[R] Fractional Factorial - Wrong values using lm-function
Ståle Nordås
stale.nordas at bergen-plastics.no
Mon Jun 25 14:43:06 CEST 2012
Hello.
Thank you for the help. However, I'm not sure your reply answers my question. Let me rephrase:
I'm trying to reproduce the values in the second table in the example on http://www.itl.nist.gov/div898/handbook/pri/section4/pri472.htm. The table shows the summary of the linear model, which are the values I'm trying to reproduce, using the input in the example. When I use the lm-function on the data, I get values completely different from those given in the example (I've provided these values in my first post). Obviously I'm missing something - why can't I reproduce the values in the example using:
lm.catapult = lm(Distance~h+s+b+l+e+h*s+h*b+h*l+h*e+s*b+s*l+s*e+b*l+b*e+l*e,data=data.catapult)
> summary(lm.catapult)
?
I hope this was clearer.
Regards, Ståle Nordås
-----Original Message-----
From: arun [mailto:smartpink111 at yahoo.com]
Sent: 25. juni 2012 13:50
To: Ståle Nordås
Cc: R help
Subject: Re: [R] Fractional Factorial - Wrong values using lm-function
Hi,
You need to use,
anova(lm.catapult)
Analysis of Variance Table
Response: Distance
Df Sum Sq Mean Sq F value Pr(>F) h 1 2909.3 2909.3 15.8538 0.016378 * s 1 1963.6 1963.6 10.7005 0.030755 * b 1 7536.9 7536.9 41.0720 0.003046 ** l 1 6490.3 6490.3 35.3687 0.004010 ** e 1 2297.0 2297.0 12.5177 0.024056 * h:s 1 122.4 122.4 0.6669 0.459978 h:b 1 344.6 344.6 1.8777 0.242467 h:l 1 353.9 353.9 1.9286 0.237236 h:e 1 0.2 0.2 0.0010 0.975783 s:b 1 161.0 161.0 0.8772 0.401991 s:l 1 19.7 19.7 0.1073 0.759658 s:e 1 114.2 114.2 0.6225 0.474270 b:l 1 926.4 926.4 5.0486 0.087946 .
b:e 1 124.2 124.2 0.6769 0.456887 l:e 1 157.8 157.8 0.8600 0.406226 Residuals 4 734.0 183.5
#the summary result you got is the summary of linear model, while the summary of aov is the anova summary.
A.K.
----- Original Message -----
From: Staleno <sn at bergen-plastics.no>
To: r-help at r-project.org
Cc:
Sent: Monday, June 25, 2012 5:26 AM
Subject: [R] Fractional Factorial - Wrong values using lm-function
Hello.
I'm a new user of R, and I have a question regarding the use of aov and lm-functions. I'm doing a fractional factorial experiment at our production site, and I need to familiarize myself with the analysis before I conduct the experiment. I've been working my way through the examples provided at http://www.itl.nist.gov/div898/handbook/pri/section4/pri472.htm
http://www.itl.nist.gov/div898/handbook/pri/section4/pri472.htm , but I can't get the results provided in the trial model calculations. Why is this.
Here is how I have tried to do it:
> data.catapult=read.table("Fractional.txt",header=T) #Read the data in
> the table provided in the example.
> data.catapult
Distance h s b l e
1 28.00 3.25 0 1 0 80
2 99.00 4.00 10 2 2 62
3 126.50 4.75 20 2 4 80
4 126.50 4.75 0 2 4 45
5 45.00 3.25 20 2 4 45
6 35.00 4.75 0 1 0 45
7 45.00 4.00 10 1 2 62
8 28.25 4.75 20 1 0 80
9 85.00 4.75 0 1 4 80
10 8.00 3.25 20 1 0 45
11 36.50 4.75 20 1 4 45
12 33.00 3.25 0 1 4 45
13 84.50 4.00 10 2 2 62
14 28.50 4.75 20 2 0 45
15 33.50 3.25 0 2 0 45
16 36.00 3.25 20 2 0 80
17 84.00 4.75 0 2 0 80
18 45.00 3.25 20 1 4 80
19 37.50 4.00 10 1 2 62
20 106.00 3.25 0 2 4 80
> aov.catapult =
> aov(Distance~h+s+b+l+e+h*s+h*b+h*l+h*e+s*b+s*l+s*e+b*l+b*e+l*e,data=da
> ta.catapult)
> summary(aov.catapult)
Df Sum Sq Mean Sq F value Pr(>F) h 1 2909 2909 15.854 0.01638 * s 1 1964 1964 10.701 0.03076 * b 1 7537 7537 41.072 0.00305 ** l 1 6490 6490 35.369 0.00401 ** e 1 2297 2297 12.518 0.02406 * h:s 1 122 122 0.667 0.45998 h:b 1 345 345 1.878 0.24247 h:l 1 354 354 1.929 0.23724 h:e 1 0 0 0.001 0.97578 s:b 1 161 161 0.877 0.40199 s:l 1 20 20 0.107 0.75966 s:e 1 114 114 0.622 0.47427 b:l 1 926 926 5.049 0.08795 .
b:e 1 124 124 0.677 0.45689 l:e 1 158 158 0.860 0.40623 Residuals 4 734 184
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
This seems just about right to me. However, when I attempt to make the linear model, based on main factors and two-factor interactions, I get a completely different result:
> lm.catapult =
> lm(Distance~h+s+b+l+e+h*s+h*b+h*l+h*e+s*b+s*l+s*e+b*l+b*e+l*e,data=dat
> a.catapult)
> summary(lm.catapult)
Call:
lm(formula = Distance ~ h + s + b + l + e + h * s + h * b + h *
l + h * e + s * b + s * l + s * e + b * l + b * e + l * e,
data = data.catapult)
Residuals:
1 2 3 4 5 6 7 8 9
10
-0.8100 22.3875 -3.6763 -3.8925 -3.8925 -0.8576 7.0852 -0.8100 -0.8100
-0.8576
11 12 13 14 15 16 17 18 19
20
-0.8576 -0.8576 7.8875 -3.8925 -3.8925 -3.6763 -3.6763 -0.8100 -0.4148
-3.6763
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 25.031042 100.791955 0.248 0.8161 h -3.687500 22.466457 -0.164 0.8776 s 0.475446 2.446791 0.194 0.8554 b -39.417973 44.906164 -0.878 0.4296 l -18.938988 12.233954 -1.548 0.1965 e -0.158449 1.230683 -0.129 0.9038 h:s -0.368750 0.451546 -0.817 0.4600 h:b 12.375000 9.030925 1.370 0.2425 h:l 3.135417 2.257731 1.389 0.2372 h:e 0.008333 0.258026 0.032 0.9758 s:b -0.634375 0.677319 -0.937 0.4020 s:l -0.055469 0.169330 -0.328 0.7597 s:e 0.015268 0.019352 0.789 0.4743 b:l 7.609375 3.386597 2.247 0.0879 .
b:e 0.318397 0.387008 0.823 0.4569 l:e 0.089732 0.096760 0.927 0.4062
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 13.55 on 4 degrees of freedom Multiple R-squared: 0.9697, Adjusted R-squared: 0.8563
F-statistic: 8.545 on 15 and 4 DF, p-value: 0.02559
This result is nothing like the results provided in the example. Why is this? Any help is very much appreciated.
Regards, Ståle.
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