Decreasing pH in aging meat

Schwenke and Milliken (1991) modelled the relationship between pH and time since slaughter for steer carcasses. (They looked at it from a different perspective than we will here, so it's not necessary for you to investigate what they did in their paper.) We'll look at a subset of the data in that paper, restricting our attention to the pH levels up to 8 hours after slaughter. The data is contained in the file 2050_F21_steer_pH. Before you begin an analysis, it's a good idea to plot the data and see what you are working with. Draw a scatterplot with pH on the Y axis, and time on the X. Don't submit this, but we will work with it on the last part of this question.

a) Pretend for a moment that a simple linear regression model of pH on time is reasonable. Carry this out in R and submit the output. Clearly and concisely interpret the estimate of the slope parameter. (This should not involve any discussion of a hypothesis test - simply tell me what the slope estimate means in the context of the problem, assuming the fit was reasonable in the first place.) That's it for part a). But a straight line fit appears to be inadequate. Let's see if we can come up with a better model. For the following questions, you will need to get the results of these regressions: pH on the natural log of time (i.e. pH = ₀ + ₁ln(time) + )

pH on time and time2 (i.e. pH = ₀ + ₁time + ₂time² + )

b) In R, plot a scatterplot of pH vs time and properly label the axes. On this plot, add: The regression line from the fit of pH on time. A curve representing the fit including the quadratic term. A curve representing the fit of pH on log time. These 3 curves (1 line + 2 curves) must be superimposed on the scatter plot of the raw (untransformed) values (i.e. a scatterplot of pH on time). Use a different colour and line type for each curve, and include a legend.

c) Which of the 3 models do you feel is best? Clearly and concisely justify your response.

Data

time

ph

1	7.05
1	6.91
2	6.44
2	6.53
4	6.07
4	5.95
6	5.63
6	5.85
8	5.54
8	5.39