Fitts' Law is a robust and highly adopted model of human movement. 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 log,(2A/W) where a and b are constants estimated using simple linear regression. The quantity log,(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 = 160 trials (using different values of A and W), the following least squares prediction equation was obtained: Î = 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 model using Fitts' Law is statistically adequate for predicting performance time. Use a = .05.

Fitts' Law is a robust and highly adopted model of human movement. 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 log,(2A/W) where a and b are constants estimated using simple linear regression. The quantity log,(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 = 160 trials (using different values of A and W), the following least squares prediction equation was obtained: Î = 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 model using Fitts' Law is statistically adequate for predicting performance time. Use a = .05.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Concept explainers

Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.

Question

Fitts' Law is a robust and highly adopted model of human movement. 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)
%D
where a and b are constants estimated using simple linear regression. The quantity log,(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 = 160 trials (using different values of A and W), the
following least squares prediction equation was obtained:
Î = 175.4 + 133.2(ID)
%3D
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 model using Fitts' Law is statistically adequate for
predicting performance time. Use a = .05.
d. Çalculate the coefficient of determination, r². Interpret the result.

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