rpkm_lm
Charles Otieno
7/2/2019
library(tidyverse)
library(readr)rpkm_data <- read.csv("rpkm.csv", stringsAsFactors = FALSE)Data cleaning
Remove unnecesary and non numeric columns as linear model works best with numeric dataframes only
rpkm2 <- rpkm_data[, - c(1:2)]
str(rpkm2)## 'data.frame': 814 obs. of 23 variables:
## $ MCF7_ER_veh : int 3 4 13 2 1 1 5 2 6 1 ...
## $ MCF7_ER_E2 : int 4 4 13 2 1 2 8 2 5 4 ...
## $ MCF7_FoxA1_veh : int 1 0 3 2 1 0 3 2 3 0 ...
## $ MCF7_FoxA1_E2 : int 1 1 6 2 1 0 4 2 3 2 ...
## $ MCF7_AP2g_veh : int 0 3 4 0 0 2 2 0 2 0 ...
## $ MCF7_AP2g_E2 : int 2 4 7 1 1 1 3 1 3 1 ...
## $ MCF7_TEAD4_veh : int 2 3 6 1 1 1 3 2 3 0 ...
## $ MCF7_TCF12_veh : int 3 3 6 2 1 1 6 2 5 0 ...
## $ MCF7_P300_veh : int 2 4 7 2 0 1 3 1 2 2 ...
## $ MCF7_H3K27ac_veh : int 1 4 8 2 1 2 6 1 3 1 ...
## $ Ishikawa_TEAD4_veh : int 7 4 6 2 1 3 9 5 6 5 ...
## $ Ishikawa_TCF12_veh : int 7 4 10 2 0 3 10 5 6 6 ...
## $ Ishikawa_FoxM1_veh : int 6 4 6 2 0 3 9 5 5 5 ...
## $ Ishikawa_CEBPB_veh : int 6 4 5 2 0 2 9 5 6 6 ...
## $ Ishikawa_P300_veh : int 6 4 6 2 0 3 10 4 6 6 ...
## $ Ishikawa_H3K27ac_veh : int 1 4 4 2 0 2 3 1 3 3 ...
## $ ERE_motif.total. : int 0 4 6 2 10 2 5 2 2 4 ...
## $ Fox_motif.total. : int 1 0 3 0 0 0 1 0 0 0 ...
## $ AP2_motif.total. : int 3 2 14 0 0 0 1 0 0 0 ...
## $ TEAD_motif.total. : int 0 0 3 0 3 0 1 1 1 1 ...
## $ TCF_motif.total. : int 1 1 0 0 0 0 1 0 0 2 ...
## $ CEBP_motif.total. : int 0 0 0 0 0 0 0 2 0 1 ...
## $ Fold.Change.MCF7.Ishikawa: num 0.0274 0.4903 0.4094 0.1786 18.515 ...Remove NAs from the dataset. Previously before cleaning the data there were 82 NAs. They can either be removed or rplaced with zeros unless they have significance in the dataset.
rpkm2 <- na.omit(rpkm2)
sum(is.na(rpkm2))## [1] 0Explore the dependent variable to be modeled, check if the data is normalized or with the standard scale. The fold change is used in this case as the depended variable and the rest of the columns used as predictos of the fold chage. First, we need to examine the dependent varibe, confirm if it as a numric vector and if not transform it. Also, we can verify whether it is normally distibuted though it is not very necessary but essential for smooth modeling with linear regression.
str(rpkm2$Fold.Change.MCF7.Ishikawa)## num [1:814] 0.0274 0.4903 0.4094 0.1786 18.515 ...summary(rpkm2$Fold.Change.MCF7.Ishikawa)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.000 0.175 0.580 23.225 1.937 6659.016
Normalize the dataset
normalize <- function(x){
return((x - min(x)) / (max(x) -min(x)))
}Confirm whether the normalize function is effective
normalize(c(1:5))## [1] 0.00 0.25 0.50 0.75 1.00Normalize the dataset
lm_rpkm2_n <- as.data.frame(lapply(rpkm2, normalize))summary(lm_rpkm2_n$Fold.Change.MCF7.Ishikawa)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0000000 0.0000263 0.0000872 0.0034878 0.0002909 1.0000000par(mar = c(1,1,1,1))Explore relationship between the variables using corelation function
cor(lm_rpkm2_n[c("MCF7_ER_veh" ,"MCF7_ER_E2" , "MCF7_FoxA1_veh" , "MCF7_FoxA1_E2",
"MCF7_AP2g_veh" , "MCF7_AP2g_E2", "MCF7_TEAD4_veh", "MCF7_TCF12_veh",
"MCF7_P300_veh", "MCF7_H3K27ac_veh","Ishikawa_TEAD4_veh","Ishikawa_TCF12_veh",
"Ishikawa_FoxM1_veh" , "Ishikawa_CEBPB_veh" , "Ishikawa_P300_veh","Ishikawa_H3K27ac_veh",
"ERE_motif.total.", "Fox_motif.total." , "AP2_motif.total." , "TEAD_motif.total." ,
"TCF_motif.total." ,"CEBP_motif.total.", "Fold.Change.MCF7.Ishikawa")])## MCF7_ER_veh MCF7_ER_E2 MCF7_FoxA1_veh
## MCF7_ER_veh 1.00000000 0.97932075 0.86970220
## MCF7_ER_E2 0.97932075 1.00000000 0.84589467
## MCF7_FoxA1_veh 0.86970220 0.84589467 1.00000000
## MCF7_FoxA1_E2 0.92896064 0.91825502 0.95039846
## MCF7_AP2g_veh 0.83675811 0.80346260 0.88823013
## MCF7_AP2g_E2 0.91154864 0.89243428 0.90693301
## MCF7_TEAD4_veh 0.95218988 0.93737590 0.89900390
## MCF7_TCF12_veh 0.94475119 0.92911808 0.90445835
## MCF7_P300_veh 0.93998872 0.92663191 0.83085478
## MCF7_H3K27ac_veh 0.91425766 0.91168687 0.81931297
## Ishikawa_TEAD4_veh 0.58917357 0.58190060 0.39213694
## Ishikawa_TCF12_veh 0.64281754 0.64066914 0.42573510
## Ishikawa_FoxM1_veh 0.48902265 0.47884432 0.31503373
## Ishikawa_CEBPB_veh 0.48305327 0.47412466 0.31048212
## Ishikawa_P300_veh 0.58689557 0.58308853 0.37300717
## Ishikawa_H3K27ac_veh 0.63193564 0.62478882 0.45045749
## ERE_motif.total. 0.72942212 0.76158422 0.50914615
## Fox_motif.total. 0.61731980 0.61329182 0.68547671
## AP2_motif.total. 0.71732599 0.73029739 0.46557780
## TEAD_motif.total. 0.45664430 0.45096984 0.41967373
## TCF_motif.total. 0.35936871 0.35422283 0.18494779
## CEBP_motif.total. 0.45380117 0.44975855 0.48050084
## Fold.Change.MCF7.Ishikawa 0.03840663 0.03217865 0.09166449
## MCF7_FoxA1_E2 MCF7_AP2g_veh MCF7_AP2g_E2
## MCF7_ER_veh 0.92896064 0.83675811 0.91154864
## MCF7_ER_E2 0.91825502 0.80346260 0.89243428
## MCF7_FoxA1_veh 0.95039846 0.88823013 0.90693301
## MCF7_FoxA1_E2 1.00000000 0.87383965 0.92485082
## MCF7_AP2g_veh 0.87383965 1.00000000 0.93819786
## MCF7_AP2g_E2 0.92485082 0.93819786 1.00000000
## MCF7_TEAD4_veh 0.93565685 0.86738593 0.92678504
## MCF7_TCF12_veh 0.93676044 0.87888074 0.93226104
## MCF7_P300_veh 0.87826175 0.88194606 0.92644187
## MCF7_H3K27ac_veh 0.86384799 0.85807770 0.90568939
## Ishikawa_TEAD4_veh 0.44455461 0.45156837 0.49876960
## Ishikawa_TCF12_veh 0.48612611 0.48857998 0.54321581
## Ishikawa_FoxM1_veh 0.34681035 0.38310746 0.41539445
## Ishikawa_CEBPB_veh 0.34781076 0.38077441 0.41328814
## Ishikawa_P300_veh 0.43168290 0.44113940 0.48967645
## Ishikawa_H3K27ac_veh 0.49770212 0.52623299 0.55786781
## ERE_motif.total. 0.61781685 0.51128127 0.61547356
## Fox_motif.total. 0.67547279 0.57558845 0.61545269
## AP2_motif.total. 0.56445337 0.51296661 0.60924232
## TEAD_motif.total. 0.42222672 0.37961696 0.40603947
## TCF_motif.total. 0.23680327 0.23637306 0.27568640
## CEBP_motif.total. 0.46429440 0.40367221 0.43333146
## Fold.Change.MCF7.Ishikawa 0.06997451 0.08843374 0.07080236
## MCF7_TEAD4_veh MCF7_TCF12_veh MCF7_P300_veh
## MCF7_ER_veh 0.95218988 0.94475119 0.93998872
## MCF7_ER_E2 0.93737590 0.92911808 0.92663191
## MCF7_FoxA1_veh 0.89900390 0.90445835 0.83085478
## MCF7_FoxA1_E2 0.93565685 0.93676044 0.87826175
## MCF7_AP2g_veh 0.86738593 0.87888074 0.88194606
## MCF7_AP2g_E2 0.92678504 0.93226104 0.92644187
## MCF7_TEAD4_veh 1.00000000 0.97450583 0.92982099
## MCF7_TCF12_veh 0.97450583 1.00000000 0.92397710
## MCF7_P300_veh 0.92982099 0.92397710 1.00000000
## MCF7_H3K27ac_veh 0.90024782 0.89586237 0.93920799
## Ishikawa_TEAD4_veh 0.55373240 0.54042656 0.61917703
## Ishikawa_TCF12_veh 0.59704648 0.58274268 0.67275128
## Ishikawa_FoxM1_veh 0.46839256 0.45281278 0.52817677
## Ishikawa_CEBPB_veh 0.45976532 0.45023949 0.52248940
## Ishikawa_P300_veh 0.54363017 0.53145953 0.62227581
## Ishikawa_H3K27ac_veh 0.59526988 0.58016072 0.66429167
## ERE_motif.total. 0.65770977 0.64752562 0.69893406
## Fox_motif.total. 0.59600224 0.59221425 0.56408760
## AP2_motif.total. 0.64425403 0.62888744 0.72192430
## TEAD_motif.total. 0.45385770 0.42338192 0.42951859
## TCF_motif.total. 0.29604213 0.28336815 0.38828890
## CEBP_motif.total. 0.47780070 0.47905281 0.41026363
## Fold.Change.MCF7.Ishikawa 0.05372959 0.05945942 0.04585309
## MCF7_H3K27ac_veh Ishikawa_TEAD4_veh
## MCF7_ER_veh 0.91425766 0.58917357
## MCF7_ER_E2 0.91168687 0.58190060
## MCF7_FoxA1_veh 0.81931297 0.39213694
## MCF7_FoxA1_E2 0.86384799 0.44455461
## MCF7_AP2g_veh 0.85807770 0.45156837
## MCF7_AP2g_E2 0.90568939 0.49876960
## MCF7_TEAD4_veh 0.90024782 0.55373240
## MCF7_TCF12_veh 0.89586237 0.54042656
## MCF7_P300_veh 0.93920799 0.61917703
## MCF7_H3K27ac_veh 1.00000000 0.61938363
## Ishikawa_TEAD4_veh 0.61938363 1.00000000
## Ishikawa_TCF12_veh 0.66645290 0.96920689
## Ishikawa_FoxM1_veh 0.53328934 0.95457756
## Ishikawa_CEBPB_veh 0.53321753 0.94515475
## Ishikawa_P300_veh 0.62181210 0.97513805
## Ishikawa_H3K27ac_veh 0.68197726 0.88458045
## ERE_motif.total. 0.67965988 0.45423220
## Fox_motif.total. 0.57472842 0.21241283
## AP2_motif.total. 0.68151280 0.55536471
## TEAD_motif.total. 0.44152828 0.54079312
## TCF_motif.total. 0.38480685 0.48779443
## CEBP_motif.total. 0.38807826 0.32638685
## Fold.Change.MCF7.Ishikawa 0.04594538 -0.08190802
## Ishikawa_TCF12_veh Ishikawa_FoxM1_veh
## MCF7_ER_veh 0.64281754 0.48902265
## MCF7_ER_E2 0.64066914 0.47884432
## MCF7_FoxA1_veh 0.42573510 0.31503373
## MCF7_FoxA1_E2 0.48612611 0.34681035
## MCF7_AP2g_veh 0.48857998 0.38310746
## MCF7_AP2g_E2 0.54321581 0.41539445
## MCF7_TEAD4_veh 0.59704648 0.46839256
## MCF7_TCF12_veh 0.58274268 0.45281278
## MCF7_P300_veh 0.67275128 0.52817677
## MCF7_H3K27ac_veh 0.66645290 0.53328934
## Ishikawa_TEAD4_veh 0.96920689 0.95457756
## Ishikawa_TCF12_veh 1.00000000 0.92829952
## Ishikawa_FoxM1_veh 0.92829952 1.00000000
## Ishikawa_CEBPB_veh 0.92493926 0.95561394
## Ishikawa_P300_veh 0.97176311 0.94317156
## Ishikawa_H3K27ac_veh 0.89916605 0.86182682
## ERE_motif.total. 0.51083356 0.34703814
## Fox_motif.total. 0.24198020 0.14166582
## AP2_motif.total. 0.60711626 0.47594055
## TEAD_motif.total. 0.53803575 0.52727707
## TCF_motif.total. 0.48968910 0.46612118
## CEBP_motif.total. 0.32568462 0.29140231
## Fold.Change.MCF7.Ishikawa -0.08202009 -0.08296293
## Ishikawa_CEBPB_veh Ishikawa_P300_veh
## MCF7_ER_veh 0.48305327 0.58689557
## MCF7_ER_E2 0.47412466 0.58308853
## MCF7_FoxA1_veh 0.31048212 0.37300717
## MCF7_FoxA1_E2 0.34781076 0.43168290
## MCF7_AP2g_veh 0.38077441 0.44113940
## MCF7_AP2g_E2 0.41328814 0.48967645
## MCF7_TEAD4_veh 0.45976532 0.54363017
## MCF7_TCF12_veh 0.45023949 0.53145953
## MCF7_P300_veh 0.52248940 0.62227581
## MCF7_H3K27ac_veh 0.53321753 0.62181210
## Ishikawa_TEAD4_veh 0.94515475 0.97513805
## Ishikawa_TCF12_veh 0.92493926 0.97176311
## Ishikawa_FoxM1_veh 0.95561394 0.94317156
## Ishikawa_CEBPB_veh 1.00000000 0.94257666
## Ishikawa_P300_veh 0.94257666 1.00000000
## Ishikawa_H3K27ac_veh 0.85387405 0.88950428
## ERE_motif.total. 0.34829488 0.47639890
## Fox_motif.total. 0.14134456 0.20601074
## AP2_motif.total. 0.45258459 0.56760255
## TEAD_motif.total. 0.51280466 0.52674344
## TCF_motif.total. 0.44097579 0.49038683
## CEBP_motif.total. 0.30743884 0.30646605
## Fold.Change.MCF7.Ishikawa -0.07892432 -0.08502347
## Ishikawa_H3K27ac_veh ERE_motif.total.
## MCF7_ER_veh 0.63193564 0.7294221242
## MCF7_ER_E2 0.62478882 0.7615842158
## MCF7_FoxA1_veh 0.45045749 0.5091461478
## MCF7_FoxA1_E2 0.49770212 0.6178168474
## MCF7_AP2g_veh 0.52623299 0.5112812749
## MCF7_AP2g_E2 0.55786781 0.6154735565
## MCF7_TEAD4_veh 0.59526988 0.6577097702
## MCF7_TCF12_veh 0.58016072 0.6475256153
## MCF7_P300_veh 0.66429167 0.6989340608
## MCF7_H3K27ac_veh 0.68197726 0.6796598830
## Ishikawa_TEAD4_veh 0.88458045 0.4542321964
## Ishikawa_TCF12_veh 0.89916605 0.5108335561
## Ishikawa_FoxM1_veh 0.86182682 0.3470381383
## Ishikawa_CEBPB_veh 0.85387405 0.3482948799
## Ishikawa_P300_veh 0.88950428 0.4763988971
## Ishikawa_H3K27ac_veh 1.00000000 0.4770300805
## ERE_motif.total. 0.47703008 1.0000000000
## Fox_motif.total. 0.26405968 0.4123863266
## AP2_motif.total. 0.58142840 0.6395932708
## TEAD_motif.total. 0.50049054 0.2998504417
## TCF_motif.total. 0.46285836 0.3430600542
## CEBP_motif.total. 0.31010263 0.2841958812
## Fold.Change.MCF7.Ishikawa -0.06873507 -0.0002950973
## Fox_motif.total. AP2_motif.total.
## MCF7_ER_veh 0.61731980 0.71732599
## MCF7_ER_E2 0.61329182 0.73029739
## MCF7_FoxA1_veh 0.68547671 0.46557780
## MCF7_FoxA1_E2 0.67547279 0.56445337
## MCF7_AP2g_veh 0.57558845 0.51296661
## MCF7_AP2g_E2 0.61545269 0.60924232
## MCF7_TEAD4_veh 0.59600224 0.64425403
## MCF7_TCF12_veh 0.59221425 0.62888744
## MCF7_P300_veh 0.56408760 0.72192430
## MCF7_H3K27ac_veh 0.57472842 0.68151280
## Ishikawa_TEAD4_veh 0.21241283 0.55536471
## Ishikawa_TCF12_veh 0.24198020 0.60711626
## Ishikawa_FoxM1_veh 0.14166582 0.47594055
## Ishikawa_CEBPB_veh 0.14134456 0.45258459
## Ishikawa_P300_veh 0.20601074 0.56760255
## Ishikawa_H3K27ac_veh 0.26405968 0.58142840
## ERE_motif.total. 0.41238633 0.63959327
## Fox_motif.total. 1.00000000 0.31906576
## AP2_motif.total. 0.31906576 1.00000000
## TEAD_motif.total. 0.26563031 0.28931817
## TCF_motif.total. 0.12286996 0.40521788
## CEBP_motif.total. 0.33988717 0.20438752
## Fold.Change.MCF7.Ishikawa 0.07325088 -0.01808033
## TEAD_motif.total. TCF_motif.total.
## MCF7_ER_veh 0.45664430 0.35936871
## MCF7_ER_E2 0.45096984 0.35422283
## MCF7_FoxA1_veh 0.41967373 0.18494779
## MCF7_FoxA1_E2 0.42222672 0.23680327
## MCF7_AP2g_veh 0.37961696 0.23637306
## MCF7_AP2g_E2 0.40603947 0.27568640
## MCF7_TEAD4_veh 0.45385770 0.29604213
## MCF7_TCF12_veh 0.42338192 0.28336815
## MCF7_P300_veh 0.42951859 0.38828890
## MCF7_H3K27ac_veh 0.44152828 0.38480685
## Ishikawa_TEAD4_veh 0.54079312 0.48779443
## Ishikawa_TCF12_veh 0.53803575 0.48968910
## Ishikawa_FoxM1_veh 0.52727707 0.46612118
## Ishikawa_CEBPB_veh 0.51280466 0.44097579
## Ishikawa_P300_veh 0.52674344 0.49038683
## Ishikawa_H3K27ac_veh 0.50049054 0.46285836
## ERE_motif.total. 0.29985044 0.34306005
## Fox_motif.total. 0.26563031 0.12286996
## AP2_motif.total. 0.28931817 0.40521788
## TEAD_motif.total. 1.00000000 0.21084411
## TCF_motif.total. 0.21084411 1.00000000
## CEBP_motif.total. 0.28007361 0.10305200
## Fold.Change.MCF7.Ishikawa -0.02589946 -0.01946583
## CEBP_motif.total. Fold.Change.MCF7.Ishikawa
## MCF7_ER_veh 0.45380117 0.0384066325
## MCF7_ER_E2 0.44975855 0.0321786467
## MCF7_FoxA1_veh 0.48050084 0.0916644912
## MCF7_FoxA1_E2 0.46429440 0.0699745094
## MCF7_AP2g_veh 0.40367221 0.0884337407
## MCF7_AP2g_E2 0.43333146 0.0708023599
## MCF7_TEAD4_veh 0.47780070 0.0537295859
## MCF7_TCF12_veh 0.47905281 0.0594594223
## MCF7_P300_veh 0.41026363 0.0458530871
## MCF7_H3K27ac_veh 0.38807826 0.0459453763
## Ishikawa_TEAD4_veh 0.32638685 -0.0819080185
## Ishikawa_TCF12_veh 0.32568462 -0.0820200926
## Ishikawa_FoxM1_veh 0.29140231 -0.0829629313
## Ishikawa_CEBPB_veh 0.30743884 -0.0789243191
## Ishikawa_P300_veh 0.30646605 -0.0850234748
## Ishikawa_H3K27ac_veh 0.31010263 -0.0687350679
## ERE_motif.total. 0.28419588 -0.0002950973
## Fox_motif.total. 0.33988717 0.0732508751
## AP2_motif.total. 0.20438752 -0.0180803304
## TEAD_motif.total. 0.28007361 -0.0258994587
## TCF_motif.total. 0.10305200 -0.0194658348
## CEBP_motif.total. 1.00000000 0.0303455193
## Fold.Change.MCF7.Ishikawa 0.03034552 1.0000000000Visualize relationships among variables in a scatter plot
pairs(lm_rpkm2_n[c("MCF7_ER_veh" ,"MCF7_ER_E2", "Ishikawa_TEAD4_veh","Ishikawa_TCF12_veh",
"ERE_motif.total.", "Fox_motif.total.", "Fold.Change.MCF7.Ishikawa")])
Advanced visulaization with psych package by replacing scatter plot with a corelation matrix
library(psych)pairs.panels(lm_rpkm2_n[c("MCF7_ER_veh" ,"MCF7_ER_E2", "Ishikawa_TEAD4_veh","Ishikawa_TCF12_veh",
"ERE_motif.total.", "Fox_motif.total.", "Fold.Change.MCF7.Ishikawa")])
Model 1
foldchange_model <- lm(Fold.Change.MCF7.Ishikawa ~ ., data = lm_rpkm2_n)
foldchange_model##
## Call:
## lm(formula = Fold.Change.MCF7.Ishikawa ~ ., data = lm_rpkm2_n)
##
## Coefficients:
## (Intercept) MCF7_ER_veh MCF7_ER_E2
## 0.0070849 -0.0051824 -0.0158358
## MCF7_FoxA1_veh MCF7_FoxA1_E2 MCF7_AP2g_veh
## 0.0463409 -0.0309478 0.0358553
## MCF7_AP2g_E2 MCF7_TEAD4_veh MCF7_TCF12_veh
## -0.0208824 -0.0077336 0.0169270
## MCF7_P300_veh MCF7_H3K27ac_veh Ishikawa_TEAD4_veh
## 0.0286557 0.0265647 -0.0105124
## Ishikawa_TCF12_veh Ishikawa_FoxM1_veh Ishikawa_CEBPB_veh
## -0.0497439 0.0051204 0.0218875
## Ishikawa_P300_veh Ishikawa_H3K27ac_veh ERE_motif.total.
## -0.0126960 -0.0200706 -0.0003442
## Fox_motif.total. AP2_motif.total. TEAD_motif.total.
## 0.0073116 -0.0010414 -0.0020741
## TCF_motif.total. CEBP_motif.total.
## 0.0065529 0.0049985Evaluate model performance
summary(foldchange_model)##
## Call:
## lm(formula = Fold.Change.MCF7.Ishikawa ~ ., data = lm_rpkm2_n)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.03921 -0.00558 -0.00281 0.00048 0.98408
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.0070849 0.0025142 2.818 0.00495 **
## MCF7_ER_veh -0.0051824 0.0748158 -0.069 0.94479
## MCF7_ER_E2 -0.0158358 0.0710112 -0.223 0.82359
## MCF7_FoxA1_veh 0.0463409 0.0556191 0.833 0.40499
## MCF7_FoxA1_E2 -0.0309478 0.0587183 -0.527 0.59830
## MCF7_AP2g_veh 0.0358553 0.0491120 0.730 0.46556
## MCF7_AP2g_E2 -0.0208824 0.0551927 -0.378 0.70527
## MCF7_TEAD4_veh -0.0077336 0.0695724 -0.111 0.91152
## MCF7_TCF12_veh 0.0169270 0.0693525 0.244 0.80724
## MCF7_P300_veh 0.0286557 0.0502272 0.571 0.56849
## MCF7_H3K27ac_veh 0.0265647 0.0359297 0.739 0.45991
## Ishikawa_TEAD4_veh -0.0105124 0.0591543 -0.178 0.85900
## Ishikawa_TCF12_veh -0.0497439 0.0538556 -0.924 0.35595
## Ishikawa_FoxM1_veh 0.0051204 0.0374910 0.137 0.89140
## Ishikawa_CEBPB_veh 0.0218875 0.0295697 0.740 0.45940
## Ishikawa_P300_veh -0.0126960 0.0524470 -0.242 0.80879
## Ishikawa_H3K27ac_veh -0.0200706 0.0222062 -0.904 0.36636
## ERE_motif.total. -0.0003442 0.0194229 -0.018 0.98587
## Fox_motif.total. 0.0073116 0.0207898 0.352 0.72516
## AP2_motif.total. -0.0010414 0.0169557 -0.061 0.95104
## TEAD_motif.total. -0.0020741 0.0132117 -0.157 0.87529
## TCF_motif.total. 0.0065529 0.0099412 0.659 0.50998
## CEBP_motif.total. 0.0049985 0.0163569 0.306 0.76000
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.039 on 791 degrees of freedom
## Multiple R-squared: 0.03399, Adjusted R-squared: 0.007127
## F-statistic: 1.265 on 22 and 791 DF, p-value: 0.1858Outcome analysis
The summary output gives us detailed information baou the model. The residuls section provides summary statistics for the errors in our prediction. A residual equals the true value minus the predicted value.
How do we impove the model performance?
Fold change has a higher corelation with: * MCF7_FoxA1_veh 9% * MCF7_AP2g_veh 8% * MCF7_AP2g_E2 7%
- Add non-linear relationships to the model by: Square the independent variables having higher corelation with the dependent variable.
lm_rpkm2_n$MCF7_FoxA1_veh2 <-lm_rpkm2_n$MCF7_FoxA1_veh^2
lm_rpkm2_n$MCF7_AP2g_veh2 <- lm_rpkm2_n$MCF7_AP2g_veh^2
lm_rpkm2_n$MCF7_AP2g_E2b <- lm_rpkm2_n$MCF7_AP2g_E2^2- Add interaction effects. Some of the variables have combined effects in the fold change. These varibles include:
- MCF7_ER_E2 and MCF7_ER_veh 97%
- MCF7_FoxA1_E2 and MCF7_ER_veh 92%
- MCF7_FoxA1_E2 and MCF7_FoxA1_veh 95%
- Ishikawa_P300_veh and Ishikawa_TCF12_veh 97%
colnames(lm_rpkm2_n)## [1] "MCF7_ER_veh" "MCF7_ER_E2"
## [3] "MCF7_FoxA1_veh" "MCF7_FoxA1_E2"
## [5] "MCF7_AP2g_veh" "MCF7_AP2g_E2"
## [7] "MCF7_TEAD4_veh" "MCF7_TCF12_veh"
## [9] "MCF7_P300_veh" "MCF7_H3K27ac_veh"
## [11] "Ishikawa_TEAD4_veh" "Ishikawa_TCF12_veh"
## [13] "Ishikawa_FoxM1_veh" "Ishikawa_CEBPB_veh"
## [15] "Ishikawa_P300_veh" "Ishikawa_H3K27ac_veh"
## [17] "ERE_motif.total." "Fox_motif.total."
## [19] "AP2_motif.total." "TEAD_motif.total."
## [21] "TCF_motif.total." "CEBP_motif.total."
## [23] "Fold.Change.MCF7.Ishikawa" "MCF7_FoxA1_veh2"
## [25] "MCF7_AP2g_veh2" "MCF7_AP2g_E2b"Model 2
foldchange_model2 <- lm(Fold.Change.MCF7.Ishikawa ~ MCF7_ER_veh + MCF7_ER_E2 + MCF7_FoxA1_veh + MCF7_FoxA1_veh2 + MCF7_FoxA1_E2 + MCF7_AP2g_veh + MCF7_AP2g_veh2 + MCF7_AP2g_E2 + MCF7_AP2g_E2b + MCF7_TEAD4_veh + MCF7_TCF12_veh + MCF7_P300_veh + MCF7_H3K27ac_veh + MCF7_ER_E2*MCF7_ER_veh + MCF7_FoxA1_E2*MCF7_ER_veh + MCF7_FoxA1_E2*MCF7_FoxA1_veh + Ishikawa_TEAD4_veh + Ishikawa_TCF12_veh +Ishikawa_P300_veh*Ishikawa_TCF12_veh + Ishikawa_FoxM1_veh + Ishikawa_CEBPB_veh + Ishikawa_P300_veh + Ishikawa_H3K27ac_veh + ERE_motif.total. + Fox_motif.total. + AP2_motif.total. + TEAD_motif.total. + TCF_motif.total. + CEBP_motif.total., data = lm_rpkm2_n)
foldchange_model##
## Call:
## lm(formula = Fold.Change.MCF7.Ishikawa ~ ., data = lm_rpkm2_n)
##
## Coefficients:
## (Intercept) MCF7_ER_veh MCF7_ER_E2
## 0.0070849 -0.0051824 -0.0158358
## MCF7_FoxA1_veh MCF7_FoxA1_E2 MCF7_AP2g_veh
## 0.0463409 -0.0309478 0.0358553
## MCF7_AP2g_E2 MCF7_TEAD4_veh MCF7_TCF12_veh
## -0.0208824 -0.0077336 0.0169270
## MCF7_P300_veh MCF7_H3K27ac_veh Ishikawa_TEAD4_veh
## 0.0286557 0.0265647 -0.0105124
## Ishikawa_TCF12_veh Ishikawa_FoxM1_veh Ishikawa_CEBPB_veh
## -0.0497439 0.0051204 0.0218875
## Ishikawa_P300_veh Ishikawa_H3K27ac_veh ERE_motif.total.
## -0.0126960 -0.0200706 -0.0003442
## Fox_motif.total. AP2_motif.total. TEAD_motif.total.
## 0.0073116 -0.0010414 -0.0020741
## TCF_motif.total. CEBP_motif.total.
## 0.0065529 0.0049985summary(foldchange_model2)##
## Call:
## lm(formula = Fold.Change.MCF7.Ishikawa ~ MCF7_ER_veh + MCF7_ER_E2 +
## MCF7_FoxA1_veh + MCF7_FoxA1_veh2 + MCF7_FoxA1_E2 + MCF7_AP2g_veh +
## MCF7_AP2g_veh2 + MCF7_AP2g_E2 + MCF7_AP2g_E2b + MCF7_TEAD4_veh +
## MCF7_TCF12_veh + MCF7_P300_veh + MCF7_H3K27ac_veh + MCF7_ER_E2 *
## MCF7_ER_veh + MCF7_FoxA1_E2 * MCF7_ER_veh + MCF7_FoxA1_E2 *
## MCF7_FoxA1_veh + Ishikawa_TEAD4_veh + Ishikawa_TCF12_veh +
## Ishikawa_P300_veh * Ishikawa_TCF12_veh + Ishikawa_FoxM1_veh +
## Ishikawa_CEBPB_veh + Ishikawa_P300_veh + Ishikawa_H3K27ac_veh +
## ERE_motif.total. + Fox_motif.total. + AP2_motif.total. +
## TEAD_motif.total. + TCF_motif.total. + CEBP_motif.total.,
## data = lm_rpkm2_n)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.04694 -0.00658 -0.00215 0.00187 0.97909
##
## Coefficients:
## Estimate Std. Error t value
## (Intercept) 0.0097124 0.0032522 2.986
## MCF7_ER_veh 0.0142526 0.0844825 0.169
## MCF7_ER_E2 -0.0329994 0.0875929 -0.377
## MCF7_FoxA1_veh 0.0300464 0.0807396 0.372
## MCF7_FoxA1_veh2 0.0597872 0.6658711 0.090
## MCF7_FoxA1_E2 -0.0205208 0.0953446 -0.215
## MCF7_AP2g_veh 0.0415445 0.0759843 0.547
## MCF7_AP2g_veh2 0.0553216 0.2274725 0.243
## MCF7_AP2g_E2 0.0197627 0.0900946 0.219
## MCF7_AP2g_E2b -0.1487454 0.2510729 -0.592
## MCF7_TEAD4_veh -0.0173425 0.0722948 -0.240
## MCF7_TCF12_veh 0.0084150 0.0712026 0.118
## MCF7_P300_veh 0.0324118 0.0516171 0.628
## MCF7_H3K27ac_veh 0.0196931 0.0372757 0.528
## Ishikawa_TEAD4_veh -0.0139188 0.0603615 -0.231
## Ishikawa_TCF12_veh -0.0620911 0.0545138 -1.139
## Ishikawa_P300_veh -0.0468861 0.0560645 -0.836
## Ishikawa_FoxM1_veh 0.0050049 0.0379774 0.132
## Ishikawa_CEBPB_veh 0.0213810 0.0306297 0.698
## Ishikawa_H3K27ac_veh -0.0210718 0.0229861 -0.917
## ERE_motif.total. 0.0011219 0.0198377 0.057
## Fox_motif.total. 0.0105198 0.0209760 0.502
## AP2_motif.total. -0.0002350 0.0172643 -0.014
## TEAD_motif.total. 0.0005493 0.0134460 0.041
## TCF_motif.total. 0.0064602 0.0100552 0.642
## CEBP_motif.total. 0.0085591 0.0167558 0.511
## MCF7_ER_veh:MCF7_ER_E2 0.0207265 0.3472578 0.060
## MCF7_ER_veh:MCF7_FoxA1_E2 -0.1034627 0.6956808 -0.149
## MCF7_FoxA1_veh:MCF7_FoxA1_E2 0.0399019 0.9490079 0.042
## Ishikawa_TCF12_veh:Ishikawa_P300_veh 0.1126627 0.0542089 2.078
## Pr(>|t|)
## (Intercept) 0.00291 **
## MCF7_ER_veh 0.86607
## MCF7_ER_E2 0.70647
## MCF7_FoxA1_veh 0.70989
## MCF7_FoxA1_veh2 0.92848
## MCF7_FoxA1_E2 0.82965
## MCF7_AP2g_veh 0.58471
## MCF7_AP2g_veh2 0.80791
## MCF7_AP2g_E2 0.82643
## MCF7_AP2g_E2b 0.55373
## MCF7_TEAD4_veh 0.81048
## MCF7_TCF12_veh 0.90595
## MCF7_P300_veh 0.53023
## MCF7_H3K27ac_veh 0.59743
## Ishikawa_TEAD4_veh 0.81769
## Ishikawa_TCF12_veh 0.25505
## Ishikawa_P300_veh 0.40325
## Ishikawa_FoxM1_veh 0.89519
## Ishikawa_CEBPB_veh 0.48536
## Ishikawa_H3K27ac_veh 0.35957
## ERE_motif.total. 0.95492
## Fox_motif.total. 0.61615
## AP2_motif.total. 0.98915
## TEAD_motif.total. 0.96742
## TCF_motif.total. 0.52075
## CEBP_motif.total. 0.60963
## MCF7_ER_veh:MCF7_ER_E2 0.95242
## MCF7_ER_veh:MCF7_FoxA1_E2 0.88181
## MCF7_FoxA1_veh:MCF7_FoxA1_E2 0.96647
## Ishikawa_TCF12_veh:Ishikawa_P300_veh 0.03801 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.03905 on 784 degrees of freedom
## Multiple R-squared: 0.04047, Adjusted R-squared: 0.004972
## F-statistic: 1.14 on 29 and 784 DF, p-value: 0.2802Model 3
foldchange_model3 <- lm(Fold.Change.MCF7.Ishikawa ~ MCF7_ER_veh + MCF7_ER_E2 + MCF7_FoxA1_veh + MCF7_FoxA1_veh2 + MCF7_FoxA1_E2 + MCF7_AP2g_veh + MCF7_AP2g_veh2 + MCF7_AP2g_E2 + MCF7_AP2g_E2b + MCF7_TEAD4_veh + MCF7_TCF12_veh + MCF7_P300_veh + MCF7_H3K27ac_veh + MCF7_ER_E2*MCF7_ER_veh + MCF7_FoxA1_E2*MCF7_ER_veh + MCF7_FoxA1_E2*MCF7_FoxA1_veh + Ishikawa_TEAD4_veh + Ishikawa_TCF12_veh +Ishikawa_P300_veh*Ishikawa_TCF12_veh + Ishikawa_FoxM1_veh + Ishikawa_CEBPB_veh + Ishikawa_P300_veh + Ishikawa_H3K27ac_veh + Fox_motif.total., data = lm_rpkm2_n)
foldchange_model##
## Call:
## lm(formula = Fold.Change.MCF7.Ishikawa ~ ., data = lm_rpkm2_n)
##
## Coefficients:
## (Intercept) MCF7_ER_veh MCF7_ER_E2
## 0.0070849 -0.0051824 -0.0158358
## MCF7_FoxA1_veh MCF7_FoxA1_E2 MCF7_AP2g_veh
## 0.0463409 -0.0309478 0.0358553
## MCF7_AP2g_E2 MCF7_TEAD4_veh MCF7_TCF12_veh
## -0.0208824 -0.0077336 0.0169270
## MCF7_P300_veh MCF7_H3K27ac_veh Ishikawa_TEAD4_veh
## 0.0286557 0.0265647 -0.0105124
## Ishikawa_TCF12_veh Ishikawa_FoxM1_veh Ishikawa_CEBPB_veh
## -0.0497439 0.0051204 0.0218875
## Ishikawa_P300_veh Ishikawa_H3K27ac_veh ERE_motif.total.
## -0.0126960 -0.0200706 -0.0003442
## Fox_motif.total. AP2_motif.total. TEAD_motif.total.
## 0.0073116 -0.0010414 -0.0020741
## TCF_motif.total. CEBP_motif.total.
## 0.0065529 0.0049985summary(foldchange_model3)##
## Call:
## lm(formula = Fold.Change.MCF7.Ishikawa ~ MCF7_ER_veh + MCF7_ER_E2 +
## MCF7_FoxA1_veh + MCF7_FoxA1_veh2 + MCF7_FoxA1_E2 + MCF7_AP2g_veh +
## MCF7_AP2g_veh2 + MCF7_AP2g_E2 + MCF7_AP2g_E2b + MCF7_TEAD4_veh +
## MCF7_TCF12_veh + MCF7_P300_veh + MCF7_H3K27ac_veh + MCF7_ER_E2 *
## MCF7_ER_veh + MCF7_FoxA1_E2 * MCF7_ER_veh + MCF7_FoxA1_E2 *
## MCF7_FoxA1_veh + Ishikawa_TEAD4_veh + Ishikawa_TCF12_veh +
## Ishikawa_P300_veh * Ishikawa_TCF12_veh + Ishikawa_FoxM1_veh +
## Ishikawa_CEBPB_veh + Ishikawa_P300_veh + Ishikawa_H3K27ac_veh +
## Fox_motif.total., data = lm_rpkm2_n)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.04579 -0.00652 -0.00213 0.00192 0.97865
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.009931 0.003218 3.086 0.0021
## MCF7_ER_veh 0.017696 0.082925 0.213 0.8311
## MCF7_ER_E2 -0.029268 0.085446 -0.343 0.7320
## MCF7_FoxA1_veh 0.031818 0.079282 0.401 0.6883
## MCF7_FoxA1_veh2 0.043253 0.662078 0.065 0.9479
## MCF7_FoxA1_E2 -0.026021 0.094378 -0.276 0.7828
## MCF7_AP2g_veh 0.039586 0.074670 0.530 0.5962
## MCF7_AP2g_veh2 0.057539 0.222160 0.259 0.7957
## MCF7_AP2g_E2 0.021213 0.088728 0.239 0.8111
## MCF7_AP2g_E2b -0.157928 0.246266 -0.641 0.5215
## MCF7_TEAD4_veh -0.018673 0.071132 -0.263 0.7930
## MCF7_TCF12_veh 0.006860 0.070338 0.098 0.9223
## MCF7_P300_veh 0.035225 0.049654 0.709 0.4783
## MCF7_H3K27ac_veh 0.020129 0.036990 0.544 0.5865
## Ishikawa_TEAD4_veh -0.010889 0.059937 -0.182 0.8559
## Ishikawa_TCF12_veh -0.063861 0.054281 -1.176 0.2398
## Ishikawa_P300_veh -0.046562 0.055368 -0.841 0.4006
## Ishikawa_FoxM1_veh 0.006530 0.037478 0.174 0.8617
## Ishikawa_CEBPB_veh 0.022259 0.029835 0.746 0.4559
## Ishikawa_H3K27ac_veh -0.020998 0.022823 -0.920 0.3578
## Fox_motif.total. 0.010873 0.020854 0.521 0.6022
## MCF7_ER_veh:MCF7_ER_E2 0.016146 0.343470 0.047 0.9625
## MCF7_ER_veh:MCF7_FoxA1_E2 -0.092300 0.690408 -0.134 0.8937
## MCF7_FoxA1_veh:MCF7_FoxA1_E2 0.059938 0.944407 0.063 0.9494
## Ishikawa_TCF12_veh:Ishikawa_P300_veh 0.110429 0.053449 2.066 0.0391
##
## (Intercept) **
## MCF7_ER_veh
## MCF7_ER_E2
## MCF7_FoxA1_veh
## MCF7_FoxA1_veh2
## MCF7_FoxA1_E2
## MCF7_AP2g_veh
## MCF7_AP2g_veh2
## MCF7_AP2g_E2
## MCF7_AP2g_E2b
## MCF7_TEAD4_veh
## MCF7_TCF12_veh
## MCF7_P300_veh
## MCF7_H3K27ac_veh
## Ishikawa_TEAD4_veh
## Ishikawa_TCF12_veh
## Ishikawa_P300_veh
## Ishikawa_FoxM1_veh
## Ishikawa_CEBPB_veh
## Ishikawa_H3K27ac_veh
## Fox_motif.total.
## MCF7_ER_veh:MCF7_ER_E2
## MCF7_ER_veh:MCF7_FoxA1_E2
## MCF7_FoxA1_veh:MCF7_FoxA1_E2
## Ishikawa_TCF12_veh:Ishikawa_P300_veh *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.03894 on 789 degrees of freedom
## Multiple R-squared: 0.03964, Adjusted R-squared: 0.01042
## F-statistic: 1.357 on 24 and 789 DF, p-value: 0.1185Model 4
foldchange_model4 <- lm(Fold.Change.MCF7.Ishikawa ~ MCF7_ER_veh + MCF7_ER_E2, data = lm_rpkm2_n)
foldchange_model##
## Call:
## lm(formula = Fold.Change.MCF7.Ishikawa ~ ., data = lm_rpkm2_n)
##
## Coefficients:
## (Intercept) MCF7_ER_veh MCF7_ER_E2
## 0.0070849 -0.0051824 -0.0158358
## MCF7_FoxA1_veh MCF7_FoxA1_E2 MCF7_AP2g_veh
## 0.0463409 -0.0309478 0.0358553
## MCF7_AP2g_E2 MCF7_TEAD4_veh MCF7_TCF12_veh
## -0.0208824 -0.0077336 0.0169270
## MCF7_P300_veh MCF7_H3K27ac_veh Ishikawa_TEAD4_veh
## 0.0286557 0.0265647 -0.0105124
## Ishikawa_TCF12_veh Ishikawa_FoxM1_veh Ishikawa_CEBPB_veh
## -0.0497439 0.0051204 0.0218875
## Ishikawa_P300_veh Ishikawa_H3K27ac_veh ERE_motif.total.
## -0.0126960 -0.0200706 -0.0003442
## Fox_motif.total. AP2_motif.total. TEAD_motif.total.
## 0.0073116 -0.0010414 -0.0020741
## TCF_motif.total. CEBP_motif.total.
## 0.0065529 0.0049985summary(foldchange_model4)##
## Call:
## lm(formula = Fold.Change.MCF7.Ishikawa ~ MCF7_ER_veh + MCF7_ER_E2,
## data = lm_rpkm2_n)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.01575 -0.00394 -0.00281 -0.00197 0.99623
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.002296 0.001928 1.191 0.234
## MCF7_ER_veh 0.058901 0.060636 0.971 0.332
## MCF7_ER_E2 -0.045391 0.059280 -0.766 0.444
##
## Residual standard error: 0.03915 on 811 degrees of freedom
## Multiple R-squared: 0.002196, Adjusted R-squared: -0.0002642
## F-statistic: 0.8926 on 2 and 811 DF, p-value: 0.41Conclusion
- There are no significant determinants of the fold change from the independent variables in the data set. However, the interaction between Ishikawa_TCF12_veh and Ishikawa_P300_veh seems to have effect on the fold change having a p-value of 0.0391. It can be further investigated to determine ultimate effects of their interaction.
- Non linear and interaction varibles were introduced in the second and third models respectively.
- The second model indicated 1% improvement over the first model.
- Removing motif total varibles in the third model decreased the model performance by 1%, restoring it back to the original model. However, this change did not significantly bring up predictors of the fold change other than the interaction between Ishikawa_TCF12_veh and Ishikawa_P300_veh.