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
Although no transformations were needed, here is an example of how we would interpret and code for a few different variable transformations.
#attempt transformations within plot to create a more linear relationship
# ORIGINAL
plot((body_mass_g)~flipper_length_mm,data=pendata)
#You can transform both x and y in any function
# ATTEMPT combinations of log and square root of x and y
plot(sqrt(body_mass_g)~sqrt(flipper_length_mm),data=pendata)
# compute correlations
cor(pendata$body_mass_g,pendata$flipper_length_mm)[1] NA# note the NA because of missing values
# add the use= argument
cor(pendata$body_mass_g,pendata$flipper_length_mm, use="complete.obs")[1] 0.8712018cor(log(pendata$body_mass_g),log(pendata$flipper_length_mm), use="complete.obs")[1] 0.8588604#Within lm() we can add both transformations
# try several
penmodT<-lm(body_mass_g~bill_depth_mm+bill_length_mm+flipper_length_mm+bill_depth_mm*bill_length_mm+species+sex,data=pendata)
summary(penmodT)
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-16NOTE:
- When we transform the explanatory variables, the interpretations do not change drastically
- EX: for a one unit increase in the transformed value of X (square root of flipper length), the predicted value of y changes by beta hat_i
- Similarly, the transformation for y follow:
- EX: for a one unit increase in the value of x, the predicted value of the transformed value of y (square root of y) changes by beta hat_i
- Prediction Interval: When we have ~ this set of explanatory variables~ we expect the square root of y to be between the interval computed.
- Prediction Interval Transformed: When we have ~ this set of explanatory variables~ we expect the value y to be between the interval computed if we inverse the transformation of the end points
- Confidence Interval: When we have ~ This set of explanatory variables~ we expect the average of the transformed value of y to be between the interval computed.
- Confidence Interval: we cannot perform the inverse of the transformation to get the original units.
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
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307 2.222478e-02 4.246051e-03 8.269808e-03 -5.600996e-03
308 -4.943889e-02 7.656349e-02 -4.666698e-02 2.066912e-01
309 7.299275e-02 9.206061e-03 2.350198e-02 -2.870739e-02
310 5.264133e-04 -5.589803e-04 5.398850e-04 2.057440e-04
311 -8.233314e-02 -9.095839e-03 -8.832824e-02 4.719030e-03
312 7.136670e-02 -1.459091e-01 -3.192034e-02 -1.339348e-01
313 6.091075e-02 3.257887e-04 -7.873429e-02 -3.671271e-02
314 -4.064124e-04 7.753382e-02 -1.000344e-01 3.671179e-01
315 -1.638647e-01 1.804764e-01 -1.915482e-03 2.522256e-01
316 -3.844702e-02 6.637485e-03 -3.248204e-02 1.764864e-01
317 -7.397138e-02 2.258771e-02 -1.962419e-02 -2.814781e-02
318 8.971433e-02 2.011702e-02 -1.464786e-02 -6.703005e-02
319 -5.792320e-02 -3.643684e-02 -6.501107e-02 -6.245157e-02
320 1.756138e-02 -1.093209e-02 -1.290800e-03 -1.514922e-02
321 -5.699774e-03 -2.127262e-02 -3.004073e-02 -1.521576e-02
322 6.094367e-02 -6.312448e-02 7.524529e-02 -9.918608e-03
323 -2.287507e-06 3.798757e-03 1.576579e-02 9.467938e-03
324 1.699802e-02 -6.531350e-03 3.043735e-03 7.369955e-03
325 -5.650885e-02 -1.029239e-01 -1.409802e-01 -5.000041e-02
326 2.991025e-03 -3.367656e-02 -2.012436e-02 -2.859736e-02
327 -3.350774e-02 1.094548e-01 1.282046e-02 9.712011e-02
328 -1.139791e-02 7.332487e-03 -1.334333e-02 -1.477295e-02
329 5.877659e-02 -1.634564e-02 -8.489053e-03 -4.569704e-02
330 -7.456243e-03 -3.939381e-03 -2.188449e-03 -1.442869e-02
331 5.452913e-02 1.695344e-02 9.975386e-03 -1.987255e-02
332 -2.103361e-02 2.434869e-02 -7.623139e-02 -6.041348e-02
333 -3.038676e-02 1.402478e-02 -5.760742e-03 2.669455e-02
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 because 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
# You can store the subset data in a new object or you can include the subset
# directly into whatever code you perform, plot, lm, cor, etc
##Quantitative Variables
quantsubsetpen<-pendata[which(pendata$bill_depth_mm<17.3),]
#Example
plot((body_mass_g)~flipper_length_mm,data=quantsubsetpen)
plot((body_mass_g)~flipper_length_mm,data=pendata[which(pendata$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),]