Interpreting Multiple Linear Regression Summary
On Nov 9, 2011, at 1:17 PM, Rich Shepard wrote:
On Wed, 9 Nov 2011, Daniel Nordlund wrote:
I would guess that there is something problematic with the how the data frame is structured relative to what lm() is expecting.
Dan, I was not comfortable with my explanation, but the formula (and data frame) was equivalent to those of the other 8 streams.
So, I would not give up looking for a solution just yet.
OK. I'm always up for learning more about R and its processes.
Can you show us the result of str() on the data frame that you attached?
Sure. I subset the original data frame to select only the 6 predictor
variables and the response variable. Same lm() results. I'll provide the
data frame, too.
summary(lm(formula = TDS ~ Cond + Ca + Cl + Mg + Na + SO4, data =
mod.stump.cast))
Call:
lm(formula = TDS ~ Cond + Ca + Cl + Mg + Na + SO4, data = mod.stump.cast)
Residuals:
ALL 1 residuals are 0: no residual degrees of freedom!
Coefficients: (6 not defined because of singularities)
Estimate Std. Error t value Pr(>|t|)
(Intercept) 125 NA NA NA
Cond NA NA NA NA
Ca NA NA NA NA
Cl NA NA NA NA
Mg NA NA NA NA
Na NA NA NA NA
SO4 NA NA NA NA
Residual standard error: NaN on 0 degrees of freedom
(63 observations deleted due to missingness)
str(mod.stump.cast)
'data.frame': 64 obs. of 7 variables:
$ Ca : num NA NA 24.4 NA 21.4 NA NA NA NA NA ...
$ Cl : num 1.58 5.6 3 NA 1 5 1.2 4 4 8.4 ...
$ Cond: num NA NA 190 187 184 NA NA NA NA NA ...
$ Mg : num NA NA 10 NA 9.1 NA NA NA NA NA ...
$ Na : num NA NA NA NA NA NA NA NA NA NA ...
$ SO4 : num 9.4 6.5 9 NA 7 55 6.8 105 15.6 8.4 ...
$ TDS : num 105 181 112 144 114 308 96 430 108 108 ...
summary(mod.stump.cast)
Ca Cl Cond Mg Na
Min. : 0.60 Min. : 1.000 Min. : 2.2 Min. : 9.10 Min. : 4
1st Qu.:23.35 1st Qu.: 2.000 1st Qu.:214.8 1st Qu.:11.00 1st Qu.: 4
Median :28.35 Median : 4.000 Median :282.5 Median :17.40 Median : 4
Mean :32.77 Mean : 4.076 Mean :294.6 Mean :17.85 Mean : 4
3rd Qu.:40.55 3rd Qu.: 5.600 3rd Qu.:372.0 3rd Qu.:22.10 3rd Qu.: 4
Max. :64.30 Max. :13.000 Max. :636.0 Max. :32.40 Max. : 4
NA's :50.00 NA's :11.000 NA's : 42.0 NA's :51.00 NA's :62
SO4 TDS
Min. : 4.00 Min. : 14.0
1st Qu.: 7.00 1st Qu.:131.2
Median : 9.40 Median :174.0
Mean : 16.31 Mean :176.9
3rd Qu.: 17.00 3rd Qu.:195.5
Max. :105.00 Max. :430.0
NA's : 3.00 NA's : 2.0
mod.stump.cast
Ca Cl Cond Mg Na SO4 TDS
1 NA 1.58 NA NA NA 9.4 105
2 NA 5.60 NA NA NA 6.5 181
3 24.4 3.00 190.0 10.0 NA 9.0 112
4 NA NA 187.0 NA NA NA 144
5 21.4 1.00 184.0 9.1 NA 7.0 114
6 NA 5.00 NA NA NA 55.0 308
7 NA 1.20 NA NA NA 6.8 96
8 NA 4.00 NA NA NA 105.0 430
9 NA 4.00 NA NA NA 15.6 108
10 NA 8.40 NA NA NA 8.4 108
11 NA 1.00 NA NA NA 8.8 125
12 NA 1.40 NA NA NA 19.4 129
13 NA 4.90 NA NA NA 37.0 360
14 NA 1.70 NA NA NA 12.0 140
15 NA 2.00 NA NA NA 10.0 95
16 NA 1.60 NA NA NA 9.1 120
17 NA 3.30 NA NA NA 34.0 280
18 NA 2.20 NA NA NA 11.0 130
19 NA 9.00 NA NA NA 69.0 352
20 NA 1.00 NA NA NA 18.0 148
21 NA 2.00 NA NA NA 9.0 107
22 28.0 1.00 248.0 11.0 4 13.0 125
23 32.0 1.00 NA 12.0 4 9.0 139
24 NA 5.00 NA NA NA 7.0 188
25 NA 4.00 NA NA NA 6.0 201
26 NA 3.00 NA NA NA 5.0 178
27 NA 2.27 NA NA NA 7.8 197
28 NA 1.76 NA NA NA 7.8 187
29 NA 5.81 NA NA NA 7.5 182
30 NA 4.23 NA NA NA 6.0 165
31 NA 4.23 NA NA NA 7.3 186
32 NA 6.25 NA NA NA 7.0 191
33 NA 6.72 NA NA NA 7.5 190
34 34.7 4.00 304.0 17.4 NA 6.0 176
35 NA NA 354.0 NA NA 7.0 175
36 42.5 5.00 379.0 21.1 NA 7.0 220
37 NA 5.80 NA NA NA 5.6 163
38 26.0 5.80 300.0 24.0 NA 5.6 163
39 NA 2.20 NA NA NA 5.4 152
40 NA 5.40 NA NA NA 11.0 221
41 NA 5.40 NA NA NA 10.5 171
42 NA 4.80 NA NA NA 9.9 204
43 NA 8.00 NA NA NA 11.7 174
44 NA 1.00 NA NA NA 8.4 190
45 NA 4.80 NA NA NA 12.1 174
46 NA 5.90 NA NA NA 16.0 210
47 NA 5.90 NA NA NA 20.0 190
48 NA 13.00 NA NA NA 7.6 180
49 NA 5.60 NA NA NA 17.0 200
50 NA 1.20 NA NA NA 6.5 180
51 0.6 NA 2.2 NA NA NA NA
52 21.4 NA 187.0 9.5 NA 8.0 120
53 NA NA 285.0 NA NA 22.0 135
54 48.3 3.00 378.0 22.1 NA 24.0 228
55 63.5 7.00 533.0 29.9 NA 44.0 14
56 NA NA 207.0 NA NA NA NA
57 NA NA 262.0 NA NA 13.0 156
58 28.7 2.00 244.0 12.6 NA 13.0 140
59 NA NA 238.0 NA NA 12.0 128
60 NA NA 280.0 NA NA 18.0 160
61 NA NA 380.0 NA NA 23.0 215
62 NA NA 402.0 NA NA 23.0 230
63 64.3 7.00 636.0 32.4 NA 73.0 316
64 23.0 4.10 300.0 21.0 NA 4.0 163
Thanks,
Rich
Here is your problem:
# 'DF' is the result of copying your data above from the
# clipboard on OSX
DF <- read.table(pipe("pbpaste"), header = TRUE)
str(DF)
'data.frame': 64 obs. of 7 variables: $ Ca : num NA NA 24.4 NA 21.4 NA NA NA NA NA ... $ Cl : num 1.58 5.6 3 NA 1 5 1.2 4 4 8.4 ... $ Cond: num NA NA 190 187 184 NA NA NA NA NA ... $ Mg : num NA NA 10 NA 9.1 NA NA NA NA NA ... $ Na : int NA NA NA NA NA NA NA NA NA NA ... $ SO4 : num 9.4 6.5 9 NA 7 55 6.8 105 15.6 8.4 ... $ TDS : int 105 181 112 144 114 308 96 430 108 108 ?
na.omit(DF)
Ca Cl Cond Mg Na SO4 TDS 22 28 1 248 11 4 13 125 After removing incomplete records (any records with NA values) which is the default behavior for R model functions, you only have one record left to fit the model to. HTH, Marc Schwartz