# Problem_14_9_39.r
# 1.0 Read in data ----
# See Problem 14.9.39
# Data from Knafl et al. (1984)
#
tankvolume=read.table(file="Rice 3e Datasets/ASCII Comma/Chapter 14/tankvolume.txt",
sep=",",stringsAsFactors = FALSE,
header=TRUE)
Volume=tankvolume$Volume
Pressure=tankvolume$Pressure
# (a). Plot pressure versus volume. The relationship appears linear
plot(Volume, Pressure)
#summary(Volume)
# (b). Calculate the linear regression of pressure on volume
lmfit1=lm( Pressure~ Volume)
summary(lmfit1)
##
## Call:
## lm(formula = Pressure ~ Volume)
##
## Residuals:
## Min 1Q Median 3Q Max
## -28.429 -15.610 2.047 10.819 36.634
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -257.301 9.430 -27.29 <2e-16 ***
## Volume 2316.469 9.243 250.61 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 19.44 on 19 degrees of freedom
## Multiple R-squared: 0.9997, Adjusted R-squared: 0.9997
## F-statistic: 6.28e+04 on 1 and 19 DF, p-value: < 2.2e-16
abline(lmfit1,col='green')
![](data:image/png;base64,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)
# Plot the residuals versus volume
plot(Volume, lmfit1$residuals)
![](data:image/png;base64,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)
#
# The residuals plot shows a non-linear relationship with volume
#
# (c). Fit Pressure as a quadratic function of volume.
VolumeSq=Volume*Volume
lmfit2=lm(Pressure ~ Volume + VolumeSq)
summary(lmfit2)
##
## Call:
## lm(formula = Pressure ~ Volume + VolumeSq)
##
## Residuals:
## Min 1Q Median 3Q Max
## -18.645 -7.189 1.944 7.371 15.528
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -204.995 9.274 -22.104 1.70e-14 ***
## Volume 2164.032 23.052 93.877 < 2e-16 ***
## VolumeSq 83.191 12.276 6.777 2.39e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 10.6 on 18 degrees of freedom
## Multiple R-squared: 0.9999, Adjusted R-squared: 0.9999
## F-statistic: 1.057e+05 on 2 and 18 DF, p-value: < 2.2e-16
plot(Volume, lmfit2$residuals)
abline(h=0,col='gray')
![](data:image/png;base64,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)
# The fit looks much better, but the residuals at specific volume
# levels tend to be all positive or all negative together.
# There is variability within given Volume level which is smaller
# than variability across Volume levels.
# There appears to be two sources of varability: across volume levels and within.