49 Eye movement and spatial distortion. 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 medical term for fast voluntary movement of the eyes when focusing on an object is saccadic eye movement . The researchers designed several experiments in which volunteers fixated 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 eye movement was monitored during each session. The researchers used spatial position of the probe ( x 1 , measured in degrees) and position of the cross ( x 2 , degrees) to predict the amplitude ( y ) of saccadic eye movement. The following model was fit to the data:

a. The model yielded R2 = .994 . Interpret this result.

b. In the words of the problem, what does it mean to say that “ x 1 and x 2 interact”?

c. The least squares prediction equation was determined as: yn = .91 + .70x1-.06x2-.03x1x2 . Illustrate interaction by graphing the relationship between predicted amplitude ( yn ) and cross position ( x 2 ) for probe positions x1 = 3.5 and x1 = 6.5 .

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= E(y) Bo+Bx1 + Bx2 + B3x142