Question

Fitt's Law. A robust and highly adopted model of human movement is Fitt's Law. According to Fitt's Law, the time T required to move and select a target of width W that lies at a distance (or amplitude) A is

T = a + b log₂(2A/W)

where a and b are constants estimated using simple linear regression. The quantity log₂(2A/W) is termed the Index of Difficulty (ID) and represents the independent variable (measured in "bits") in the model. Research reported in the Special Interest Group on Computer-Human Interaction Bulletin (July 1993) used Fitt's Law to model the time (in milliseconds) required to perform a certain task on a computer. Based on data collected for n=160 trials (using different values of A and W), the following least-squares prediction was obtained:

T_hat = 175.4 + 133.2(ID)

a. Interpret the estimates, 175.4 and 133.2.

b. The coefficient of correlation for the analysis is r = .951. Interpret this value.

c. Conduct a test to determine whether the Fitt's Law model is statistically adequate for predicting performance time. Use alpha = .05. (SPECIFICALLY, I WOULD LIKE AN EXPLANATION OF WHAT TO DO WHEN THE CRITICAL VALUE FOR THE STUDENT'S T IS NOT GIVEN IN THE TABLE WHEN THE DEGREES OF FREEDOM (FOR THIS PROBLEM)=n-2=160-2=158. THE t-DISTRIBUTION TABLE STOPS AT 120 FOR DEGREES OF FREEDOM.)

d. Calculate the coefficient of determination, r². Interpret the result.

Answer 1

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