GasolineYield: Estimation of Gasoline Yields from Crude Oil
In betareg: Beta Regression

Description Usage Format Details Source References See Also Examples

Operational data of the proportion of crude oil converted to gasoline after distillation and fractionation.

1	data("GasolineYield")

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.

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.

Taken from Prater (1956).

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. http://www.jstatsoft.org/v34/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.

Prater, N.H. (1956). Estimate Gasoline Yields from Crudes. Petroleum Refiner, 35(5), 236–238.

betareg

data("GasolineYield", package = "betareg")

gy1 <- betareg(yield ~ gravity + pressure + temp10 + temp, data = GasolineYield)
summary(gy1)

## Ferrari and Cribari-Neto (2004)
gy2 <- betareg(yield ~ batch + temp, data = GasolineYield)
## Table 1
summary(gy2)
## Figure 2
par(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)
par(mfrow = c(1, 1))

## exclude 4th observation
gy2a <- update(gy2, subset = -4)
gy2a
summary(gy2a)

Call:
betareg(formula = yield ~ gravity + pressure + temp10 + temp, data = GasolineYield)

Standardized weighted residuals 2:
    Min      1Q  Median      3Q     Max 
-2.1189 -0.6985 -0.0088  0.6306  2.1572 

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: 144 (BFGS) + 5 (Fisher scoring) 

Call:
betareg(formula = yield ~ batch + temp, data = GasolineYield)

Standardized weighted residuals 2:
    Min      1Q  Median      3Q     Max 
-2.8750 -0.8149  0.1601  0.8384  2.0483 

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) 

Call:
betareg(formula = yield ~ batch + temp, data = GasolineYield, subset = -4)

Coefficients (mean model with logit link):
(Intercept)       batch1       batch2       batch3       batch4       batch5  
   -6.35647      1.88688      1.37039      1.62512      1.08066      1.15158  
     batch6       batch7       batch8       batch9         temp  
    1.05766      0.56522      0.50066      0.38523      0.01146  

Phi coefficients (precision model with identity link):
(phi)  
577.8  


Call:
betareg(formula = yield ~ batch + temp, data = GasolineYield, subset = -4)

Standardized weighted residuals 2:
    Min      1Q  Median      3Q     Max 
-2.3747 -1.0482  0.1391  0.8703  2.4165 

Coefficients (mean model with logit link):
              Estimate Std. Error z value Pr(>|z|)    
(Intercept) -6.3564713  0.1716020 -37.042  < 2e-16 ***
batch1       1.8868782  0.1001837  18.834  < 2e-16 ***
batch2       1.3703911  0.1042352  13.147  < 2e-16 ***
batch3       1.6251199  0.1028326  15.804  < 2e-16 ***
batch4       1.0806596  0.0897855  12.036  < 2e-16 ***
batch5       1.1515826  0.0906857  12.699  < 2e-16 ***
batch6       1.0576556  0.0929172  11.383  < 2e-16 ***
batch7       0.5652219  0.0956100   5.912 3.39e-09 ***
batch8       0.5006625  0.0953210   5.252 1.50e-07 ***
batch9       0.3852258  0.1037500   3.713 0.000205 ***
temp         0.0114588  0.0003945  29.050  < 2e-16 ***

Phi coefficients (precision model with identity link):
      Estimate Std. Error z value Pr(>|z|)    
(phi)    577.8      146.7   3.938 8.22e-05 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Type of estimator: ML (maximum likelihood)
Log-likelihood: 86.62 on 12 Df
Pseudo R-squared: 0.9662
Number of iterations: 51 (BFGS) + 4 (Fisher scoring)