title: “Coursera Regresion model” author: “Makasani Christopher” date: “2023/09/11” output: html_document
Executive summary
library(ggplot2)
data(mtcars)
summary(mtcars)## mpg cyl disp hp
## Min. :10.40 Min. :4.000 Min. : 71.1 Min. : 52.0
## 1st Qu.:15.43 1st Qu.:4.000 1st Qu.:120.8 1st Qu.: 96.5
## Median :19.20 Median :6.000 Median :196.3 Median :123.0
## Mean :20.09 Mean :6.188 Mean :230.7 Mean :146.7
## 3rd Qu.:22.80 3rd Qu.:8.000 3rd Qu.:326.0 3rd Qu.:180.0
## Max. :33.90 Max. :8.000 Max. :472.0 Max. :335.0
## drat wt qsec vs
## Min. :2.760 Min. :1.513 Min. :14.50 Min. :0.0000
## 1st Qu.:3.080 1st Qu.:2.581 1st Qu.:16.89 1st Qu.:0.0000
## Median :3.695 Median :3.325 Median :17.71 Median :0.0000
## Mean :3.597 Mean :3.217 Mean :17.85 Mean :0.4375
## 3rd Qu.:3.920 3rd Qu.:3.610 3rd Qu.:18.90 3rd Qu.:1.0000
## Max. :4.930 Max. :5.424 Max. :22.90 Max. :1.0000
## am gear carb
## Min. :0.0000 Min. :3.000 Min. :1.000
## 1st Qu.:0.0000 1st Qu.:3.000 1st Qu.:2.000
## Median :0.0000 Median :4.000 Median :2.000
## Mean :0.4062 Mean :3.688 Mean :2.812
## 3rd Qu.:1.0000 3rd Qu.:4.000 3rd Qu.:4.000
## Max. :1.0000 Max. :5.000 Max. :8.000dim(mtcars)## [1] 32 11Regression Analysis Starting regression on mpg and am.
am_model <- lm(mpg ~ am,mtcars)
summary(am_model)##
## Call:
## lm(formula = mpg ~ am, data = mtcars)
##
## Residuals:
## Min 1Q Median 3Q Max
## -9.3923 -3.0923 -0.2974 3.2439 9.5077
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 17.147 1.125 15.247 1.13e-15 ***
## am 7.245 1.764 4.106 0.000285 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.902 on 30 degrees of freedom
## Multiple R-squared: 0.3598, Adjusted R-squared: 0.3385
## F-statistic: 16.86 on 1 and 30 DF, p-value: 0.000285Explaining more of variables in the data and variance
fullmodel <- lm(mpg ~ .,data =mtcars)
summary(fullmodel)##
## Call:
## lm(formula = mpg ~ ., data = mtcars)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.4506 -1.6044 -0.1196 1.2193 4.6271
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 12.30337 18.71788 0.657 0.5181
## cyl -0.11144 1.04502 -0.107 0.9161
## disp 0.01334 0.01786 0.747 0.4635
## hp -0.02148 0.02177 -0.987 0.3350
## drat 0.78711 1.63537 0.481 0.6353
## wt -3.71530 1.89441 -1.961 0.0633 .
## qsec 0.82104 0.73084 1.123 0.2739
## vs 0.31776 2.10451 0.151 0.8814
## am 2.52023 2.05665 1.225 0.2340
## gear 0.65541 1.49326 0.439 0.6652
## carb -0.19942 0.82875 -0.241 0.8122
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.65 on 21 degrees of freedom
## Multiple R-squared: 0.869, Adjusted R-squared: 0.8066
## F-statistic: 13.93 on 10 and 21 DF, p-value: 3.793e-07stepmodel<- step(fullmodel)## Start: AIC=70.9
## mpg ~ cyl + disp + hp + drat + wt + qsec + vs + am + gear + carb
##
## Df Sum of Sq RSS AIC
## - cyl 1 0.0799 147.57 68.915
## - vs 1 0.1601 147.66 68.932
## - carb 1 0.4067 147.90 68.986
## - gear 1 1.3531 148.85 69.190
## - drat 1 1.6270 149.12 69.249
## - disp 1 3.9167 151.41 69.736
## - hp 1 6.8399 154.33 70.348
## - qsec 1 8.8641 156.36 70.765
## <none> 147.49 70.898
## - am 1 10.5467 158.04 71.108
## - wt 1 27.0144 174.51 74.280
##
## Step: AIC=68.92
## mpg ~ disp + hp + drat + wt + qsec + vs + am + gear + carb
##
## Df Sum of Sq RSS AIC
## - vs 1 0.2685 147.84 66.973
## - carb 1 0.5201 148.09 67.028
## - gear 1 1.8211 149.40 67.308
## - drat 1 1.9826 149.56 67.342
## - disp 1 3.9009 151.47 67.750
## - hp 1 7.3632 154.94 68.473
## <none> 147.57 68.915
## - qsec 1 10.0933 157.67 69.032
## - am 1 11.8359 159.41 69.384
## - wt 1 27.0280 174.60 72.297
##
## Step: AIC=66.97
## mpg ~ disp + hp + drat + wt + qsec + am + gear + carb
##
## Df Sum of Sq RSS AIC
## - carb 1 0.6855 148.53 65.121
## - gear 1 2.1437 149.99 65.434
## - drat 1 2.2139 150.06 65.449
## - disp 1 3.6467 151.49 65.753
## - hp 1 7.1060 154.95 66.475
## <none> 147.84 66.973
## - am 1 11.5694 159.41 67.384
## - qsec 1 15.6830 163.53 68.200
## - wt 1 27.3799 175.22 70.410
##
## Step: AIC=65.12
## mpg ~ disp + hp + drat + wt + qsec + am + gear
##
## Df Sum of Sq RSS AIC
## - gear 1 1.565 150.09 63.457
## - drat 1 1.932 150.46 63.535
## <none> 148.53 65.121
## - disp 1 10.110 158.64 65.229
## - am 1 12.323 160.85 65.672
## - hp 1 14.826 163.35 66.166
## - qsec 1 26.408 174.94 68.358
## - wt 1 69.127 217.66 75.350
##
## Step: AIC=63.46
## mpg ~ disp + hp + drat + wt + qsec + am
##
## Df Sum of Sq RSS AIC
## - drat 1 3.345 153.44 62.162
## - disp 1 8.545 158.64 63.229
## <none> 150.09 63.457
## - hp 1 13.285 163.38 64.171
## - am 1 20.036 170.13 65.466
## - qsec 1 25.574 175.67 66.491
## - wt 1 67.572 217.66 73.351
##
## Step: AIC=62.16
## mpg ~ disp + hp + wt + qsec + am
##
## Df Sum of Sq RSS AIC
## - disp 1 6.629 160.07 61.515
## <none> 153.44 62.162
## - hp 1 12.572 166.01 62.682
## - qsec 1 26.470 179.91 65.255
## - am 1 32.198 185.63 66.258
## - wt 1 69.043 222.48 72.051
##
## Step: AIC=61.52
## mpg ~ hp + wt + qsec + am
##
## Df Sum of Sq RSS AIC
## - hp 1 9.219 169.29 61.307
## <none> 160.07 61.515
## - qsec 1 20.225 180.29 63.323
## - am 1 25.993 186.06 64.331
## - wt 1 78.494 238.56 72.284
##
## Step: AIC=61.31
## mpg ~ wt + qsec + am
##
## Df Sum of Sq RSS AIC
## <none> 169.29 61.307
## - am 1 26.178 195.46 63.908
## - qsec 1 109.034 278.32 75.217
## - wt 1 183.347 352.63 82.790summary(stepmodel)##
## Call:
## lm(formula = mpg ~ wt + qsec + am, data = mtcars)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.4811 -1.5555 -0.7257 1.4110 4.6610
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 9.6178 6.9596 1.382 0.177915
## wt -3.9165 0.7112 -5.507 6.95e-06 ***
## qsec 1.2259 0.2887 4.247 0.000216 ***
## am 2.9358 1.4109 2.081 0.046716 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.459 on 28 degrees of freedom
## Multiple R-squared: 0.8497, Adjusted R-squared: 0.8336
## F-statistic: 52.75 on 3 and 28 DF, p-value: 1.21e-11Inference
t.test(mpg ~am,mtcars)##
## Welch Two Sample t-test
##
## data: mpg by am
## t = -3.7671, df = 18.332, p-value = 0.001374
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -11.280194 -3.209684
## sample estimates:
## mean in group 0 mean in group 1
## 17.14737 24.39231Appendix and Plots
boxplot(mpg~am,data = mtcars,col =(c("Yellow","Red")),ylab = "Miles per Gallon",xlab = "Transmission Type")
Potting using base graphics
par(mfrow=c(2,2))
plot(stepmodel)
data(mtcars)
pairs(mtcars,mapping = aes(colour=am))## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in axis(side = side, at = at, labels = labels, ...): "mapping" is not a
## graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in axis(side = side, at = at, labels = labels, ...): "mapping" is not a
## graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in axis(side = side, at = at, labels = labels, ...): "mapping" is not a
## graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in axis(side = side, at = at, labels = labels, ...): "mapping" is not a
## graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in axis(side = side, at = at, labels = labels, ...): "mapping" is not a
## graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in axis(side = side, at = at, labels = labels, ...): "mapping" is not a
## graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in axis(side = side, at = at, labels = labels, ...): "mapping" is not a
## graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in axis(side = side, at = at, labels = labels, ...): "mapping" is not a
## graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in axis(side = side, at = at, labels = labels, ...): "mapping" is not a
## graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in axis(side = side, at = at, labels = labels, ...): "mapping" is not a
## graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in axis(side = side, at = at, labels = labels, ...): "mapping" is not a
## graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in axis(side = side, at = at, labels = labels, ...): "mapping" is not a
## graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in axis(side = side, at = at, labels = labels, ...): "mapping" is not a
## graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in axis(side = side, at = at, labels = labels, ...): "mapping" is not a
## graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in axis(side = side, at = at, labels = labels, ...): "mapping" is not a
## graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in axis(side = side, at = at, labels = labels, ...): "mapping" is not a
## graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in axis(side = side, at = at, labels = labels, ...): "mapping" is not a
## graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in axis(side = side, at = at, labels = labels, ...): "mapping" is not a
## graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in axis(side = side, at = at, labels = labels, ...): "mapping" is not a
## graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in axis(side = side, at = at, labels = labels, ...): "mapping" is not a
## graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy.coords(x, y), type = type, ...): "mapping" is not a
## graphical parameter## Warning in plot.window(...): "mapping" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "mapping" is not a graphical parameter## Warning in title(...): "mapping" is not a graphical parameter## Warning in axis(side = side, at = at, labels = labels, ...): "mapping" is not a
## graphical parameter
## Warning in axis(side = side, at = at, labels = labels, ...): "mapping" is not a
## graphical parameter