People swam across Lake Ontario from Niagara on the Lake to Toronto (52 km, or about 32.3 mi) 62 times between 1954 and 2016. We might be interested in whether the swimmers are getting any faster or slower. Here are the regression of the crossing Times (minutes) against the Year since 1954 of the crossing and a plot of the residuals against Year since 1954:

a) What does the R² mean for this regression?
b) Are the swimmers getting faster or slower? Explain.
c) The outlier seen in the residuals plot is a crossing by Vicki Keith in 1987 in which she swam a round trip, north to south, and then back again. Clearly, this swim doesn’t belong with the others. Would removing it change the model a lot?

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Residuals 1500 750 of Dependent variable is Time R-squared = 1.1% s = 405.5 Variable Intercept Year since 1954 + 0.0 12.5 Coefficient 1188.04 2.544 25.0 37.5 Year since 1954 50.0