Gasoline {MEMSS}

Refinery yield of gasoline

Description

The Gasoline data frame has 32 rows and 6 columns.

Format

This data frame contains the following columns:

yield

a numeric vector giving the percentage of crude oil converted to gasoline after distillation and fractionation

endpoint

a numeric vector giving the temperature (degrees F) at which all the gasoline is vaporized

Sample

the inferred crude oil sample number - a factor with levels A to J

API

a numeric vector giving the crude oil gravity (degrees API)

vapor

a numeric vector giving the vapor pressure of the crude oil (\mathrm{lbf}/\mathrm{in}^2)

ASTM

a numeric vector giving the crude oil 10% point ASTM—the temperature at which 10% of the crude oil has become vapor.

Details

Prater (1955) provides data on crude oil properties and gasoline yields. Atkinson (1985) uses these data to illustrate the use of diagnostics in multiple regression analysis. Three of the covariates—API, vapor, and ASTM—measure characteristics of the crude oil used to produce the gasoline. The other covariate — endpoint—is a characteristic of the refining process. Daniel and Wood (1980) notice that the covariates characterizing the crude oil occur in only ten distinct groups and conclude that the data represent responses measured on ten different crude oil samples.

Source

Prater, N. H. (1955), Estimate gasoline yields from crudes, Petroleum Refiner, 35 (5).

Atkinson, A. C. (1985), Plots, Transformations, and Regression, Oxford Press, New York.

Daniel, C. and Wood, F. S. (1980), Fitting Equations to Data, Wiley, New York

Venables, W. N. and Ripley, B. D. (1999) Modern Applied Statistics with S-PLUS (3rd ed), Springer, New York.

Examples

require(lattice)
str(Gasoline)
xyplot(yield ~ endpoint | Sample, Gasoline, aspect = 'xy',
       main = "Gasoline data", xlab = "Endpoint (degrees F)",
       ylab = "Percentage yield",
       type = c("g", "p", "r"),
       index.cond = function(x,y) coef(lm(y~x))[2],
       layout = c(5,2))
print(m1 <- lmer(yield ~ endpoint + (1|Sample), Gasoline), corr = FALSE)
m2 <- lmer(yield ~ endpoint + (endpoint|Sample), Gasoline, verbose = 1)
print(m2)
Gasoline$endptC <- with(Gasoline, endpoint - mean(endpoint))
m3 <- lmer(yield ~ endpoint + (endptC|Sample), Gasoline, verbose = 1)
print(m3)
xyplot(endptC ~ `(Intercept)`, ranef(m3)[[1]], type = c("g", "p", "r"),
       aspect = 1)