Use the pressure data to fit a model with pressure as the response and temperature as the predictor. Use the Box-Cox method to determine the best transformation on the response.

library(faraway) 
data(pressure) 
plot(pressure$temperature, pressure$pressure)

lmodt <- lm(pressure ~ temperature, data=pressure)
library(MASS) 
boxcox(lmodt, plotit=T)

boxcox(lmodt, lambda=seq(0.05,0.15,by=0.001), plotit=T)

Maximum transformation at lambda=0.12

plot(pressure$temperature, pressure$pressure^0.12) 
lmodt2 = lm(pressure^0.12 ~ temperature, data=pressure) 
abline(lmodt2$coefficients)

x = seq(0,360,by=0.1) 
y = (lmodt2$coeff[1]+lmodt2$coeff[2]*x)^(1/0.12) 
plot(pressure$temperature, pressure$pressure) 
lines(x,y)

summary(lmodt2)
## 
## Call:
## lm(formula = pressure^0.12 ~ temperature, data = pressure)
## 
## Residuals:
##        Min         1Q     Median         3Q        Max 
## -0.0175875 -0.0087058 -0.0001531  0.0083502  0.0212483 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 3.386e-01  4.773e-03   70.94   <2e-16 ***
## temperature 5.309e-03  2.265e-05  234.37   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.01082 on 17 degrees of freedom
## Multiple R-squared:  0.9997, Adjusted R-squared:  0.9997 
## F-statistic: 5.493e+04 on 1 and 17 DF,  p-value: < 2.2e-16

we can write an eqution of the model from these intercepts for the reponse of pressure^0.12