A robust and highly adopted model of human movement is Fitts’ Law. According to Fitts’ 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 Fitts’ Law to model the time (in milliseconds) required to perform a certain task on a computer. Based on data collected for n = 10 trials (using different values of A and W), the following least squares prediction was obtained:

T̂ = 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 Fitts’ Law model is statistically adequate for predicting performance time. Use α = .05.

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