Question

Does pre-season success indicate regular season success in the US National Football League? We looked at the number of preseason wins and regular season wins for all 32 NFL teams over a 10 -year span. (a) What would a positive association imply about the relationship between pre-season and regular season success in the NFL? What would a negative association imply? (b) The correlation between these two variables is \(r=0.067\). What does this correlation tell you about the strength of a linear relationship between these two variables?

Short answer

A positive association implies teams with more wins in the preseason also have more wins in the regular season. A negative association implies the opposite, teams with more preseason wins tend to have fewer regular season wins. The correlation coefficient \(r=0.067\) tells us that there is a very weak positive correlation between preseason and regular season wins.

Step-by-step solution

Interpretation of positive and negative association

Part (a) of the question asks about the implications of positive and negative association. From this, a positive association would imply that teams that have more preseason wins also tend to have more regular season wins. A negative association, on the other hand, would imply that teams that have more preseason wins tend to have fewer regular season wins.

Interpretation of correlation

Part (b) of the question mentions a correlation coefficient of \(r = 0.067\). This is a value very close to 0, which indicates a very weak positive correlation between preseason wins and regular season wins. This suggests that there is almost no linear relationship between these two variables and preseason success does not strongly predict regular season success.