match each correlation coefficient to the appropriate scatter plot. r = 0.4 r = 0.9 r = -0.4 r = -1

match each correlation coefficient to the appropriate scatter plot. r = 0.4 r = 0.9 r = -0.4 r = -1

match each correlation coefficient to the appropriate scatter plot. r = 0.4 r = 0.9 r = -0.4 r = -1

Answer

Answer:

  1. For the scatter - plot with points showing a weak positive linear trend: $r = 0.4$
  2. For the scatter - plot with points showing a strong positive linear trend: $r = 0.9$
  3. For the scatter - plot with points showing a weak negative linear trend: $r=-0.4$
  4. For the scatter - plot with points showing a perfect negative linear trend (falling on a straight line): $r = - 1$

Explanation:

Step1: Understand correlation coefficient

The correlation coefficient $r$ ranges from - 1 to 1. Positive $r$ values indicate a positive linear relationship (as $x$ increases, $y$ increases), and negative $r$ values indicate a negative linear relationship (as $x$ increases, $y$ decreases).

Step2: Analyze strength of correlation

The closer $|r|$ is to 1, the stronger the linear relationship. When $r = 1$, there is a perfect positive linear relationship, and when $r=-1$, there is a perfect negative linear relationship. When $|r|$ is close to 0, the linear relationship is weak.

Step3: Match with scatter - plots

Based on the above rules, match the given $r$ values to the scatter - plots according to the direction (positive or negative) and strength (weak or strong) of the linear trends shown in the scatter - plots.