Correlation and Regression
Solve the following problem:
The coach of the Ottawa football team wants to determine if there is a relationship between how fast players can run 60 m and how far they can throw the football. The results for the Ottawa players were as follows:
Player Spring Time (s) Throwing Distances (m)
Jon H. 7.92 32
Tom M. 8.66 29
Sarjay P. 6.58 35
Brandon F. 8.9 32
Tyler C. 7.12 34
Steve K. 8.76 29
Matt H. 7.55 40
Robin L. 7.37 33
Alex H. 7.96 30
Mike N. 8.45 31
Ankit K. 7.75 26
Scott R. 8.05 32
a.Using technology, create a scatter plot of sprint times versus throwing distances.
b.Perform a linear-regression analysis of the data to find the line of best fit and the correlation coefficient.
c.Describe the relationship between these sprint times and throwing distances.
d.State which data points could be identified as outliers, and explain why you chose them.
e.Remove the outliers and repeat the regression analysis. Determine the lines of best fit and the correlation coefficient for this smaller sample.
f.What might the coach conclude from this analysis? What limits the predictions he could make?
g.Use the two regression equations from parts b) and e) to estimate the throwing distance for a player whose sprint time is 6.50s.