I used `regsubsets`

to find a model with lowest BIC; height is our D.V. , the code I typed is below:

`male = read.table(file.choose(), header=TRUE) mreg = regsubsets(height ~ biacromial + pelvic.breadth + bitrochanteric + chest.depth + chest.diam + elbow.diam + wrist.diam + knee.diam + ankle.diam + shoulder.girth + chest.girth + waist.girth + navel.girth + hip.girth + thigh.girth + bicep.girth + forearm.girth + knee.girth + calf.girth + ankle.girth + wrist.girth + age + weight , data=male) plot(mreg) `

so the best subset for male is: `bitrochanteric,waist.girth+hip.girth+thigh.girth+bicep.girth, calf.girth+weight`

I regress the model using `lm`

` mreg2 = lm(height ~ bitrochanteric + waist.girth + hip.girth + thigh.girth + bicep.girth + calf.girth + weight, data=male) BIC(reg2) `

Then I got a value of 1461.665 ,which is totally different from my graph and so I don't understand at all why it is different.

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#### Best Answer

*Just an investigation, I have never used this command before.*

The vertical axis probably means "Drop in BIC" compared to the intercept-only model, not the model BIC.

For instance, if your ideal model has a BIC of 1451.665, corresponding to a drop of 220.

Then the model with just `waist.girth`

and `weight`

should have a BIC of about 1551. Because that model only has a drop of 120, which is still 100 higher than your ideal model.

Here is the track of my investigation:

`library(leaps) b<-regsubsets(Fertility~.,data=swiss,nbest=2) summary(b) plot(b) `

Now compare the best and the worst models:

`attach(swiss) m01 <- glm(Fertility ~ Agriculture + Education + Catholic + Infant.Mortality) m02 <- glm(Fertility ~ Examination) m03 <- glm(Fertility ~ 1) BIC(m01) BIC(m02) BIC(m03) BIC(m02) - BIC(m03) # Should be about -18 BIC(m01) - BIC(m03) # Should be about -37 BIC(m02) - BIC(m01) # Difference from the models (-18) - (-37) # Difference taken from the axis `

Results:

`> BIC(m01) [1] 336.3417 > BIC(m02) [1] 355.9029 > BIC(m03) [1] 377.4258 > BIC(m02) - BIC(m03) # Should be about -18 [1] -21.52281 > BIC(m01) - BIC(m03) # Should be about -37 [1] -41.08403 > BIC(m02) - BIC(m01) # Difference from the models [1] 19.56122 > (-18) - (-37) # Difference taken from the axis [1] 19 `

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