I've recently come across the following results reported from the lm() function
when applied to a particular type of admittedly difficult data. When working
with
small data sets (for instance 3 points) with the same response for different
predicting variable, the resulting slope estimate is a reasonable approximation
of the expected 0.0, but the p-value of that slope estimate is a surprising
value. A reproducible example is included below, along with the output of the
summary of results
######### example code
x <- c(1,2,3)
y <- c(1,1,1)
#above results in{ (1,1) (2,1) (3,1)} data set to regress
new.rez <- lm (y ~ x) # regress constant y on changing x)
summary(new.rez) # display results of regression
######## end of example code
Results:
Call:
lm(formula = y ~ x)
Residuals:
1 2 3
5.906e-17 -1.181e-16 5.906e-17
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 1.000e+00 2.210e-16 4.525e+15 <2e-16 ***
x -1.772e-16 1.023e-16 -1.732e+00 0.333
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 1.447e-16 on 1 degrees of freedom
Multiple R-squared: 0.7794, Adjusted R-squared: 0.5589
F-statistic: 3.534 on 1 and 1 DF, p-value: 0.3112
Warning message:
In summary.lm(new.rez) : essentially perfect fit: summary may be unreliable
##############
There is a warning that the summary may be unreliable sue to the essentially
perfect fit, but a p-value of 0.3112 doesn’t seem reasonable.
As a side note, the various r^2 values seem odd too.
Tim Glover
Senior Scientist II (Geochemistry, Statistics), Americas - Environment &
Infrastructure, Amec Foster Wheeler
271 Mill Road, Chelmsford, Massachusetts, USA 01824-4105
T +01 978 692 9090 D +01 978 392 5383 M +01 850 445 5039
tim.glo...@amecfw.com amecfw.com
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