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 , $\mathrm{A}+=12,\mathrm{A}=11,\mathrm{A}-=10,\mathrm{B}+=9,\dots ,\mathrm{D}-=1,and\mathrm{F}=0.{)}^2$

(a) Say in words what a positive association betweenIQ and GPA would mean. Does the plot show a positive association?

(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 of this student?

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.

The plot shows a positive association between the variables because the pattern in the scatterplot slopes upwards.

This makes sense because we expect the grade point average to increase as the IQ score increases (as we expect more intelligent people to get higher grades), which is implied by a positive association.

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.

This graph has a linear form. The form of the relationships is important. The most important form we look for is a linear relationship. We also can look for curved relationships and clusters.
The strength is moderately strong because most of the points would be close to the linear form.

The strength is determined by how close the points in the scatterplot lie to the linear form.

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.

The point at the bottom center of the scatter plot does not seem to fit, as it shows a relatively average IQ but a very low GPA. An outlier is data that really does not seem to fit in the scatterplot. When we draw perpendiculars from point $P$to $X$axis and $Y$axis we see the coordinate of point $$" width="9">Pis approximately $(103,0,4)$.