Question

name:

1. a group of high school students were asked how many ap classes they are taking and also how many extracurricular activities they participate in (such as sports or theater). a scatterplot of the data is shown.

a) what is the explanatory variable? what is the response variable?
b) describe the relationship between the number of ap courses and the number of extracurricular activities.

Explanation:

Part (a)

The explanatory variable is the one used to explain or predict changes in another variable. Here, we're looking at how the number of AP courses might relate to extracurricular activities, so the number of AP courses is the explanatory variable (plotted on the x - axis). The response variable is the one that is being measured or responded to, which is the number of extracurricular activities (plotted on the y - axis).

To describe the relationship, we look at direction, form, and strength. From the scatterplot, as the number of AP courses (x - variable) increases, the number of extracurricular activities (y - variable) generally increases, so the direction is positive. The form appears to be roughly linear (the points seem to follow a general upward - sloping trend). The strength: while there is some scatter, there is a noticeable positive association, so it's a moderately strong positive linear relationship (we can also note that as AP courses increase, extracurricular activities tend to increase, with a linear trend and some variability).

Answer:

Explanatory variable: Number of AP courses
Response variable: Number of extracurricular activities

Part (b)