The article “Low-Temperature Heat Capacity and Thermodynamic Properties of 1,1,1-trifluoro-2, 2-dichloroethane” (R. Varushchenko and A. Druzhinina, Fluid Phase Equilibria, 2002:109–119) presents measurements of the molar heat capacity \((y)\) of 1,1,1-trifluoro-2,2-dichloroethane (in \(\mathrm {J \cdot K^{-1} \cdot mol^{-1}}\)) at several temperatures \((x)\) in units of 10 K. The results for every tenth measurement are presented in the following table.

a. Fit the simple linear model \(y=\beta_{0}+\beta_{1} x+\varepsilon\). Make a residual plot, and comment on the appropriateness of the model.

b. Fit the simple linear model \(y=\beta_{0}+\beta_{1} \ln x+\varepsilon\). Make a residual plot, and comment on the appropriateness of the model.

c. Compute the coefficients and their standard deviations for polynomials of degrees 2, 3, 4, and 5. Make residual plots for each.

d. The article cited at the beginning of this exercise recommends the quartic model \(y=\beta_{0}+\beta_{1} x+\beta_{2} x^{2}+\beta_{3} x^{3}+\beta_{4} x^{4}+\varepsilon\). Does this seem reasonable? Why or why not?

Equation Transcription:

Text Transcription:

(y)

J{cdot}K^{-1}{cdot}mol^-1

(x)

y=beta_0+beta_1x+varepsilon

y=beta_0+beta_1 ln x+varepsilon

y=beta_0+beta_1x+beta_2x^2+beta_3x^3+beta_4x^4+varepsilon

09.20 Lecture Tuesday, September 20, 2016 12:35 PM I. Quiz Review (Questions and Answers onR eading notes for 09.20) II. Lecture Slides • Treisman's -‐ Attentuation theory ○ Called a "Leaky Filter" Model • Late selection model ○ We make the selection or determination of what we are going to attend to after we know what everyone else is doing/saying ○ Think about this in terms of two messages coming into separate ears, this model says that we receive all info, process it for meaning, and then decide which to pay attention to ○ Selection occurs after meaning ○ Studies that exemplify this model: ▪ McKay (1973) -‐separate messages in each ear • Left ear hears, "They were throwing stones at the bank" • Right hears, "-‐-‐-‐ -‐-‐-‐ -‐-‐-‐-‐ -‐-‐-‐ -‐-‐-‐-‐-‐-‐-‐river" or " -‐-‐-‐ -‐-‐-‐ -‐-‐-‐-‐ -‐-‐-‐-‐ money" • Heard the words "bank" and either "river" or "money" at the same time • They