AJ’s Project
# READ the Data
data <- read.csv("CEO_salary.csv")
attach(data)
# Divide the Salary.
salary1 <- salary/1000
# Create data frame from age, height and Salary
data1 <- data.frame(age, height, salary1)
plot(salary1, age)
plot(salary1, height)
# Calculate the Correlation Coefficient
cor(data1)
## age height salary1
## age 1.00000000 -0.06286351 0.9291975
## height -0.06286351 1.00000000 0.3104400
## salary1 0.92919747 0.31044002 1.0000000
# Plot it with scatter plot
pairs(data1)
# Fit a Multiple Linear Regression model into data.
lm(formula = salary1 ~ age + height)
##
## Call:
## lm(formula = salary1 ~ age + height)
##
## Coefficients:
## (Intercept) age height
## 190.697 2.503 2.507
model <- lm(salary1~age+height)
# Summarize the model
summary(model)
##
## Call:
## lm(formula = salary1 ~ age + height)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.0025475 -0.0005824 -0.0001572 0.0006634 0.0026843
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.907e+02 1.884e-03 101223 <2e-16 ***
## age 2.503e+00 9.862e-06 253808 <2e-16 ***
## height 2.507e+00 2.541e-05 98679 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.001153 on 97 degrees of freedom
## Multiple R-squared: 1, Adjusted R-squared: 1
## F-statistic: 3.564e+10 on 2 and 97 DF, p-value: < 2.2e-16
# Calculate R squared and the P Value
# Total Sum of Squared.
total_sum_of_squared <- sum((salary1 - mean(salary1))^2)
# Regression and Residual Sum of the Squared.
reggression <- sum((fitted(model) - mean(salary1))^2)
residual_sum_of_squared <- sum((salary1-fitted(model))^2)
# Calculate the F Value.
fstatistic <- (reggression/2)/(residual_sum_of_squared/97)
# The P-Value for F-Statistic.
pvalue <- 1-pf(fstatistic, df1=2, df2=97)
# Calculate the R squared.
R2 <- reggression/total_sum_of_squared
# Residual Plots
resid(model)
## 1 2 3 4 5
## 0.0005665957 -0.0014026842 -0.0003260399 0.0019161955 0.0004113886
## 6 7 8 9 10
## 0.0014437155 -0.0001951258 0.0004592313 -0.0021496332 -0.0002581727
## 11 12 13 14 15
## -0.0001979076 -0.0006680376 0.0004568812 0.0005885386 0.0008635325
## 16 17 18 19 20
## -0.0003950821 -0.0004122047 -0.0005447256 0.0026843441 -0.0005036216
## 21 22 23 24 25
## -0.0022861109 -0.0003080538 0.0008487600 0.0018723097 0.0014723970
## 26 27 28 29 30
## 0.0006296426 0.0006612261 -0.0005886114 -0.0004225886 0.0003100195
## 31 32 33 34 35
## 0.0006815622 0.0007841064 -0.0002498272 -0.0015020148 -0.0015802659
## 36 37 38 39 40
## 0.0016268608 0.0005259234 -0.0001101360 -0.0004246271 0.0006420650
## 41 42 43 44 45
## 0.0004568812 -0.0006504832 0.0015123260 -0.0012997084 0.0008004856
## 46 47 48 49 50
## 0.0015829750 0.0016531923 0.0006963348 0.0019118069 -0.0012653431
## 51 52 53 54 55
## 0.0005347006 -0.0005359484 -0.0011292971 -0.0004788969 -0.0012777655
## 56 57 58 59 60
## 0.0006360697 0.0004053933 0.0007138891 -0.0001189131 0.0007933153
## 61 62 63 64 65
## -0.0002394433 0.0006700033 -0.0003863050 0.0014437155 -0.0003140492
## 66 67 68 69 70
## -0.0001292971 -0.0006592604 0.0006596193 0.0004640516 -0.0002888927
## 71 72 73 74 75
## -0.0005802659 -0.0021276903 0.0015211031 -0.0005276030 0.0026580126
## 76 77 78 79 80
## -0.0022039029 -0.0023024902 -0.0006548718 0.0005933589 -0.0002613862
## 81 82 83 84 85
## 0.0005151078 -0.0014186318 -0.0013228263 -0.0002071165 0.0013056310
## 86 87 88 89 90
## -0.0001851736 0.0004963784 0.0014772173 -0.0003068788 -0.0025475074
## 91 92 93 94 95
## -0.0015638867 0.0015785864 -0.0015156123 -0.0024992330 -0.0012027279
## 96 97 98 99 100
## -0.0011939507 0.0006444151 -0.0002066847 0.0005642456 0.0003934026
par(mfrow=c(2,2))
plot(age, resid(model), axes=TRUE, frame.plot=TRUE, xlab='age', ylab='residue')
plot(height, resid(model), axes=TRUE, frame.plot=TRUE, xlab='height', ylab='residue')
plot(fitted(model), resid(model), axes=TRUE, frame.plot=TRUE, xlab='fitted values', ylab='residue')
hist(resid(model))
# influence function
influence(model)
## $hat
## 1 2 3 4 5 6 7
## 0.02566420 0.04160169 0.01331072 0.05200382 0.03678001 0.03355961 0.02628633
## 8 9 10 11 12 13 14
## 0.05814680 0.03237010 0.02598707 0.03888080 0.04449630 0.02723060 0.03631704
## 15 16 17 18 19 20 21
## 0.03366497 0.01313441 0.04297304 0.02103765 0.01164763 0.01613921 0.02055159
## 22 23 24 25 26 27 28
## 0.02754226 0.03157044 0.03525930 0.06657725 0.03852292 0.04347023 0.03678001
## 29 30 31 32 33 34 35
## 0.02803151 0.05457105 0.01721591 0.02274559 0.03086409 0.02137396 0.04075108
## 36 37 38 39 40 41 42
## 0.01916401 0.02169436 0.04020252 0.02948669 0.03221787 0.02723060 0.03906838
## 43 44 45 46 47 48 49
## 0.02243175 0.02157802 0.02656210 0.01076018 0.03122463 0.02585170 0.04967140
## 50 51 52 53 54 55 56
## 0.04824449 0.01840382 0.01964377 0.03969556 0.02483945 0.03248835 0.01846432
## 57 58 59 60 61 62 63
## 0.02991290 0.02055159 0.03743848 0.04196536 0.02274226 0.03818830 0.01510760
## 64 65 66 67 68 69 70
## 0.03355961 0.01628011 0.03969556 0.04148991 0.02408818 0.01964377 0.03798677
## 71 72 73 74 75 76 77
## 0.04075108 0.03525930 0.02483945 0.06657725 0.01317260 0.02698409 0.01285905
## 78 79 80 81 82 83 84
## 0.04020604 0.01144801 0.01645518 0.04049660 0.01695549 0.01829794 0.02565171
## 85 86 87 88 89 90 91
## 0.05702464 0.03547578 0.01613921 0.01864954 0.01230903 0.02919406 0.02366479
## 92 93 94 95 96 97 98
## 0.01072398 0.02832161 0.01563791 0.02732410 0.03110751 0.02661956 0.04196536
## 99 100
## 0.03552196 0.03573362
##
## $coefficients
## (Intercept) age height
## 1 -8.744512e-05 5.132007e-07 9.880666e-07
## 2 2.627091e-04 -2.040612e-06 -2.608067e-06
## 3 -3.289247e-06 -1.551802e-07 9.943211e-08
## 4 3.506401e-04 2.431160e-06 -6.229489e-06
## 5 -2.936430e-05 -4.922959e-07 7.913270e-07
## 6 -5.060000e-05 -1.739579e-06 2.042983e-06
## 7 -4.278083e-05 2.030629e-08 5.630683e-07
## 8 -1.514924e-04 6.316208e-07 1.803632e-06
## 9 -5.240245e-04 -2.358186e-07 7.241127e-06
## 10 -5.506071e-05 1.593665e-07 6.381307e-07
## 11 -5.799584e-05 1.437344e-07 6.979934e-07
## 12 1.328652e-04 5.765906e-07 -2.346182e-06
## 13 -2.177135e-05 -4.439197e-07 6.590026e-07
## 14 -1.045410e-04 7.622090e-07 1.073831e-06
## 15 1.996344e-04 2.908482e-07 -2.881002e-06
## 16 2.227772e-05 -1.682195e-07 -2.632883e-07
## 17 -6.769767e-05 6.530154e-07 4.762783e-07
## 18 6.140820e-05 2.345804e-07 -1.096838e-06
## 19 1.782739e-04 2.505271e-07 -2.295855e-06
## 20 4.289646e-05 1.470151e-07 -7.727766e-07
## 21 -3.937286e-04 1.205080e-06 4.459126e-06
## 22 -6.002658e-05 2.793466e-07 6.239403e-07
## 23 1.506378e-04 5.519254e-07 -2.358837e-06
## 24 4.174124e-04 9.154240e-07 -6.210951e-06
## 25 -5.097948e-04 2.389369e-06 5.891100e-06
## 26 -9.470582e-05 9.053114e-07 8.492246e-07
## 27 1.511239e-04 -9.633542e-07 -1.418858e-06
## 28 4.201420e-05 7.043728e-07 -1.132224e-06
## 29 -4.412577e-05 4.950997e-07 2.440765e-07
## 30 -5.549465e-05 -3.902977e-07 1.080995e-06
## 31 9.279460e-05 -3.498425e-07 -9.884042e-07
## 32 8.193246e-05 5.242779e-07 -1.380861e-06
## 33 -8.320219e-07 -3.064672e-07 1.721266e-07
## 34 3.038187e-05 1.244427e-06 -1.445172e-06
## 35 4.501587e-04 -1.050126e-06 -5.918402e-06
## 36 -1.268048e-04 1.303247e-06 1.189018e-06
## 37 1.034672e-05 -4.815396e-07 2.389815e-07
## 38 -2.277038e-05 -8.768198e-08 3.617977e-07
## 39 6.943352e-05 -4.500991e-07 -7.537695e-07
## 40 1.136158e-04 -7.711994e-07 -1.016254e-06
## 41 -2.177135e-05 -4.439197e-07 6.590026e-07
## 42 1.399093e-04 3.603133e-07 -2.303685e-06
## 43 -2.544097e-04 8.180967e-07 3.287617e-06
## 44 1.993931e-05 -1.206513e-06 3.053546e-07
## 45 1.789757e-04 -1.434467e-07 -2.320327e-06
## 46 -5.575582e-05 8.745639e-08 9.576555e-07
## 47 -1.730627e-04 2.089366e-06 1.344530e-06
## 48 1.324764e-04 -5.780900e-07 -1.399464e-06
## 49 3.573488e-04 2.272566e-06 -6.223786e-06
## 50 -3.723302e-04 1.689843e-06 3.987454e-06
## 51 5.951197e-06 -4.082878e-07 2.550542e-07
## 52 6.488209e-05 1.505385e-07 -1.090576e-06
## 53 -1.776585e-04 -1.170429e-06 3.095432e-06
## 54 8.484757e-05 -3.315057e-07 -1.055264e-06
## 55 4.729869e-05 -1.682275e-06 2.254025e-07
## 56 7.219581e-05 -4.613628e-07 -6.321915e-07
## 57 -5.374058e-05 -2.934325e-07 1.006725e-06
## 58 1.229505e-04 -3.763132e-07 -1.392461e-06
## 59 -2.554247e-05 -7.633469e-08 3.924343e-07
## 60 2.401164e-04 -6.990918e-07 -2.826533e-06
## 61 -1.443443e-05 -1.988246e-07 2.969886e-07
## 62 1.464922e-04 -8.689270e-07 -1.413301e-06
## 63 2.509039e-05 -2.221619e-07 -2.672427e-07
## 64 -5.060000e-05 -1.739579e-06 2.042983e-06
## 65 -4.138877e-05 1.377072e-07 4.512223e-07
## 66 -2.034072e-05 -1.340064e-07 3.544065e-07
## 67 1.364318e-04 4.666639e-07 -2.324381e-06
## 68 1.045008e-04 -5.880306e-07 -1.003331e-06
## 69 -5.617824e-05 -1.303439e-07 9.442762e-07
## 70 -7.112725e-05 3.342334e-07 7.478573e-07
## 71 1.652961e-04 -3.856012e-07 -2.173208e-06
## 72 -4.743470e-04 -1.040287e-06 7.058116e-06
## 73 -2.694983e-04 1.052950e-06 3.351798e-06
## 74 1.826744e-04 -8.561810e-07 -2.110954e-06
## 75 2.440398e-04 -9.330348e-07 -2.468189e-06
## 76 -5.023950e-04 5.607000e-07 6.417928e-06
## 77 -1.239870e-04 -7.267192e-07 1.888833e-06
## 78 1.381812e-04 4.130557e-07 -2.313897e-06
## 79 1.250973e-05 -1.937086e-07 3.244743e-08
## 80 -2.118530e-05 -1.185127e-07 3.378653e-07
## 81 -1.248803e-04 6.042325e-07 1.452196e-06
## 82 1.426496e-04 -8.344671e-07 -1.683443e-06
## 83 -1.859077e-04 7.782596e-07 1.936436e-06
## 84 -1.993757e-05 -1.699784e-07 3.607995e-07
## 85 -2.285600e-04 -1.749219e-06 4.548006e-06
## 86 -1.401284e-05 -2.236955e-07 3.144950e-07
## 87 -4.227952e-05 -1.449007e-07 7.616624e-07
## 88 -1.974407e-04 -8.435976e-08 3.056340e-06
## 89 -1.780871e-05 -7.408936e-08 2.552845e-07
## 90 1.107213e-04 2.672085e-06 -3.650872e-06
## 91 2.526411e-04 3.050094e-07 -3.991547e-06
## 92 -4.895990e-05 -2.944686e-08 9.360730e-07
## 93 3.174048e-04 -9.573439e-07 -4.090017e-06
## 94 2.233301e-04 5.435787e-07 -3.863028e-06
## 95 -1.108319e-04 -1.079162e-06 2.084130e-06
## 96 -1.001983e-04 -1.255649e-06 2.047819e-06
## 97 -6.163162e-05 7.137826e-07 5.059421e-07
## 98 -6.255822e-05 1.821364e-07 7.364049e-07
## 99 6.667731e-05 -7.945069e-07 -3.492046e-07
## 100 -1.012975e-04 8.110653e-08 1.436720e-06
##
## $sigma
## 1 2 3 4 5 6
## 0.001157892 0.001150114 0.001158889 0.001141841 0.001158584 0.001149644
## 7 8 9 10 11 12
## 0.001159198 0.001158367 0.001137718 0.001159066 0.001159190 0.001157273
## 13 14 15 16 17 18
## 0.001158409 0.001157758 0.001155902 0.001158663 0.001158576 0.001158011
## 19 20 21 22 23 24
## 0.001126145 0.001158215 0.001135149 0.001158935 0.001156027 0.001142933
## 25 26 27 28 29 30
## 0.001148892 0.001157520 0.001157318 0.001157757 0.001158548 0.001158917
## 31 32 33 34 35 36
## 0.001157248 0.001156544 0.001159084 0.001148970 0.001147619 0.001147187
## 37 38 39 40 41 42
## 0.001158103 0.001159317 0.001158539 0.001157458 0.001158409 0.001157394
## 43 44 45 46 47 48
## 0.001148815 0.001151591 0.001156413 0.001147938 0.001146630 0.001157135
## 49 50 51 52 53 54
## 0.001141965 0.001151791 0.001158064 0.001158057 0.001153392 0.001158317
## 55 56 57 58 59 60
## 0.001151768 0.001157520 0.001158612 0.001157034 0.001159308 0.001156419
## 61 62 63 64 65 66
## 0.001159110 0.001157275 0.001158693 0.001149644 0.001158923 0.001159295
## 67 68 69 70 71 72
## 0.001157335 0.001157369 0.001158386 0.001158984 0.001157796 0.001138098
## 73 74 75 76 77 78
## 0.001148665 0.001158033 0.001126752 0.001136727 0.001134991 0.001157364
## 79 80 81 82 83 84
## 0.001157772 0.001159061 0.001158131 0.001150140 0.001151338 0.001159176
## 85 86 87 88 89 90
## 0.001151224 0.001159214 0.001158248 0.001149341 0.001158945 0.001128943
## 91 92 93 94 95 96
## 0.001148065 0.001148002 0.001148704 0.001130508 0.001152673 0.001152745
## 97 98 99 100
## 0.001157455 0.001159173 0.001157890 0.001158652
##
## $wt.res
## 1 2 3 4 5
## 0.0005665957 -0.0014026842 -0.0003260399 0.0019161955 0.0004113886
## 6 7 8 9 10
## 0.0014437155 -0.0001951258 0.0004592313 -0.0021496332 -0.0002581727
## 11 12 13 14 15
## -0.0001979076 -0.0006680376 0.0004568812 0.0005885386 0.0008635325
## 16 17 18 19 20
## -0.0003950821 -0.0004122047 -0.0005447256 0.0026843441 -0.0005036216
## 21 22 23 24 25
## -0.0022861109 -0.0003080538 0.0008487600 0.0018723097 0.0014723970
## 26 27 28 29 30
## 0.0006296426 0.0006612261 -0.0005886114 -0.0004225886 0.0003100195
## 31 32 33 34 35
## 0.0006815622 0.0007841064 -0.0002498272 -0.0015020148 -0.0015802659
## 36 37 38 39 40
## 0.0016268608 0.0005259234 -0.0001101360 -0.0004246271 0.0006420650
## 41 42 43 44 45
## 0.0004568812 -0.0006504832 0.0015123260 -0.0012997084 0.0008004856
## 46 47 48 49 50
## 0.0015829750 0.0016531923 0.0006963348 0.0019118069 -0.0012653431
## 51 52 53 54 55
## 0.0005347006 -0.0005359484 -0.0011292971 -0.0004788969 -0.0012777655
## 56 57 58 59 60
## 0.0006360697 0.0004053933 0.0007138891 -0.0001189131 0.0007933153
## 61 62 63 64 65
## -0.0002394433 0.0006700033 -0.0003863050 0.0014437155 -0.0003140492
## 66 67 68 69 70
## -0.0001292971 -0.0006592604 0.0006596193 0.0004640516 -0.0002888927
## 71 72 73 74 75
## -0.0005802659 -0.0021276903 0.0015211031 -0.0005276030 0.0026580126
## 76 77 78 79 80
## -0.0022039029 -0.0023024902 -0.0006548718 0.0005933589 -0.0002613862
## 81 82 83 84 85
## 0.0005151078 -0.0014186318 -0.0013228263 -0.0002071165 0.0013056310
## 86 87 88 89 90
## -0.0001851736 0.0004963784 0.0014772173 -0.0003068788 -0.0025475074
## 91 92 93 94 95
## -0.0015638867 0.0015785864 -0.0015156123 -0.0024992330 -0.0012027279
## 96 97 98 99 100
## -0.0011939507 0.0006444151 -0.0002066847 0.0005642456 0.0003934026
# Cooks distance
cooks.dist <- cooks.distance(model)
which(cooks.dist > (4/(nrow(data1)-2-1)))
## 4 25 49 72 90
## 4 25 49 72 90