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Unformatted text preview: PUBH 7430 Assignment 1 Solutions J. Wolfson September 29, 2011 On this assignment, as in all homeworks, UNEDITED COMPUTER OUTPUT IS NOT ACCEPTABLE . Tables and plots prepared from statistical output should be appro- priate for inclusion in a scientific report, with all statistics rounded to a reasonable number of significant digits. Background Each year the U.S. Naval Postgraduate School sets aside a Discovery Day during which the general public is invited into their laboratories. This dataset is from October 21st 1995, when visitors could test their reaction times and hand-eye coordination in the Human Systems Integration Laboratory. The variable of interest, anticipatory timing, was measured by a Bassin timer, which measures a persons ability to estimate the speed of a moving light and its arrival at a designated point. The timer consists of a 10 foot row of lights which is controlled by a variable speed potentiometer. The lights are switched on sequentially from one end to the other so that light travels at 5 miles per hour down the timer. Each visitor was instructed to anticipate the arrival of the light at one end of the timer and at that time to swing a plastic bat across a light beam at the same end of the timer. An automatic timing device measured the difference between the breaking of the beam and the actual arrival of the light. In the original data, a negative time value for a trial indicated that the bat broke 1 the beam before the light actually arrived; in the version provided to you, all times have been transformed to positive values, so that the values reflect the magnitude of how far off the participant was in timing. Each of 113 visitors completed the trial five times. Age and gender were also recorded, since the researchers were interested in age and gender differences in reaction times. Visitors tended to come in family groups, but that information was not recorded. You can find these data from the file timetrial.dat from the class webpage. These data are organized in wide format, with one row per person and one column for each of the five trials. Depending on what software you use for graphing, they may need to be reshaped to long format, i.e. to have one row per trial instead. 1. Notation. Consider the notation presented in Lecture 3, where outcomes are denoted by Y and covariates/predictors by X . Suppose we are interested in modeling the response times in this dataset as a function of age, gender, and trial number, via the simple linear model Y = X + For this model as applied to the time-trial data: (a) Let Y i denote the response vector for each individual. What is the length of Y i ? 5 (b) What is the length of Y ? 113 5 = 565 (c) Let X i denote the vector of covariates/predictors for each individual. What is the dimension of X i ? 5 3, 5 4 if you include the column for the intercept....
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This note was uploaded on 11/21/2011 for the course PUBH 7430 taught by Professor Prof.eberly during the Fall '04 term at Minnesota.
- Fall '04