STAT 3220 Unit 3
These data were collected from 2007 - 2009 by Dr. Kristen Gorman with the Palmer Station Long Term Ecological Research Program, part of the US Long Term Ecological Research Network. The data were imported directly from the Environmental Data Initiative (EDI) Data Portal, and are available for use by CC0 license (“No Rights Reserved”) in accordance with the Palmer Station Data Policy.
Unit 3: Penguins Classwork
pendata<-read.csv("https://raw.githubusercontent.com/kvaranyak4/STAT3220/main/penguins.csv")
head(pendata)names(pendata)[1] "X" "species" "island"
[4] "bill_length_mm" "bill_depth_mm" "flipper_length_mm"
[7] "body_mass_g" "sex" "year" \(E(bodymass)=\beta_0+\beta_1BillDep+\beta_2BillLen+\beta_3FlipperLen+\beta_4SpeciesC+\beta_5SpeciesG+\beta_6SexM+\beta_7BillDep*BillLen\)
- where Species C= 1 if Chinstrap, 0 otherwise
- SpeciesG = 1 if Gentoo, 0 otherwise
- SexM = 1 if male, 0 otherwise
Check the model assumptions.
penmod3<-lm(body_mass_g~bill_depth_mm+bill_length_mm+flipper_length_mm+bill_depth_mm*bill_length_mm+species+sex,data=pendata)
summary(penmod3)
Call:
lm(formula = body_mass_g ~ bill_depth_mm + bill_length_mm + flipper_length_mm +
bill_depth_mm * bill_length_mm + species + sex, data = pendata)
Residuals:
Min 1Q Median 3Q Max
-706.90 -175.12 -6.14 176.80 880.08
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -6290.446 1832.633 -3.432 0.000675 ***
bill_depth_mm 333.924 98.231 3.399 0.000760 ***
bill_length_mm 130.274 41.058 3.173 0.001653 **
flipper_length_mm 16.535 2.888 5.725 2.35e-08 ***
speciesChinstrap -200.763 82.322 -2.439 0.015273 *
speciesGentoo 923.788 132.379 6.978 1.68e-11 ***
sexmale 391.603 47.370 8.267 3.55e-15 ***
bill_depth_mm:bill_length_mm -6.344 2.290 -2.770 0.005919 **
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 284.4 on 325 degrees of freedom
(11 observations deleted due to missingness)
Multiple R-squared: 0.8778, Adjusted R-squared: 0.8752
F-statistic: 333.7 on 7 and 325 DF, p-value: < 2.2e-16#There are a few options to view plots for assumptions
#Residuals Plots of explanatory variables vs residuals
residualPlots(penmod3,tests=F)
#Residual vs Fitted and QQ plot
plot(penmod3, which=c(1,2))
#histogram of residuals
hist(residuals(penmod3))
- Lack of Fit Plot: Residual Plots
- Constant Variance: Residual Plots and Residual vs Fitted
- Normality: QQ Plot and Histogram of Residuals
- Independence: We do not have time series data
Then we will identify outliers and influential observations.
#Cooks Distance Thresholds
plot(penmod3,which=4)
#Leverage vs Studentized Residuals
influencePlot(penmod3,fill=F)
#We can use various functions to store and view these statistics for all observations
dfpen<-dffits(penmod3)
dfbetas(penmod3) (Intercept) bill_depth_mm bill_length_mm flipper_length_mm
1 -3.734434e-03 -1.787127e-03 -1.514125e-03 1.754799e-02
2 2.645405e-02 -3.148788e-02 -8.508086e-03 -2.825000e-02
3 3.030694e-02 4.758209e-04 -1.219175e-02 -7.522431e-02
5 5.714196e-02 -5.528885e-02 -3.734536e-02 -3.152131e-02
6 9.291589e-02 -1.317467e-01 -8.299088e-02 7.237964e-02
7 2.392107e-02 -8.894979e-03 -2.158378e-03 -7.725239e-02
8 -9.026747e-02 9.802911e-02 6.788538e-02 3.914817e-02
13 -1.240662e-02 9.245781e-03 -2.431387e-03 4.073133e-02
14 1.308675e-01 -1.680057e-01 -1.098506e-01 4.907086e-02
15 -8.557838e-02 9.310769e-02 6.910227e-02 2.660027e-02
16 1.329667e-02 -3.474638e-03 -9.828072e-03 -2.273476e-02
17 4.420920e-02 -3.319768e-02 -2.377362e-02 -4.338327e-02
18 -9.806600e-03 6.740117e-03 -8.543630e-03 3.445592e-03
19 3.381855e-03 -5.986498e-03 -2.678368e-03 2.875290e-03
20 -2.331672e-03 2.344125e-03 2.621185e-03 1.588756e-03
21 1.407871e-02 9.029376e-03 4.835431e-03 -8.562134e-02
22 -1.022895e-02 -1.364490e-02 -8.642154e-03 6.628194e-02
23 -7.029185e-02 7.844033e-02 5.172880e-02 1.168274e-02
24 1.570679e-02 -3.137914e-03 -1.444776e-03 -3.336493e-02
25 4.247259e-02 -2.603737e-02 -1.474211e-02 -5.987649e-02
26 -6.971866e-02 8.531873e-02 5.292304e-02 -1.073897e-03
27 -3.050141e-02 3.791128e-03 -3.567294e-03 1.022801e-01
28 -1.458146e-03 5.824167e-03 -5.762251e-03 1.822887e-02
29 -5.212508e-03 -8.059650e-03 -4.836305e-03 4.840837e-02
30 1.647259e-02 1.962845e-03 2.999234e-03 -6.791989e-02
31 1.309392e-02 -1.021765e-02 -4.638575e-03 -1.984284e-02
32 4.068736e-02 -3.350704e-03 -5.088166e-03 -1.081465e-01
33 -4.212235e-04 3.590168e-03 -1.275853e-03 1.676236e-03
34 1.772907e-03 7.798824e-05 3.840267e-04 -7.152141e-03
35 -7.775764e-03 1.664248e-02 1.437234e-02 -3.373364e-02
36 3.229722e-02 -3.624424e-02 -2.295062e-02 -4.278072e-03
37 1.747998e-02 -2.515212e-02 -1.673550e-02 1.239939e-02
38 1.015877e-02 -2.920943e-03 3.139716e-03 -5.599917e-02
39 2.060663e-02 -3.448744e-02 -2.270906e-02 4.100531e-02
40 2.653293e-02 5.209415e-02 3.999337e-02 -2.511215e-01
41 -5.706751e-03 -4.656694e-03 4.605620e-04 2.964481e-02
42 7.826487e-04 2.563446e-03 -2.397172e-03 -1.029562e-02
43 3.506601e-02 -4.861119e-02 -2.689529e-02 1.340248e-02
44 1.764189e-02 -2.673283e-02 -2.006786e-02 -3.190702e-03
45 -4.923959e-02 4.871837e-02 3.878120e-02 1.051854e-02
46 -5.759667e-03 3.078084e-02 2.926567e-02 -5.738595e-02
47 -4.604662e-02 -5.786749e-04 -5.961018e-03 1.825429e-01
49 -6.805967e-04 4.317718e-04 -2.338152e-04 2.460340e-03
50 -3.069068e-05 -5.642090e-04 3.171735e-04 2.273985e-03
51 3.098811e-03 -3.617912e-03 8.634883e-05 -7.522866e-03
52 6.414709e-03 1.391856e-02 1.420809e-02 -6.394050e-02
53 -1.321542e-03 1.129259e-03 -7.412941e-04 5.248956e-03
54 1.056105e-02 -1.763442e-03 -2.032868e-03 -2.754767e-02
55 2.478297e-02 -4.037258e-02 -6.287646e-03 -1.854321e-02
56 -1.020994e-02 7.345859e-03 -3.770895e-03 2.268986e-02
57 9.842211e-03 -1.088483e-02 -4.005412e-03 -1.056913e-02
58 3.179779e-03 -3.645490e-03 -6.945879e-03 2.973737e-04
59 -9.103761e-02 8.011545e-02 6.637049e-02 5.102432e-02
60 4.176279e-02 -4.859656e-02 -3.370419e-02 -2.442710e-02
61 -1.861888e-02 1.773438e-02 1.650322e-02 1.473197e-03
62 -2.275519e-02 2.782265e-02 1.027431e-02 -8.565939e-03
63 4.849334e-02 -4.831089e-02 -3.500018e-02 -1.675010e-02
64 3.596262e-03 -4.098465e-03 8.771195e-04 -1.870544e-03
65 -7.119571e-02 6.285026e-02 5.634545e-02 2.941826e-02
66 -2.930827e-04 3.686344e-04 -4.728709e-05 1.203920e-04
67 8.102288e-03 -1.127058e-02 -9.743983e-03 1.152157e-02
68 4.986836e-03 2.228221e-03 3.235205e-03 -2.848213e-02
69 -5.296834e-02 6.418729e-02 5.584057e-02 -4.124741e-02
70 -1.683462e-02 4.423792e-03 5.523973e-03 3.734705e-02
71 -2.597507e-02 2.893594e-02 1.805378e-02 1.125142e-02
72 -7.421244e-04 4.044343e-05 -4.788913e-04 1.822767e-03
73 -4.917133e-04 -1.584764e-03 -3.285737e-04 5.568348e-03
74 4.672407e-04 -8.753814e-04 -3.345241e-04 1.493281e-04
75 1.512799e-02 -2.145365e-02 -2.819216e-02 4.736449e-02
76 4.622451e-03 -1.256440e-02 1.087116e-03 7.570309e-03
77 7.117559e-03 -2.826550e-02 5.213378e-04 2.941140e-02
78 -1.100175e-03 2.485575e-03 1.667819e-03 -2.945633e-03
79 1.200037e-01 -1.318051e-01 -1.079223e-01 2.660015e-02
80 3.740169e-04 1.567564e-03 -6.002191e-04 -2.171192e-03
81 -1.489794e-02 1.623937e-02 1.853316e-02 -1.511031e-02
82 1.273571e-02 -6.130450e-02 2.313967e-02 8.127776e-02
83 -4.990967e-02 6.075560e-02 3.845786e-02 -9.455874e-03
84 -5.246332e-02 6.384102e-02 4.342050e-02 1.735822e-02
85 2.941618e-03 7.547453e-04 1.336127e-03 -1.507527e-02
86 4.725556e-02 -5.940494e-02 -2.659996e-02 2.888313e-02
87 4.391029e-02 -6.026373e-02 -4.120158e-02 8.439630e-03
88 -2.021865e-04 2.142585e-04 1.335584e-04 6.618750e-05
89 1.003218e-03 -1.819529e-03 -1.262996e-03 1.346512e-03
90 -5.637798e-03 5.114738e-03 3.757936e-03 1.388928e-03
91 1.581876e-02 -5.331400e-03 -1.581900e-03 -4.836613e-02
92 -1.232617e-02 -5.081612e-03 3.257012e-03 6.010741e-02
93 3.857534e-02 -3.367622e-02 -3.844063e-02 1.074954e-03
94 6.217424e-02 -2.458169e-02 -2.493717e-03 -1.275045e-01
95 -2.339997e-03 2.368101e-03 2.326801e-03 -6.939887e-04
96 -4.536348e-03 9.419373e-04 1.309767e-03 1.371447e-02
97 -2.129651e-02 1.948391e-02 1.358575e-02 9.690263e-03
98 -1.001768e-02 4.754553e-04 8.710433e-03 3.920850e-02
99 -3.581212e-02 3.142869e-02 3.076757e-02 1.262435e-02
100 5.623531e-03 -6.999576e-03 -1.474116e-04 -6.935898e-03
101 -1.608734e-02 9.312769e-03 -4.951238e-03 6.034534e-02
102 -8.086360e-02 4.942170e-02 3.011830e-02 1.355515e-01
103 -2.851663e-02 2.906112e-02 2.030878e-02 8.027188e-03
104 -4.625789e-02 6.313497e-02 4.313685e-02 -1.949737e-02
105 1.062983e-01 -8.156305e-02 -5.657804e-02 -1.117309e-01
106 -1.555159e-02 -1.537583e-02 -1.333116e-02 9.932878e-02
107 -7.965475e-03 -1.783325e-02 -8.118032e-03 8.228164e-02
108 3.111093e-02 -4.322341e-02 -2.926775e-02 1.607359e-02
109 -1.095595e-02 8.889439e-03 5.885174e-03 1.213643e-02
110 7.727232e-03 -4.230158e-02 -9.585209e-03 5.149718e-02
111 2.635960e-02 -7.680817e-02 -4.786966e-02 1.556294e-01
112 1.236174e-01 -1.192420e-01 -1.093615e-01 -1.326645e-01
113 1.362948e-02 1.012681e-02 -3.693739e-03 -5.544024e-02
114 -4.015086e-03 -2.965650e-04 3.566425e-04 9.762439e-03
115 -5.083804e-02 5.375387e-02 3.311882e-02 -4.293800e-03
116 2.204087e-04 -1.125201e-03 2.128430e-04 1.461817e-03
117 -4.651413e-02 6.244161e-02 3.444468e-02 -1.728488e-02
118 2.100963e-01 -2.173425e-01 -1.524263e-01 -1.084404e-01
119 5.945508e-03 -6.894499e-03 -6.537612e-03 4.726980e-03
120 -3.216510e-02 1.253821e-02 -8.924160e-03 9.159963e-02
121 -2.066215e-02 2.129602e-02 2.012102e-02 -5.793198e-03
122 1.963354e-01 -1.984239e-01 -1.382942e-01 -1.374915e-01
123 4.956939e-02 -3.183381e-02 -9.173975e-03 -1.092296e-01
124 2.146053e-02 5.522475e-03 -7.406930e-03 -8.990017e-02
125 -3.527405e-02 3.713563e-02 3.232388e-02 -4.855510e-03
126 1.211655e-02 -5.514910e-03 -6.141683e-03 -2.717461e-02
127 1.046553e-03 8.508788e-03 2.402738e-03 -2.274311e-02
128 2.361807e-03 -1.201308e-02 4.065066e-03 2.058888e-02
129 -1.834117e-02 4.229146e-02 1.862393e-02 -5.115768e-02
130 3.897136e-02 2.301327e-02 -1.398268e-02 -1.770273e-01
131 4.393588e-03 1.287970e-04 -1.370768e-03 -1.115459e-02
132 -5.702438e-03 3.621146e-02 1.247382e-02 -4.526312e-02
133 8.957119e-03 -7.273543e-03 -4.503772e-03 -1.049544e-02
134 -4.919198e-02 3.323075e-02 2.378259e-02 1.248865e-01
135 1.543274e-03 -1.796253e-03 -1.087391e-03 -4.851391e-04
136 2.229269e-03 -2.280481e-03 -1.577260e-04 -1.397529e-03
137 -7.848521e-03 1.446834e-02 1.870756e-02 -4.025825e-02
138 5.170731e-02 -4.367365e-02 -2.773773e-02 -5.265217e-02
139 4.415999e-02 -4.561276e-02 -3.525202e-02 -4.422923e-03
140 1.386602e-02 -1.756482e-02 -2.157336e-03 1.759038e-02
141 -2.522883e-04 8.132448e-03 8.102575e-04 -1.627399e-02
142 -5.081273e-02 4.335762e-02 1.015681e-02 4.835190e-02
143 2.284359e-02 -2.403256e-02 -2.319976e-02 6.211102e-03
144 -1.469729e-02 1.586965e-02 3.366372e-03 3.589329e-03
145 -4.517440e-02 7.140820e-02 5.290567e-02 -8.067982e-02
146 -8.336864e-03 -1.018974e-02 -8.579733e-03 5.288378e-02
147 4.782795e-04 1.122221e-02 1.170617e-02 -2.270791e-02
148 -4.734508e-03 9.138486e-03 4.946141e-03 -1.014222e-02
149 3.605688e-03 -3.172610e-04 1.148205e-03 -1.619162e-02
150 -1.993954e-03 7.546418e-04 1.604153e-05 -1.442838e-02
151 6.121879e-02 -6.333994e-02 -5.963423e-02 1.741296e-02
152 8.877499e-03 3.258752e-03 -3.367615e-03 -3.915922e-02
153 1.351263e-02 -1.467283e-02 -2.593794e-02 8.504621e-03
154 -7.005912e-03 -2.889643e-04 -1.982786e-03 2.582758e-02
155 9.142357e-02 -9.911045e-02 -1.210271e-01 5.847090e-02
156 -4.908842e-02 5.303170e-02 6.548222e-02 -1.972011e-02
157 -6.906673e-03 1.347333e-02 1.920678e-02 -1.566679e-02
158 1.231283e-02 -1.510505e-02 -2.272407e-02 1.464496e-02
159 9.483280e-03 -6.212387e-03 -8.626163e-03 -1.089719e-02
160 -7.951869e-03 5.615318e-03 8.131401e-03 -1.123185e-03
161 -3.737116e-02 3.248237e-02 3.225022e-02 1.296939e-02
162 -1.176017e-02 5.815177e-03 8.506337e-03 1.370932e-02
163 6.978394e-02 -6.882514e-02 -7.659949e-02 1.169923e-02
164 1.552358e-02 -5.346801e-03 -1.075719e-02 -3.556706e-02
165 -3.348522e-05 7.634811e-04 -1.019504e-03 -2.692450e-03
166 -4.968005e-02 8.587742e-02 1.137360e-01 -1.155877e-01
167 -3.920989e-02 1.749170e-02 2.702077e-02 8.028030e-02
168 -7.337764e-03 2.365313e-02 2.389386e-02 -5.923002e-02
169 -1.531377e-01 1.405156e-01 1.499055e-01 2.063840e-02
170 -1.216827e-01 1.114737e-01 1.354394e-01 4.868884e-02
171 4.413107e-03 4.632039e-04 -1.479101e-04 -1.942128e-02
172 8.480116e-03 -7.140307e-03 -8.715549e-03 -6.946947e-03
173 -1.116072e-01 1.112072e-01 1.412989e-01 -3.237982e-03
174 1.940744e-02 -2.022309e-02 -2.643408e-02 8.917484e-03
175 9.857098e-03 -1.337737e-02 -1.321958e-02 1.988962e-02
176 -3.758280e-02 2.352938e-02 3.516307e-02 3.095456e-02
177 1.200079e-01 -1.294585e-01 -1.246641e-01 5.525448e-02
178 -1.599486e-02 9.323118e-03 1.197999e-02 1.287624e-02
180 1.041808e-03 1.791339e-02 2.268405e-02 -5.063775e-02
181 3.335546e-02 -3.842490e-02 -4.619403e-02 3.205819e-02
182 -1.934805e-02 1.881551e-02 2.300722e-02 1.279273e-04
183 -1.635907e-04 1.364048e-03 2.965656e-03 -1.391750e-02
184 5.358100e-02 -4.488042e-02 -5.257744e-02 -2.078821e-02
185 7.089914e-02 -3.981311e-02 -5.098578e-02 -1.082340e-01
186 -3.707691e-02 6.621875e-03 3.125833e-02 1.952527e-02
187 -4.379479e-02 3.404247e-02 3.864469e-02 2.287600e-02
188 -5.453186e-04 4.282895e-04 7.145164e-04 2.162278e-04
189 1.278986e-01 -1.240813e-01 -1.343032e-01 1.250470e-02
190 -2.691052e-02 2.054825e-02 3.582183e-02 5.319670e-03
191 -4.639778e-02 3.632986e-02 3.561513e-02 3.156628e-02
192 1.758060e-02 9.584205e-04 -6.788218e-04 -6.649628e-02
193 -2.126255e-01 1.806869e-01 1.949618e-01 8.314435e-02
194 -1.194372e-02 4.685045e-03 2.772705e-03 2.655821e-02
195 -2.272941e-02 1.299823e-02 5.467966e-03 3.579946e-02
196 8.886685e-02 -1.075533e-01 -1.346141e-01 7.201063e-02
197 -5.867937e-03 4.824536e-03 5.489325e-03 1.668439e-03
198 3.772217e-02 -4.334227e-02 -4.731884e-02 3.193857e-02
199 -2.629720e-02 1.185841e-02 5.171226e-03 5.406706e-02
200 1.813810e-02 -1.173781e-02 -1.331253e-02 -1.902032e-02
201 2.605449e-02 -2.888565e-02 -1.252757e-02 1.336411e-02
202 2.192717e-02 -1.518740e-02 -2.203935e-02 -1.223398e-02
203 -4.183257e-03 8.343574e-03 1.065274e-02 -1.889311e-02
204 1.235132e-02 -1.151986e-02 -1.541394e-02 -4.865252e-03
205 -3.445589e-02 2.307433e-02 2.856914e-02 3.744142e-02
206 1.468417e-01 -1.172297e-01 -1.455354e-01 -1.038625e-01
207 -4.720882e-03 2.888688e-03 3.212436e-03 5.880229e-03
208 -4.180192e-02 3.661969e-02 4.994013e-02 -1.451666e-02
209 -6.755521e-02 5.279707e-02 5.708493e-02 4.417586e-02
210 -3.449738e-02 3.092890e-02 3.869642e-02 -2.159661e-02
211 -3.921100e-02 3.063926e-02 3.785660e-02 2.314167e-02
212 -9.046892e-03 7.328533e-03 8.986194e-03 5.409828e-03
213 -3.903872e-02 1.854484e-02 1.178577e-02 7.579927e-02
214 -3.307208e-04 3.405112e-04 4.049063e-04 -6.911433e-04
215 2.547713e-03 1.696521e-05 -6.151747e-03 -8.709915e-03
216 4.818555e-02 -3.481792e-02 -4.440349e-02 -3.278709e-02
217 6.737473e-03 9.950855e-05 -4.339390e-04 -2.589272e-02
218 1.607295e-03 -7.900494e-03 -1.213920e-02 2.249159e-02
220 -1.469969e-02 -1.403615e-03 -6.439236e-03 6.069575e-02
221 -1.033683e-02 1.339088e-02 1.570587e-02 -1.548897e-02
222 -1.510381e-02 1.309392e-02 1.629231e-02 5.868100e-03
223 1.441880e-02 -1.217341e-02 -1.129852e-02 -1.659546e-03
224 -3.487155e-02 3.146786e-02 4.707464e-02 -2.409830e-02
225 2.378526e-03 -2.435666e-03 1.528671e-03 -1.315446e-02
226 -1.401934e-02 5.971252e-03 1.903818e-04 2.595501e-02
227 4.708368e-04 9.278476e-04 5.170484e-03 -4.164730e-03
228 -1.585596e-02 -3.004304e-03 -9.489338e-03 7.914677e-02
229 1.555110e-02 -2.084489e-02 -2.561925e-02 2.696596e-02
230 -1.059810e-02 1.256785e-02 1.218559e-02 -4.185323e-02
231 6.573381e-04 -1.035670e-03 -7.055203e-04 1.621952e-03
232 1.182366e-01 -1.108679e-01 -1.762504e-01 6.914479e-02
233 6.000405e-02 -6.169709e-02 -7.275894e-02 2.868947e-02
234 2.233804e-02 -2.043051e-02 -2.568581e-02 1.482533e-03
235 6.293060e-03 -7.506340e-03 -8.259442e-03 7.781477e-03
236 1.468789e-02 -9.382998e-03 -9.746868e-03 -1.702800e-02
237 8.007818e-03 -6.936500e-03 -6.159926e-03 -2.748049e-03
238 -1.715541e-03 2.529501e-03 3.420423e-03 -2.162357e-03
239 -2.752669e-02 3.110801e-02 3.801780e-02 -2.334611e-02
240 6.631120e-02 -6.528843e-02 -8.189912e-02 2.279205e-03
241 -1.545174e-02 1.599216e-02 2.017743e-02 -6.646255e-03
242 -4.792295e-04 1.143153e-02 1.411981e-02 -2.720528e-02
243 -3.885385e-03 2.676104e-03 2.330512e-03 3.076706e-03
244 -1.178108e-02 2.856021e-02 3.483901e-02 -3.378971e-02
245 2.067798e-03 -1.429971e-03 -1.937010e-03 -2.097757e-03
246 -4.760157e-03 5.481908e-04 -2.155929e-03 1.564501e-02
247 1.875871e-02 -1.720086e-02 -2.301435e-02 -3.127698e-04
248 7.244897e-02 -5.062801e-02 -6.078841e-02 -6.592844e-02
249 -3.050358e-03 -1.607315e-02 -1.462287e-02 7.194017e-02
250 1.044975e-02 -5.084705e-03 -5.215462e-03 -1.847986e-02
251 6.208811e-03 -1.169053e-02 -1.395075e-02 2.514682e-02
252 9.347278e-03 3.494835e-03 7.136374e-03 -2.758609e-02
253 2.313449e-02 -1.745425e-02 -1.842213e-02 -1.285088e-02
254 7.874302e-03 4.186402e-03 -1.650408e-03 -1.027331e-02
255 2.367966e-04 2.160953e-04 -4.251695e-03 -4.812601e-03
256 6.653464e-03 -4.394440e-03 -5.422608e-03 -9.020886e-03
258 4.412740e-02 -2.732087e-02 -4.252304e-02 -4.137121e-02
259 6.334885e-02 -5.407460e-02 -6.835776e-02 -1.629526e-02
260 6.530679e-03 -6.357542e-03 -8.161516e-03 3.102158e-03
261 1.028050e-02 -8.290417e-03 -9.305194e-03 -5.545206e-03
262 1.855185e-02 1.575073e-02 1.957149e-02 -1.156072e-01
263 -2.944933e-03 2.660204e-03 3.006105e-03 -3.993198e-04
264 -4.989987e-02 2.056734e-02 2.022262e-02 1.070731e-01
265 -1.374153e-02 1.175314e-02 1.675057e-02 2.743235e-03
266 2.240059e-02 -7.852130e-03 -8.946838e-03 -4.284500e-02
267 3.362067e-02 -1.838676e-02 -2.568869e-02 -5.204559e-02
268 -3.802550e-02 2.659382e-02 3.510045e-02 2.322594e-02
270 2.164113e-02 -2.332518e-02 -4.327302e-02 1.956028e-02
271 -2.531716e-02 2.305945e-02 3.055151e-02 2.780636e-03
273 -3.372246e-03 2.858945e-03 3.431944e-03 9.677802e-04
274 -3.529292e-02 3.004373e-02 3.548838e-02 1.121512e-02
275 5.751102e-02 -4.305039e-02 -6.236149e-02 -4.247277e-02
276 4.957133e-03 5.015895e-04 -3.323399e-04 -2.210732e-02
277 -1.022365e-02 1.140285e-02 1.013337e-02 -2.102049e-04
278 -1.689618e-02 1.398956e-02 1.652359e-02 1.092584e-02
279 -6.705528e-02 5.288343e-02 5.053228e-02 7.329707e-02
280 -9.772559e-03 2.068948e-02 9.200741e-03 -2.322556e-02
281 -1.183355e-01 1.163802e-01 1.167091e-01 5.337378e-02
282 -1.055394e-01 9.195080e-02 7.531303e-02 1.090126e-01
283 4.028402e-04 5.817632e-03 4.075111e-03 -2.014752e-02
284 9.339234e-03 -8.584551e-03 -2.451380e-02 1.016503e-02
285 -7.446261e-02 8.231851e-02 2.835117e-02 3.832947e-02
286 -1.111902e-01 1.075696e-01 1.178057e-01 3.897935e-02
287 -6.454926e-02 6.697222e-02 6.241596e-02 1.279794e-02
288 -9.687166e-02 8.694801e-02 9.607736e-02 5.841216e-02
289 -6.072264e-02 8.903797e-02 9.745721e-02 -9.214157e-02
290 2.098052e-03 -1.078861e-03 -2.844046e-03 -2.063676e-03
291 -4.463597e-02 5.063340e-02 5.348734e-02 -4.398101e-03
292 -3.625446e-03 3.897512e-03 4.407660e-03 -5.411869e-04
293 -2.241064e-01 2.017456e-01 2.407178e-01 9.898992e-02
294 -1.852371e-02 2.920232e-02 8.105004e-02 -1.710815e-01
295 -1.509737e-03 2.493004e-03 1.320468e-03 -2.172208e-03
296 -1.769946e-02 3.282683e-02 4.589669e-02 -3.404837e-02
297 -1.992591e-02 8.529351e-02 5.731206e-02 -1.365500e-01
298 4.734278e-02 -7.593629e-02 -1.000915e-01 7.178569e-02
299 4.010502e-02 -6.112520e-02 -5.871719e-02 1.865722e-02
300 -3.331009e-02 2.551970e-02 2.758764e-02 3.382365e-02
301 3.762708e-02 -3.550454e-02 -3.230371e-02 -1.948172e-02
302 2.346986e-02 -2.315294e-02 -1.863622e-02 -1.553712e-02
303 3.483647e-02 -1.526272e-02 -2.080990e-02 -4.373575e-02
304 -1.251735e-02 1.385677e-02 1.657111e-02 -1.256018e-02
305 -4.654294e-02 5.437323e-02 4.960777e-02 -9.172924e-03
306 1.538490e-01 -1.819515e-01 -1.861437e-01 3.889589e-02
307 -1.600719e-03 4.424529e-03 2.687275e-03 -6.710991e-04
308 1.781437e-01 -1.861673e-01 -1.937289e-01 -3.415629e-02
309 -1.412381e-02 2.408494e-02 2.051542e-02 -7.061104e-03
310 1.010950e-04 -2.978478e-04 -1.944175e-04 5.691673e-04
311 -1.409293e-02 2.217856e-03 -2.633405e-03 3.717419e-02
312 -1.390760e-01 1.115265e-01 1.335206e-01 1.104423e-01
313 -4.818631e-02 4.455313e-02 3.685850e-02 2.023312e-02
314 2.662272e-01 -3.257955e-01 -3.637243e-01 1.486059e-01
315 2.152117e-01 -2.104244e-01 -2.524853e-01 -4.511119e-02
316 1.384078e-01 -1.655629e-01 -1.628236e-01 3.039425e-02
317 -3.023636e-03 2.619315e-02 3.858526e-02 -1.033049e-01
318 -4.645856e-02 6.606823e-02 6.484262e-02 -4.994964e-02
319 -7.072603e-02 6.104532e-02 5.801846e-02 5.590536e-02
320 -1.455851e-02 1.301665e-02 1.366698e-02 1.132697e-02
321 -1.963623e-02 1.457843e-02 2.021594e-02 5.573231e-03
322 -8.728342e-03 -4.338119e-03 1.115234e-02 3.726902e-02
323 8.968628e-03 -9.730391e-03 -1.254311e-02 9.565133e-03
324 3.863644e-04 -6.774068e-03 -9.957023e-03 2.779237e-02
325 -1.125148e-01 5.396816e-02 3.035810e-02 2.651625e-01
326 -3.169930e-02 2.492092e-02 3.172102e-02 1.788170e-02
327 9.744314e-02 -7.899417e-02 -9.911748e-02 -6.776395e-02
328 -1.230288e-02 1.598651e-02 1.341019e-02 -5.806007e-03
329 -4.108419e-02 4.187201e-02 4.164628e-02 1.513439e-02
330 -1.117661e-02 1.302760e-02 1.463954e-02 -4.927394e-03
331 -1.107533e-02 1.953984e-02 1.361978e-02 -8.005602e-03
332 -6.875174e-02 6.990232e-02 4.356163e-02 5.663334e-02
333 2.085255e-02 -2.205844e-02 -2.461244e-02 -4.931453e-03
334 -8.633503e-03 9.588255e-03 1.291810e-02 -5.663228e-03
335 -4.083223e-03 1.317544e-02 9.925962e-03 -3.362141e-02
336 -1.704606e-04 2.415617e-04 -5.013673e-06 1.049817e-05
337 -3.942188e-02 5.546332e-02 5.493191e-02 -3.917388e-02
338 -8.662535e-02 9.314106e-02 1.127490e-01 -1.207010e-02
339 -5.742024e-02 5.298396e-02 5.636745e-02 3.705377e-02
340 -9.366229e-02 1.174133e-01 1.065377e-01 -2.257701e-02
341 4.642247e-02 -3.793772e-02 -2.381080e-02 -6.890020e-02
342 1.538185e-03 -7.752452e-03 -1.222137e-02 1.976207e-02
343 1.426055e-03 1.123487e-02 9.902993e-03 -4.403229e-02
344 -1.082659e-02 1.982541e-03 2.028067e-03 1.512783e-02
speciesChinstrap speciesGentoo sexmale bill_depth_mm:bill_length_mm
1 -1.275235e-03 -8.415059e-03 -1.349387e-02 1.749778e-03
2 -1.196265e-01 -6.098840e-02 -7.796553e-02 2.576984e-02
3 1.076535e-01 9.636279e-02 1.164629e-01 -5.016674e-04
5 -7.819121e-03 -9.378456e-03 6.525218e-02 4.218342e-02
6 -5.262325e-02 -1.239369e-01 -1.337826e-02 9.597361e-02
7 -6.748839e-02 1.330450e-02 -5.442725e-02 1.312956e-02
8 4.034614e-02 8.591312e-03 6.463600e-02 -8.475647e-02
13 6.323843e-02 1.411606e-02 3.817931e-02 -8.842411e-03
14 -8.191619e-02 -1.324385e-01 8.248132e-03 1.274412e-01
15 6.553984e-02 2.492217e-02 9.146321e-03 -8.271890e-02
16 -1.924408e-02 1.296358e-02 -4.535328e-02 8.298873e-03
17 2.862932e-02 1.740329e-02 8.225361e-02 2.273031e-02
18 -4.722011e-02 2.319230e-02 -3.757755e-02 1.245979e-02
19 -5.744082e-03 -7.520780e-03 4.341203e-03 4.235871e-03
20 3.351459e-03 -1.769360e-03 2.278473e-03 -3.124031e-03
21 -1.891298e-02 5.125098e-02 -2.596244e-02 -6.008050e-04
22 -2.252348e-02 -4.130386e-02 -5.872983e-02 1.284197e-02
23 2.530934e-02 3.670309e-02 -7.290325e-02 -5.993835e-02
24 1.003176e-02 7.433744e-03 5.931479e-02 -1.729236e-03
25 -4.993813e-03 1.365375e-03 7.971109e-02 1.511606e-02
26 4.058526e-02 5.453353e-02 -7.183390e-02 -6.476047e-02
27 2.659558e-02 -2.594333e-02 -7.388152e-02 -1.012895e-03
28 8.518504e-02 3.268591e-02 7.213468e-02 -7.428511e-03
29 8.265732e-03 -3.142206e-02 1.450712e-02 2.630241e-03
30 -1.021815e-02 2.929598e-02 3.509379e-02 -6.450883e-04
31 -1.943517e-02 -4.489998e-03 -3.324442e-03 8.082209e-03
32 3.332356e-02 5.631843e-02 1.106308e-01 -1.211755e-03
33 3.882950e-02 1.907006e-02 3.580416e-02 -3.950139e-03
34 -2.173724e-03 2.256475e-03 4.355727e-03 -1.918272e-05
35 9.842178e-03 2.809970e-02 1.004607e-02 -1.290369e-02
36 -1.487504e-02 -2.098811e-02 6.245500e-03 2.706792e-02
37 -1.297852e-02 -1.962420e-02 -1.171569e-02 2.002809e-02
38 -6.337790e-02 9.706449e-03 -5.226187e-02 8.955797e-03
39 4.698780e-03 -4.175310e-02 4.373015e-02 2.205821e-02
40 -4.398850e-03 1.293877e-01 1.709951e-01 -4.103063e-02
41 5.602839e-03 -2.175288e-02 2.136111e-02 1.107328e-04
42 1.404338e-02 2.541353e-02 -2.370388e-02 1.918009e-03
43 -1.315798e-02 -3.996812e-02 6.352428e-02 3.370851e-02
44 -8.357760e-02 -2.402414e-02 -1.721044e-02 3.164976e-02
45 3.813239e-02 2.485461e-02 1.102146e-02 -4.116481e-02
46 -2.669916e-03 -2.313289e-03 1.431057e-01 -3.608756e-02
47 4.994348e-02 -6.995828e-02 -8.746293e-02 -3.819430e-03
49 -7.050788e-05 -7.670697e-04 -3.021021e-03 -1.836130e-04
50 1.393829e-03 -3.066604e-03 1.500153e-03 -4.817756e-04
51 -2.551110e-02 -9.637516e-03 -2.053393e-02 3.648302e-03
52 -1.413601e-02 1.497306e-02 7.499799e-02 -1.446710e-02
53 2.533403e-03 -1.674916e-04 -4.379841e-03 -5.850731e-04
54 2.432946e-02 2.503157e-02 3.548235e-04 7.167000e-04
55 -5.872352e-02 -4.816971e-02 5.105599e-02 2.631594e-02
56 4.264127e-02 2.989876e-02 -4.943123e-02 -1.061151e-03
57 -4.156724e-02 -1.902755e-02 -3.069141e-02 9.593969e-03
58 1.783333e-02 2.089023e-02 -3.647005e-02 6.741131e-03
59 4.074364e-02 7.373976e-03 -1.048626e-02 -6.931503e-02
60 -4.834975e-02 -1.437305e-03 -6.399234e-02 4.758657e-02
61 4.879430e-03 3.408372e-03 -5.263893e-05 -1.563426e-02
62 -8.335595e-03 3.742761e-02 -2.291208e-02 -1.121779e-02
63 -5.530610e-02 -3.277290e-02 -2.251323e-02 4.032203e-02
64 -1.286371e-02 -1.617098e-02 1.990247e-02 3.448242e-04
65 3.645053e-02 8.986343e-03 1.537217e-02 -5.627246e-02
66 1.042976e-03 1.267560e-03 -1.268476e-03 -7.698655e-05
67 -3.004325e-03 -1.032888e-02 6.236776e-04 9.101746e-03
68 -1.518843e-02 6.332833e-03 2.078720e-02 -1.351771e-03
69 2.238444e-02 4.690108e-02 1.184289e-03 -5.305431e-02
70 -4.569530e-02 -4.153886e-02 8.430374e-03 -2.802257e-03
71 2.211632e-02 1.293165e-02 -1.532962e-02 -2.361503e-02
72 7.839375e-04 1.619622e-03 -6.467602e-03 6.317641e-04
73 -5.560480e-03 -7.323235e-03 -4.270252e-03 8.895526e-04
74 -2.635090e-03 -1.661701e-03 -2.211927e-04 7.437410e-04
75 7.324794e-04 -2.228083e-02 -2.955799e-02 2.008084e-02
76 -5.144043e-02 -4.915072e-02 2.275751e-02 5.567054e-03
77 -1.042642e-01 -1.027645e-01 -5.014027e-02 1.461877e-02
78 2.376671e-03 2.895736e-03 2.900826e-03 -2.141877e-03
79 -5.320045e-02 -7.305533e-02 2.172178e-02 1.083479e-01
80 1.639057e-02 1.139827e-02 -6.210661e-03 -1.110061e-03
81 -4.502782e-03 5.286813e-03 2.512584e-03 -1.471139e-02
82 -2.077134e-01 -3.006030e-01 1.459354e-01 4.294693e-03
83 2.268720e-03 3.734878e-02 -8.169907e-02 -4.284000e-02
84 7.202035e-02 2.280775e-02 5.157776e-02 -5.974517e-02
85 1.134867e-02 1.280072e-02 2.065945e-02 -1.129809e-03
86 4.724205e-02 -6.185167e-02 1.858042e-02 2.593157e-02
87 -5.971676e-02 -3.429537e-02 -4.944673e-02 5.446762e-02
88 -3.183321e-05 6.156142e-05 -3.682198e-04 -1.505935e-04
89 -1.447989e-03 -1.309363e-03 -2.694916e-03 1.649895e-03
90 -7.130060e-03 -3.928591e-04 -1.502380e-02 -3.050435e-03
91 -2.316860e-03 2.393216e-02 1.997043e-02 5.277024e-03
92 -1.978936e-02 -6.397514e-02 2.035981e-02 -3.675777e-03
93 1.320821e-02 9.378438e-03 6.104765e-03 3.170131e-02
94 -2.479083e-02 -1.259796e-02 2.034130e-01 2.357255e-03
95 1.310230e-03 1.162301e-03 1.553301e-03 -2.137162e-03
96 -2.385301e-03 -1.063051e-02 1.382081e-03 -1.747569e-03
97 -1.953186e-02 -2.447957e-03 -5.109560e-02 -1.265062e-02
98 -2.245447e-02 -6.185592e-02 5.987118e-02 -1.051099e-02
99 -2.574370e-03 -8.567250e-03 -1.355051e-02 -2.882484e-02
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334 -1.296119e-02 -7.470834e-03 -3.275151e-03 -1.154499e-02
335 -5.305340e-02 2.618428e-02 -4.585287e-02 -7.674952e-03
336 7.192639e-04 6.127100e-04 -6.012225e-04 -6.517898e-05
337 -8.847362e-03 1.388884e-02 -8.595923e-04 -5.737689e-02
338 7.382687e-02 -6.365408e-02 1.161197e-02 -1.116857e-01
339 6.793160e-02 -4.114560e-02 -5.215709e-03 -6.140538e-02
340 6.108885e-02 1.995342e-02 3.450180e-02 -1.213075e-01
341 -8.261595e-02 9.830872e-03 2.087336e-02 3.585611e-02
342 -3.241506e-02 1.964567e-03 -4.113481e-02 1.270491e-02
343 -1.638582e-02 2.744784e-02 -8.337150e-03 -8.736957e-03
344 -3.375460e-03 -9.354263e-03 -6.424057e-02 3.825931e-03#We can subset by the observations of interest
dffits(penmod3)[c(15,40,170,294,314,315)] 20 45 176 305 325 326
-0.006256213 -0.111866703 -0.100099623 0.147376774 -0.400590799 0.061502594 #Note those observation numbers do not match becasue there are missing values
# in the penguins data frame
dim(pendata)[1] 344 9length(dfpen)[1] 333#remove na values from data
pennasubset<-na.omit(pendata)
dim(pennasubset)[1] 333 9#Then we will want to renumber the observations
row.names(pennasubset) <- 1:nrow(pennasubset)
#Note this is the SAME model because the missing values were not used to fit
penmodna<-lm(body_mass_g~bill_depth_mm+bill_length_mm+flipper_length_mm+bill_depth_mm*bill_length_mm+species+sex,data=pennasubset)
summary(penmodna)
Call:
lm(formula = body_mass_g ~ bill_depth_mm + bill_length_mm + flipper_length_mm +
bill_depth_mm * bill_length_mm + species + sex, data = pennasubset)
Residuals:
Min 1Q Median 3Q Max
-706.90 -175.12 -6.14 176.80 880.08
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -6290.446 1832.633 -3.432 0.000675 ***
bill_depth_mm 333.924 98.231 3.399 0.000760 ***
bill_length_mm 130.274 41.058 3.173 0.001653 **
flipper_length_mm 16.535 2.888 5.725 2.35e-08 ***
speciesChinstrap -200.763 82.322 -2.439 0.015273 *
speciesGentoo 923.788 132.379 6.978 1.68e-11 ***
sexmale 391.603 47.370 8.267 3.55e-15 ***
bill_depth_mm:bill_length_mm -6.344 2.290 -2.770 0.005919 **
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 284.4 on 325 degrees of freedom
Multiple R-squared: 0.8778, Adjusted R-squared: 0.8752
F-statistic: 333.7 on 7 and 325 DF, p-value: < 2.2e-16#revisit outliers/influential observations
#Cooks Distance Thresholds
plot(penmodna,which=4)
#Leverage vs Studentized Residuals
influencePlot(penmodna,fill=F)
#Now subset the dffits and or dfbetas
dffits(penmodna)[c(10,35,164,283,303,304)] 10 35 164 283 303 304
0.1286874 0.3818284 0.3833745 0.3424947 0.5436063 -0.4620501 mean(dffits(penmodna))[1] 0.001632512Cautions on removing observations
- We want to retain as much data as possible
- If we remove some extreme observations then other observations may be identified as extreme
Additional Notes on subsetting
#We can subset based on variable conditions
##Quantitative Variables
quantsubsetpen<-pendata[which(pendata$bill_depth_mm<17.3),]
# Qualitative Variables
qualsubsetpen<-pendata[which(pendata$species=="Gentoo"),]
# Multiple Arguments
multaubsetpen1<-pendata[which(pendata$species=="Gentoo"&pendata$bill_depth_mm<17.3),]
multaubsetpen2<-pendata[which(pendata$species=="Gentoo"|pendata$bill_depth_mm<17.3),]