Operational data of the proportion of crude oil converted to gasoline after distillation and fractionation.
Usage
data("GasolineYield", package = "betareg")
Format
A data frame containing 32 observations on 6 variables.
yield
proportion of crude oil converted to gasoline after distillation and fractionation.
gravity
crude oil gravity (degrees API).
pressure
vapor pressure of crude oil (lbf/in2).
temp10
temperature (degrees F) at which 10 percent of crude oil has vaporized.
temp
temperature (degrees F) at which all gasoline has vaporized.
batch
factor indicating unique batch of conditions gravity, pressure, and temp10.
Details
This dataset was collected by Prater (1956), its dependent variable is the proportion of crude oil after distillation and fractionation. This dataset was analyzed by Atkinson (1985), who used the linear regression model and noted that there is “indication that the error distribution is not quite symmetrical, giving rise to some unduly large and small residuals” (p. 60).
The dataset contains 32 observations on the response and on the independent variables. It has been noted (Daniel and Wood, 1971, Chapter 8) that there are only ten sets of values of the first three explanatory variables which correspond to ten different crudes and were subjected to experimentally controlled distillation conditions. These conditions are captured in variable batch and the data were ordered according to the ascending order of temp10.
Source
Taken from Prater (1956).
References
Atkinson, A.C. (1985). Plots, Transformations and Regression: An Introduction to Graphical Methods of Diagnostic Regression Analysis. New York: Oxford University Press.
Cribari-Neto, F., and Zeileis, A. (2010). Beta Regression in R. Journal of Statistical Software, 34(2), 1–24. doi:10.18637/jss.v034.i02
Daniel, C., and Wood, F.S. (1971). Fitting Equations to Data. New York: John Wiley and Sons.
Ferrari, S.L.P., and Cribari-Neto, F. (2004). Beta Regression for Modeling Rates and Proportions. Journal of Applied Statistics, 31(7), 799–815.
library("betareg")## IGNORE_RDIFF_BEGINdata("GasolineYield", package ="betareg")gy1<-betareg(yield~gravity+pressure+temp10+temp, data =GasolineYield)summary(gy1)
Call:
betareg(formula = yield ~ gravity + pressure + temp10 + temp, data = GasolineYield)
Quantile residuals:
Min 1Q Median 3Q Max
-1.9010 -0.6829 -0.0385 0.5531 2.1314
Coefficients (mean model with logit link):
Estimate Std. Error z value Pr(>|z|)
(Intercept) -2.6949422 0.7625693 -3.534 0.000409 ***
gravity 0.0045412 0.0071419 0.636 0.524871
pressure 0.0304135 0.0281007 1.082 0.279117
temp10 -0.0110449 0.0022640 -4.879 1.07e-06 ***
temp 0.0105650 0.0005154 20.499 < 2e-16 ***
Phi coefficients (precision model with identity link):
Estimate Std. Error z value Pr(>|z|)
(phi) 248.24 62.02 4.003 6.26e-05 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Type of estimator: ML (maximum likelihood)
Log-likelihood: 75.68 on 6 Df
Pseudo R-squared: 0.9398
Number of iterations: 147 (BFGS) + 4 (Fisher scoring)
## Ferrari and Cribari-Neto (2004)gy2<-betareg(yield~batch+temp, data =GasolineYield)## Table 1summary(gy2)
Call:
betareg(formula = yield ~ batch + temp, data = GasolineYield)
Quantile residuals:
Min 1Q Median 3Q Max
-2.1396 -0.5698 0.1202 0.7040 1.7506
Coefficients (mean model with logit link):
Estimate Std. Error z value Pr(>|z|)
(Intercept) -6.1595710 0.1823247 -33.784 < 2e-16 ***
batch1 1.7277289 0.1012294 17.067 < 2e-16 ***
batch2 1.3225969 0.1179020 11.218 < 2e-16 ***
batch3 1.5723099 0.1161045 13.542 < 2e-16 ***
batch4 1.0597141 0.1023598 10.353 < 2e-16 ***
batch5 1.1337518 0.1035232 10.952 < 2e-16 ***
batch6 1.0401618 0.1060365 9.809 < 2e-16 ***
batch7 0.5436922 0.1091275 4.982 6.29e-07 ***
batch8 0.4959007 0.1089257 4.553 5.30e-06 ***
batch9 0.3857930 0.1185933 3.253 0.00114 **
temp 0.0109669 0.0004126 26.577 < 2e-16 ***
Phi coefficients (precision model with identity link):
Estimate Std. Error z value Pr(>|z|)
(phi) 440.3 110.0 4.002 6.29e-05 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Type of estimator: ML (maximum likelihood)
Log-likelihood: 84.8 on 12 Df
Pseudo R-squared: 0.9617
Number of iterations: 51 (BFGS) + 3 (Fisher scoring)
## Figure 2par(mfrow =c(3, 2))plot(gy2, which =1, type ="pearson", sub.caption ="")plot(gy2, which =1, type ="deviance", sub.caption ="")plot(gy2, which =5, type ="deviance", sub.caption ="")plot(gy2, which =4, type ="pearson", sub.caption ="")plot(gy2, which =2:3)
