Take home problems for Exam 5

1. Jigsaw puzzles are a fun group activity for the holidays. Are some brands of jigsaw puzzles more expensive than others? To investigate this question, researchers collected data on the price of various puzzles from four different brands, along with the number of pieces per puzzle. For each part of the problem, write one or more sentences explaining your results. The data are listed below:

Company    PuzzlePieces    Price
ravensburger 200  10.99
ravensburger 300  14.99   
ravensburger 300  11.99
ravensburger 500  15.99   
ravensburger 500  12.99
ravensburger 1000  16.99  
ravensburger 1500  21.99
whitemountain 300   14.99   
whitemountain 300   14.99
whitemountain 550   13.99
whitemountain 1000  16.99   
whitemountain 1000  15.99
educa 200  9.99
educa 500  12.99
educa 1000  18.99   
educa 1000  19.99
educa 1500  26.99
buffalogames 300  10.99    
buffalogames 300  7.99    
buffalogames 500  10.99
buffalogames 750  14.99
buffalogames 1000  14.99   
buffalogames 1000  14.99
buffalogames 2000  21.99
a) Conduct an analysis to investigate whether puzzle prices differ between brands, while adjusting for number of pieces. Write the equation for the linear model, identifying each term. Use a plot to illustrate the relationship between price, and number of pieces, and how price varies among brands.
b) Compute the ANOVA table, and conduct tests for brand and number of pieces, and their interaction.
c) If an interaction occurs, use graphical aids and other approaches to help understand the interaction. 
d) Use residual plots to explore model assumptions. 

2. For problem 1 above, using the data and the model assuming parallelism, calculate the standard error of each adjusted mean, and also calculate the efficiency of the covariance adjustment.

3. A researcher wants to create a quarter fraction of a 25 factorial design, with factors A, B, C, D, and E. She wants to use the defining relation I = ABD = -ACDE.

a) Write down the eight treatment combinations to be used in the design.

b) What is the resolution of the design?

c) Write out the alias structure for all main effects and two-way interactions.