula = pressure ~ boil, data = bp)

Coefficients:
 (Intercept)      boil 
   -42.13087 0.8954625

Degrees of freedom: 17 total; 15 residual
Residual standard error: 0.378886 
> #_________________________________________________________________________
> coef(bp.lm)
 (Intercept)      boil 
   -42.13087 0.8954625
>#_________________________________________________________________________

> summary(bp.lm)

Call: lm(formula = pressure ~ boil, data = bp)
Residuals:
     Min      1Q  Median      3Q   Max 
 -0.3226 -0.1453 -0.0675 0.02111 1.359

Coefficients:
               Value Std. Error  t value Pr(>|t|) 
(Intercept) -42.1309   3.3390   -12.6180   0.0000
       boil   0.8955   0.0164    54.4499   0.0000

Residual standard error: 0.3789 on 15 degrees of freedom
Multiple R-Squared: 0.995 
F-statistic: 2965 on 1 and 15 degrees of freedom, the p-value is 0 

Correlation of Coefficients:
     (Intercept) 
boil -0.9996    
> #_________________________________________________________________________
> anova(bp.lm)
Analysis of Variance Table

Response: pressure

Terms added sequentially (first to last)
          Df Sum of Sq  Mean Sq  F Value Pr(F) 
boil       1  425.6095 425.6095 2964.792     0
Residuals 15    2.1533   0.1436               
> #_________________________________________________________________________
> resid(bp.lm)
          1          2           3          4          5           6 
 -0.2465903 -0.0674978 -0.06116289 0.02110585 0.03564332 -0.04208794
          7          8          9          10         11       12          13 
 0.05244954 0.05335703 -0.1552817 -0.07573547 -0.1452993 1.359238 0.001471823
         14         15          16          17 
 -0.3226119 -0.2430832 -0.07763824 -0.08627699
> #_________________________________________________________________________
> #CONFIDENCE INTERVAL FOR BETA_1
> 
> a<-qt(.975,15)*0.0164		   #read std error from output
> #for better accuracy, compute standard error directly
> a<-qt(.975,15)*sqrt((sum(bp.lm$resid^2)/15)/sum((bp$boil-mean(bp$boil))^2))
> #for even more accuracy, see appendix of Weisberg, "Applied Linear
> # Regression" 
> 
> #95% C.I.
> c(bp.lm$coef[2]-a,bp.lm$coef[2]+a)
      boil      boil 
 0.8604095 0.9305155
> #_________________________________________________________________________
> #PREDICTION/ESTIMATION
> fitted(bp.lm)
        1        2        3        4        5        6        7        8 
 132.0366 131.8575 135.0812 135.5289 136.4244 136.8721 137.7676 137.9466
        9       10       11       12       13       14       15       16 
 138.2153 138.1257 140.1853 141.0808 145.4685 144.6626 146.5431 147.6176
       17 
 147.8863
> #Prediction for a new value of X:
> 
> predict(bp.lm,newdata=data.frame(boil=200))
        1 
 136.9616
>