A study of how eye movement behavior can distort one's judgment of the location of an object was published in Advances in Cognitive Psychology (Vol. 6, 2010). The researchers had volunteers fixate their eyes on a cross in the middle of a computer screen. A probe was then spatially extended near the cross and each volunteer was asked to judge the location of the probe. Saccadic (i.e., fast voluntary) eye movement was monitored during each session. The researchers used spatial position of the probe (x1, measured in degrees) and position of the cross (x2, degrees) to predict the amplitude (y) of saccadic eye movement. The following model was fit to the data:
E(y) = β0 + β1x1 + β2x2 + β3x1x2
a. The model yielded R2 = .994. Interpret this result.
b. In the words of the problem, what does it mean to say that "x1 and x2 interact"?
c. The least squares prediction equation was determined as: ŷ = .91 + .70x1 - .06x2 - .03x1x2. Illustrate interaction by graphing the relationship between predicted amplitude (ŷ) and cross position (x2) for probe positions x1 = 3.5 and x1 = 6.5.