Prime Rib Temperature

We started a new family Christmas Eve tradition with roast prime rib. This year was a 6.61 lb bone on prime rib.

library(dplyr)

## 
## Attaching package: 'dplyr'

## The following objects are masked from 'package:stats':
## 
##     filter, lag

## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union

library(ggplot2)
dat <- tbl_df(read.csv("../datasets/Prime_rib_temp.csv"))

I followed the Serious Eats recipe.

I cut off the bone then salted and let the bones and meat dry brine overnight. I tied them back together around noon and put them in a 200 degree Fahrenheit oven. The temperature didn’t budge for most of the first hour and then it was a reasonably linear rise in temperature until I took it out when the meat was 125 degrees. It went up to 135 while resting for an hour.

ggplot(dat, aes(x = minutes, y = temperature)) + geom_point()

What a beautiful line! Taking off the first few observations, we can put on a regression line.

dat %>% filter(temperature >45) %>% 
  ggplot(aes(x = minutes, y = temperature)) + 
  geom_point() + geom_smooth(method = "lm")

I decided to fit a regression model to that line to see how linear it was.

dat2 <- dat %>% filter(temperature > 45)
model1 <- lm(temperature ~ minutes, dat2)
summary(model1)

## 
## Call:
## lm(formula = temperature ~ minutes, data = dat2)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.5854 -0.5930 -0.2445  0.7671  1.1959 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 22.522427   0.643147   35.02   <2e-16 ***
## minutes      0.459377   0.004181  109.88   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9197 on 16 degrees of freedom
## Multiple R-squared:  0.9987, Adjusted R-squared:  0.9986 
## F-statistic: 1.207e+04 on 1 and 16 DF,  p-value: < 2.2e-16

The coefficient was 0.46 degrees per minute with an R squared of 0.999!