Exercise 2 Page 670

Our goal is to tell how we can conclude these two types of sets of data points.

1. The data points have a positive association.
2. The data points have a negative association.

Let's remember that a data point is a pair of two numerical values, usually an x-value and a y-value. Association tells us about the relationship between the variables x and y.

Positive Association

Positive association describes a situation in which the two variables move in the same direction. If x increases, so does y. We can see this trend in the following example. The data set shows how the monthly ice cream sales at an ice cream booth change with temperature. ( 81 ^(∘) F, $ 2100 ), ( 84^(∘) F, $ 2520), ( 86^(∘) F, $2700), ( 88^(∘) F, $ 2950), ( 91^(∘) F, $ 3170) The higher the temperature, the bigger the sales. To better see the trends in data, let's split it. We will write the x-values in the left column of a table, and the corresponding y-values in the right column.

We see that as the temperature x rises, the ice cream sales y rise too. This is true for all data sets with a positive association.

Negative Association

Negative association describes a situation in which the two variables move in the opposite direction. If x increases, y decreases. The data set below shows how the slippers sales at a mall kiosk change with the outside temperature. ( 81 ^(∘) F, $70 ), ( 84^(∘) F, $ 58), ( 86^(∘) F, $46), ( 88^(∘) F, $34), ( 91^(∘) F, $22) We can also present this data in a table.

Quite intuitively, the warmer it gets, the less people will come to the mall to buy new slippers. This is because slippers are an item we usually buy when it is cold.

Summary

Variable association tells us about the relationship between variables. Positive association tells us that both variables move in the same direction. cc x & y ↑ & ↑ Negative association tells us that the variables move in opposite directions. cc x & y ↑ & ↓ If we know the association that the data set has, we can tell how the variables relate.