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R version 2.9.0 (2009-04-17)

ISBN 3-900051-07-0

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> pdf("rpd07_01r.pdf")

> alldata <- matrix(

+ c(1,676,33,5,1441.67,35184.5,16.4524,

+ 2,516,35,4.75,1299.19,28170.4,13.9852,

+ 3,1052,32,4.2,1154.27,26455,15.3276,

+ 4,868,30,4.4,1045.15,25072.9,17.3128,

+ 5,1008,33,5.55,521.62,31664.2,22.3312,

+ 6,436,33,5.05,1273.02,25491.7,12.2778,

+ 7,544,36,4.25,1346.35,20877.3,17.8225,

+ 8,680,30,4.45,1253.88,25621.3,14.3516,

+ 9,640,38,4.75,1242.65,27587.3,13.6826,

+ 10,492,30,4.6,1281.95,26511.7,11.7566,

+ 11,984,30,4.1,553.69,7886.5,9.882,

+ 12,1400,37,3.45,494.74,14596,16.6752,

+ 13,1276,33,3.45,525.97,9826.8,12.373,

+ 14,1736,36,4.1,571.14,11978.4,9.4058,

+ 15,1004,30,3.5,408.64,10368.6,14.9302,

+ 16,396,30,3.25,646.65,17307.4,31.2865,

+ 17,352,27,3.35,514.03,12822,30.1652,

+ 18,328,29,3.2,350.73,8582.6,28.5901,

+ 19,392,34,3.35,496.29,12369.5,19.8795,

+ 20,236,36,3.3,580.92,14731.9,18.5056,

+ 21,392,30,3.25,535.82,15060.6,22.1344,

+ 22,268,28,3.25,490.34,11056.3,28.6101,

+ 23,252,31,3.2,552.39,8118.9,23.1908,

+ 24,236,31,3.2,661.32,13009.5,24.6917,

+ 25,340,35,3.35,672.15,15003.7,22.6758,

+ 26,2436,29,7.1,528.65,10225,0.3729,

+ 27,2216,35,7.35,563.13,8024.2,0.2703,

+ 28,2096,35,7.45,497.96,10393,0.3205,

+ 29,1660,30,7.45,458.38,8711.6,0.2648,

+ 30,2272,30,7.4,498.25,10239.6,0.2105,

+ 31,824,26,4.85,936.26,20436,18.9875,

+ 32,1196,29,4.6,894.79,12519.9,20.9687,

+ 33,1960,25,5.2,941.36,18979,23.9841,

+ 34,2080,26,4.75,1038.79,22986.1,19.9727,

+ 35,1764,26,5.2,898.05,11704.5,21.3864,

+ 36,412,25,4.55,989.87,17721,23.7063,

+ 37,416,26,3.95,951.28,16485.2,30.5589,

+ 38,504,26,3.7,939.83,17101.3,26.8415,

+ 39,492,27,3.75,925.42,17849,27.7292,

+ 40,636,27,4.15,954.11,16949.6,21.5699,

+ 41,1756,24,5.6,720.72,11344.6,19.6531,

+ 42,1232,27,5.35,782.09,14752.4,20.3295,

+ 43,1400,26,5.5,773.3,13649.8,19.588,

+ 44,1620,28,5.5,829.26,14533,20.1328,

+ 45,1560,28,5.4,856.96,16892.2,19.242),byrow=T,ncol=7)

> bio <- alldata[,2]

> sal <- alldata[,3]

> ph <- alldata[,4]

> k <- alldata[,5]

> na <- alldata[,6]

> zn <- alldata[,7]

> linth5 <- data.frame(bio,sal,ph,k,na,zn)

> attach(linth5)

The following object(s) are masked _by_ .GlobalEnv :

bio k na ph sal zn

> library(leaps)
>
> allpossreg <- regsubsets(bio ~ sal+ph+k+na+zn,nbest=5,data=linth5)
> aprout <- summary(allpossreg)
>
> with(aprout,round(cbind(which,rsq,adjr2,cp,bic),3))
(Intercept) sal ph k na zn   rsq adjr2     cp     bic
1           1   0 1 0 0 0 0.599 0.590 7.421 -33.548
1           1   0 0 0 0 1 0.390 0.376 32.738 -14.622
1           1   0 0 0 1 0 0.074 0.052 70.913   4.153
1           1   0 0 1 0 0 0.042 0.020 74.798   5.688
1           1   1 0 0 0 0 0.011 -0.012 78.573   7.132
2           1   0 1 0 1 0 0.658 0.642 2.282 -36.919
2           1   0 1 1 0 0 0.648 0.631 3.594 -35.511
2           1   0 1 0 0 1 0.608 0.590 8.343 -30.754
2           1   1 1 0 0 0 0.603 0.585 8.933 -30.197
2           1   1 0 0 0 1 0.553 0.531 15.070 -24.775
3           1   0 1 0 1 1 0.662 0.638 3.796 -33.645
3           1   0 1 1 1 0 0.660 0.636 4.049 -33.367
3           1   1 1 0 1 0 0.659 0.634 4.207 -33.194
3           1   1 1 1 0 0 0.652 0.627 5.037 -32.296
3           1   0 1 1 0 1 0.652 0.627 5.048 -32.285
4           1   1 1 1 0 1 0.675 0.642 4.296 -31.524
4           1   1 1 0 1 1 0.672 0.639 4.670 -31.099
4           1   0 1 1 1 1 0.664 0.631 5.588 -30.068
4           1   1 1 1 1 0 0.662 0.628 5.886 -29.739
4           1   1 0 1 1 1 0.577 0.535 16.087 -19.716
5           1   1 1 1 1 1 0.677 0.636 6.000 -28.058
>
>
> # These Stepwise Methods are based on Model Criteria, not individual regression coefficients
> # direction="both" begins like backward and works down
> # Criteria: k=2 uses AIC (default)   k=log(length(y)) uses BIC
>
> reg.full <- lm(bio ~ sal+ph+k+na+zn)
> reg.null <- lm(bio ~ 1)
>
> summary(reg.full)

Call:

lm(formula = bio ~ sal + ph + k + na + zn)

Residuals:

Min 1Q Median 3Q Max

-748.2 -223.7 -85.2 139.9 1072.4

Coefficients:

Estimate Std. Error t value Pr(>|t|)

(Intercept) 1.252e+03 1.235e+03 1.014 0.31674

sal -3.029e+01 2.403e+01 -1.260 0.21507

ph 3.055e+02 8.788e+01 3.477 0.00126 **

k -2.851e-01 3.484e-01 -0.818 0.41817

na -8.673e-03 1.593e-02 -0.544 0.58927

zn -2.068e+01 1.505e+01 -1.373 0.17746

---

Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 398.3 on 39 degrees of freedom

Multiple R-squared: 0.6773, Adjusted R-squared: 0.6359

F-statistic: 16.37 on 5 and 39 DF, p-value: 1.082e-08

> forward.reg <- step(reg.null,direction="forward",scope=list(upper=reg.full,lower=reg.null))

Start: AIC=585.3

bio ~ 1

Df Sum of Sq RSS AIC

+ ph 1 11490388 7680575 546

+ zn 1 7474474 11696489 565

+ na 1 1419069 17751894 584

<none> 19170963 585

+ k 1 802872 18368091 585

+ sal 1 204048 18966915 587

Step: AIC=546.14

bio ~ ph

Df Sum of Sq RSS AIC

+ na 1 1132401 6548174 541

+ k 1 924266 6756309 542

<none> 7680575 546

+ zn 1 170933 7509642 547

+ sal 1 77327 7603247 548

Step: AIC=540.96

bio ~ ph + na

Df Sum of Sq RSS AIC

<none> 6548174 541

+ zn 1 77026 6471149 542

+ k 1 36938 6511236 543

+ sal 1 11778 6536396 543

> summary(forward.reg)

Call:

lm(formula = bio ~ ph + na)

Residuals:

Min 1Q Median 3Q Max

-677.93 -229.76 -97.47 207.51 1168.40

Coefficients:

Estimate Std. Error t value Pr(>|t|)

(Intercept) -4.757e+02 2.735e+02 -1.739 0.0893 .

ph 4.049e+02 4.777e+01 8.477 1.22e-10 ***

na -2.333e-02 8.655e-03 -2.695 0.0101 *

---

Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 394.9 on 42 degrees of freedom

Multiple R-squared: 0.6584, Adjusted R-squared: 0.6422

F-statistic: 40.48 on 2 and 42 DF, p-value: 1.596e-10

> backward.reg <- step(reg.full,direction="backward",k=log(length(bio)))

Start: AIC=555.24

bio ~ sal + ph + k + na + zn

Df Sum of Sq RSS AIC

- na 1 47011 6233274 552

- k 1 106211 6292475 552

- sal 1 251921 6438184 553

- zn 1 299209 6485473 554

<none> 6186263 555

- ph 1 1917306 8103569 564

Step: AIC=551.78

bio ~ sal + ph + k + zn

Df Sum of Sq RSS AIC

- zn 1 434796 6668070 551

- sal 1 436496 6669770 551

<none> 6233274 552

- k 1 732606 6965880 553

- ph 1 1885805 8119079 560

Step: AIC=551

bio ~ sal + ph + k

Df Sum of Sq RSS AIC

- sal 1 88239 6756309 548

<none> 6668070 551

- k 1 935178 7603247 553

- ph 1 11478835 18146905 592

Step: AIC=547.79

bio ~ ph + k

Df Sum of Sq RSS AIC

<none> 6756309 548

- k 1 924266 7680575 550

- ph 1 11611782 18368091 589

> summary(backward.reg)

Call:

lm(formula = bio ~ ph + k)

Residuals:

Min 1Q Median 3Q Max

-679.4 -253.4 -95.4 259.4 1135.8

Coefficients:

Estimate Std. Error t value Pr(>|t|)

(Intercept) -506.9774 279.7714 -1.812 0.0771 .

ph 412.0395 48.4975 8.496 1.15e-10 ***

k -0.4871 0.2032 -2.397 0.0211 *

---

Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 401.1 on 42 degrees of freedom

Multiple R-squared: 0.6476, Adjusted R-squared: 0.6308

F-statistic: 38.59 on 2 and 42 DF, p-value: 3.079e-10

> stepwise.reg <- step(reg.full,direction="both")

Start: AIC=544.4

bio ~ sal + ph + k + na + zn

Df Sum of Sq RSS AIC

- na 1 47011 6233274 543

- k 1 106211 6292475 543

- sal 1 251921 6438184 544

<none> 6186263 544

- zn 1 299209 6485473 545

- ph 1 1917306 8103569 555

Step: AIC=542.74

bio ~ sal + ph + k + zn

Df Sum of Sq RSS AIC

<none> 6233274 543

- zn 1 434796 6668070 544

- sal 1 436496 6669770 544

+ na 1 47011 6186263 544

- k 1 732606 6965880 546

- ph 1 1885805 8119079 553

> summary(stepwise.reg)

Call:

lm(formula = bio ~ sal + ph + k + zn)

Residuals:

Min 1Q Median 3Q Max

-749.1 -229.2 -94.2 127.2 1037.4

Coefficients:

Estimate Std. Error t value Pr(>|t|)

(Intercept) 1505.4882 1133.6940 1.328 0.19172

sal -35.9433 21.4761 -1.674 0.10201

ph 293.8611 84.4738 3.479 0.00123 **

k -0.4388 0.2024 -2.168 0.03615 *

zn -23.4519 14.0399 -1.670 0.10265

---

Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 394.8 on 40 degrees of freedom

Multiple R-squared: 0.6749, Adjusted R-squared: 0.6423

F-statistic: 20.76 on 4 and 40 DF, p-value: 2.528e-09

> dev.off()

null device