Chapter 3.1, Problem 3E

(a)

To determine

To find: whether the plot show a positive association or not

Answer to Problem 3E

The plot shows a positive association between the two variables.

Explanation of Solution

Given:

  

Calculation:

The figure below shows a scatterplot of IQ scoresand grade point average. IQ scores will help in explaining “Grade point average”. So “IQ score” is the explanatory variable and “Grade point average” is the response variable. We want to see how grade point average changes when $IQ$ score changes, so we put IQ score(the explanatory variable) on the horizontal axis and Grade point average (the response variable) on the vertical axis. Let’s take a closer look at the scatterplot from the figure.

The graph shows a clear direction: the overall pattern moves from lower left to upper right. That is, states in which students with higher $IQ$ Scores tend to have Grade point average. We call this a positive association between the two variables.

(b)

To determine

To find:the form of the relationship and explain whether it is very strong or not

Answer to Problem 3E

The form of the relationship is linear. The relationship is moderately strong

Explanation of Solution

The form of the relationship is linear. That is, the overall pattern follows a straight line from lower left to upper right. The relationship is moderately strong because the points don’t deviate greatly from line but there are some outliers.

(c)

To determine

To find:the approximate IQ and GPA for the student

Answer to Problem 3E

The student has IQscore $103$ (approx.) but get GDP $0.4$ (approx.)

Explanation of Solution

In Figure point $P$ has a very low $GPA$ despite an average $IQ$ score. When we draw perpendiculars from point $P$ to $X$ axis and $Y$ axis we see the coordinate of point $P$ is approximately $(103,0,4)$ . This shows that that student has $IQ$ score $103$ (approx.) but get GDP $0.4$ (approx.).