Question

1. iq and grades do students with higher iq test scores tend to do better in school? the figure below shows a scatterplot of iq and school grade point average (gpa) for all 78 seventh - grade students in a rural midwestern school. (gpa was recorded on a 12 - point scale with a+ = 12, a = 11, a− = 10, b+ = 9, ..., d− = 1, and f = 0.)5

(a) does the plot show a positive or negative association between the variables? why does this make sense?
(b) what is the form of the relationship? is it very strong? explain your answers.
(c) at the bottom of the plot are several points that we might call outliers. one student in particular has a very low gpa despite an average iq score. what are the approximate iq and gpa for this student?

Explanation:

(a) As the IQ score increases, the grade - point average generally increases, so it is a positive association. Higher IQ is often associated with better learning ability and thus higher grades.
(b) The form appears to be roughly linear. It is moderately strong as the points follow a somewhat linear trend but there is still some scatter.
(c) By looking at the scatter - plot, the student with an average IQ (around 100) and a very low GPA (around 1) can be identified.

Answer:

(a) Positive association. Higher IQ may lead to better grades.
(b) Roughly linear, moderately strong. Points follow a linear trend with scatter.
(c) IQ is approximately 100, GPA is approximately 1.