A researcher conducted experiments to compare memory performance between serial and free recall. A total of 72 participants were randomly assigned to different treatment groups. Each participant viewed 11 letters on a computer screen, completed a movement task, and then recalled the presented letters. Each participant attended one session and repeated the entire procedure four times, with different sets of letters each time. The outcome measure is the average number of correctly recalled letters out of the first 5 presented. You can download the data file at the following link.

http://www.auburn.edu/~zengpen/teaching/STAT-7010/datasets/letters.csv

The meaning of the variables are as follows.

Time	Meaning
1	8:00 -- 10:00 session
2	10:00 -- 12:00 session
3	12:00 -- 2:00 session
4	2:00 -- 4:00 session

Memory	Meaning
1	serial recall
2	free recall

Movement	Meaning
1	turn two glasses upside down
2	move two cylinders from an upper shelf to a lower shelf
3	move one cylinder from an upper shelf to a lower shelf

Answer questions based on a model with all main effects, two-factor interactions, and three-factor interactions of time, memory, and movement. All effects are fixed effects.

a.Draw an interaction plot of memory against movement, where the x-axis indicates movement and different lines indicate different levels of memory. What can you observe from this plot?

b. Construct an ANOVA table that includes all effects. The columns include Source of variation, Degrees of freedom, Sum of Squares, Mean Squares, F-value, and p-value.