Tim,
I think what you're seeing is
https://en.wikipedia.org/wiki/Loss_of_significance.
Cheers,
Mark
From: "Glover, Tim" <tim.glo...@amecfw.com>
To: "r-help@r-project.org" <r-help@r-project.org>
Date: 09/05/2017 11:37 AM
Subject: [R] Interesting behavior of lm() with small, problematic
data sets
Sent by: "R-help" <r-help-boun...@r-project.org>
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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