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A positive association in statistics refers to a relationship between two variables where if one variable increases, the other tends to increase as well. It's like having a seesaw that goes up on both ends. Think of it as a friendship where whenever one friend is happy, the other one is usually happy too. In the context of the NFL example, a positive association would mean that as teams win more games during the preseason, they also win more games during the regular season.
A positive association can be visualized on a scatterplot. Points would generally rise together, moving from the lower left to the upper right corner. This kind of association implies a tendency or a trend rather than a guarantee, suggesting an overall increase for both variables.
In technical terms, when talking about correlation coefficients, a positive association is reflected by a positive value. The stronger the association, the closer the coefficient is to 1. In this case, however, the number 0.067 suggests a very weak association even though it's positive.

In contrast to a positive association, a negative association describes a relationship between two variables where if one variable increases, the other tends to decrease. Imagine a seesaw where when one end goes up, the other goes down. In our NFL example, a negative association would imply that as teams win more games in the preseason, they tend to win fewer games during the regular season.
This kind of association can be visualized as a downward trend on a scatterplot. The points would typically move from the upper left to the lower right corner. It suggests an inverse relationship.
For correlation coefficients, a negative association is represented by a negative value. The closer the value is to -1, the stronger the negative association. A strong negative association would look like a clear downward slope on a graph of the data points.

A linear relationship in statistics involves a consistent change between two variables. In simpler terms, it means that if you create a graph of the two variables, the points could be connected with a straight line. This line doesn’t have to touch all the points but should reflect the overall trend of the data.
In our NFL example, the term "linear relationship" helps us assess if there’s a consistent trend between preseason and regular season wins. Given that the correlation coefficient is 0.067, the data show a very weak linear relationship. This means we can't strongly predict the outcome of regular season wins based on preseason performance. The points are likely scattered, not forming a clear straight line.
Linear relationships are commonly assessed using correlation. A perfect linear relationship is when the points fall exactly on a straight line, with correlation coefficients close to 1 or -1 depending on whether the association is positive or negative. Here, the weak coefficient tells us the data points don’t align well to suggest a straightforward pattern between the factors.