[R] Question about variable selection

[Liaw, Andy]

That depends on whether the IV could have some significant interactions with
other Ivs not considered in the bivariate analysis.  E.g.,

> iv <- expand.grid(-2:2, -2:2)
> y <- 3 + iv[,1] * iv[,2] + rnorm(nrow(iv), sd=0.1)
> summary(lm(y ~ iv[,1]))

Call:
lm(formula = y ~ iv[, 1])

Residuals:
     Min       1Q   Median       3Q      Max 
-4.06259 -1.06048 -0.02377  1.05901  4.04315 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  3.01908    0.41482   7.278 2.09e-07 ***
iv[, 1]      0.01417    0.29332   0.048    0.962    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 2.074 on 23 degrees of freedom
Multiple R-Squared: 0.0001014,  Adjusted R-squared: -0.04337 
F-statistic: 0.002333 on 1 and 23 DF,  p-value: 0.9619 

> summary(lm(y ~ iv[,1] * iv[,2]))

Call:
lm(formula = y ~ iv[, 1] * iv[, 2])

Residuals:
     Min       1Q   Median       3Q      Max 
-0.22390 -0.08894 -0.01279  0.13525  0.17608 

Coefficients:
                 Estimate Std. Error t value Pr(>|t|)    
(Intercept)      3.019083   0.026330 114.665   <2e-16 ***
iv[, 1]          0.014167   0.018618   0.761    0.455    
iv[, 2]         -0.005486   0.018618  -0.295    0.771    
iv[, 1]:iv[, 2]  0.992865   0.013165  75.418   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 0.1316 on 21 degrees of freedom
Multiple R-Squared: 0.9963,     Adjusted R-squared: 0.9958 
F-statistic:  1896 on 3 and 21 DF,  p-value: < 2.2e-16 




Andy

From: Wensui Liu
> 
> Dear Lister,
> 
> I have a question about variable selection for regression.
> 
> if the IV is not significantly related to DV in the bivariate 
> analysis, does
> it make sense to include this IV into the full model with 
> multiple IVs?
> 
> Thank you so much!
> 
> 	[[alternative HTML version deleted]]
> 
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