> df=read.csv("yacht_hydrodynamics.csv")
> summary(df)
B.D: min 2.73->2.810

> lin1=lm(RR~.,data=df)
> summary(lin1)
> AIC(lin1)
[1] 2233.705

sig: Fr
Residual standard error: 8.96 on 301 degrees of freedom
Adjusted R-squared:  0.6507
> sqrt(sum(lin1$residuals^2)/301)
[1] 8.959608

> log1=lm(log(RR)~.,data=df)
> summary(log1)
> AIC(log1)
[1] 172.3199
sig: Intercept & log(Fr)
Residual standard error: 0.3155 on 301 degrees of freedom
Adjusted R-squared:  0.9709

> sqrt(sum((exp(log1$fitted.values)-df$RR)^2)/301)
[1] 2.164252 !much lower than lin1
> sqrt(sum((log(lin1$fitted.values/df$RR)^2))/301)
[1] NaN
lin1$fitted.values<0...can't take log

> log2=lm(log(RR)~log(Fr),data=df)
> summary(log2)
> AIC(log2)
[1] 195.2754
sig: Intercept & log(Fr)
Residual standard error: 0.3301 on 306 degrees of freedom
Adjusted R-squared:  0.9681

> plot(log(df$Fr),log(df$RR))
> abline(a=7.25812,b=4.69046)
can see line is OK but data is slightly curved

> plot(df$Fr,df$RR)
> curve(exp(7.25812+4.69046*log(x)),.125,.45,add=T)
failure at large Fr seems larger in linear-linear plot

> log3=lm(log(RR)~poly(log(Fr),2)+.-Fr,data=df)
> summary(log3)
> AIC(log3)
[1] 116.4574
sig:adds CoB
Residual standard error: 0.2877 on 300 degrees of freedom
Adjusted R-squared:  0.9758
everything improved over log1 & log2, particularly AIC

> log4=lm(log(RR)~poly(log(Fr),3)+.-Fr,data=df)
> summary(log4)
> AIC(log4)
[1] -6.010674
sig: nothing new
Residual standard error: 0.2354 on 299 degrees of freedom
Adjusted R-squared:  0.9838
everything improved over log3, particularly AIC, now negative

> log5=lm(log(RR)~poly(log(Fr),3)+CoB,data=df)
> summary(log5)
> AIC(log5)
[1] 8.637524
sig: added (Intercept)
Residual standard error: 0.2426 on 303 degrees of freedom
Adjusted R-squared:  0.9828 
everthing worse, but not by much

> log6=lm(log(RR)~poly(log(Fr),3)+CoB+L.D,data=df)
> summary(log6)
> AIC(log6)
[1] 6.82053
sig: added L.D  0.0532 .
Residual standard error: 0.2415 on 302 degrees of freedom
Adjusted R-squared:  0.9829
marginally better than previous

> log7=lm(log(RR)~poly(log(Fr),3)+CoB+L.D+L.B,data=df)
> summary(log7)
> AIC(log7)
sig: L.D & L.B both strong
[1] -6.229965
Residual standard error: 0.2361 on 301 degrees of freedom
Adjusted R-squared:  0.9837 
close to all-in case, much improved AIC

> log8=lm(log(RR)~poly(log(Fr),3)+CoB+L.D+L.B+P.C,data=df)
> summary(log8)
> AIC(log8)
[1] -7.795269
sig: added P.C.
Residual standard error: 0.2351 on 300 degrees of freedom
Adjusted R-squared:  0.9838 
best AIC, otherwise much like all in

> log9=lm(log(RR)~poly(log(Fr),3)+CoB+L.D+L.B+B.D,data=df)
> summary(log9)
> AIC(log9)
[1] -7.715569
sig: added B.D (P.C not an option)
very similar to log8
Residual standard error: 0.2352 on 300 degrees of freedom
Multiple R-squared:  0.9842,	Adjusted R-squared:  0.9838 

> plot(df$Fr,df$RR-exp(log8$fitted.values))
> pdf("log8-residuals-lin.pdf")
> plot(df$Fr,df$RR-exp(log8$fitted.values))
> dev.off()
X11cairo 
       2 
> plot(df$Fr,log8$residuals)
> pdf("log8-residuals-log.pdf")
> plot(df$Fr,log8$residuals)
> dev.off()
X11cairo 
       2 

> sqrt(sum((exp(log8$fitted.values)-df$RR)^2)/299)
[1] 2.09336
only slight improvement over log1

> lin2=lm(RR ~ poly(Fr,4) + CoB*Fr + P.C*Fr, data=df)
> summary(lin2)
> AIC(lin2)
[1] 1047.861
sig:all
Residual standard error: 1.303 on 299 degrees of freedom
Adjusted R-squared:  0.9926
huge improvement over lin1, but is it better than log8?

> plot(df$Fr,lin2$residuals)
> pdf("lin2-residuals-lin.pdf")
> plot(df$Fr,log8$residuals)
> dev.off()
X11cairo 
       2 

lin2 has lower overall residuals, log8 does better a low Fr
if you look at abs of residuals, they are much closer

> mean(abs(exp(log8$fitted.values)-df$RR))
[1] 0.9169838
> mean(abs(lin2$fitted.values-df$RR))
[1] 0.8250252

lin3=lm(RR ~ poly(Fr,6)+P.C*Fr+L.D*Fr+L.B*Fr+I(P.C*Fr^6)+I(L.B*Fr^6)+I(L.D*Fr^6)+I(CoB*Fr^6), data=df)
> AIC(lin3)
[1] 837.1401
Residual standard error: 0.9195 on 291 degrees of freedom
Adjusted R-squared:  0.9963
> mean(abs(lin3$fitted.values-df$RR))
[1] 0.5439024