GSR 516 Summer 2008
Homework Assignment 6
Due July 29, 2008
Simple Linear Regression
"Women May Outrun Men, Researchers Suggest"
Women runners might start beating men in world-class competitions within a few
generations, researchers said Thursday.
An analysis of world records for a variety of distances found that women have been
improving about twice as quickly as men. And if that continues, the top female and male
runners might start performing equally well between the years 2015 and 2055 in the 200-,
400-, 800-, and 1,500-meter events, according to a study. The findings were reported in a
letter in the journal Nature.
"None of the current women's world-record holders at these events could even meet the
men's qualifying standard to compete in the 1992 Olympic games," researchers Brian
Wipp and Susan Ward wrote.
"However, it is the rates of improvement that are so strikingly different - the gap is
progressively closing." But other researchers said they doubted the projections because
they believed women's rate of improvement would slow.
Source: Journal staff and wire services, Milwaukee Journal, January 1992
Tasks
1. Construct a scatterplot of times in the 200-meters against year for the men's data.
Construct a separate scatterplot for the women's data. Describe the patterns in the
scatterplots. Specifically, are the patterns linear or at least approximately linear?
2. Calculate the correlation between men's times in the Olympic 200-meters and the
Olympic year. Do the same for the women's times. Which gender's times in the
Olympic 200-meters exhibit a stronger correlation with Olympic year?
3. Fit a least squares regression line to the data for men's times in the 200-meters.
Use technology or draw by hand the line on the men's scatterplot.
4. Fit a line to the data for women's times. Again, draw the line on the scatterplot.
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