Question

Correlation isn’t everything Marc and Rob are both high school English teachers. Students think that Rob is a harder grader, so Rob and Marc decide to grade the same $10$ essays and see how their scores compare. The correlation is $r=0.98$ but Rob’s scores are always lower than Marc’s. Draw a possible scatterplot that illustrates this situation.

Short answer

The highest possible score is $100\%$

Step-by-step solution

Given information

Correlation,$r=0.98$

Explanation

Rob’s scores are always lower than Marc’s.

A positive linear correlation exists when $r$ is positive.

A negative linear correlation exists when $r$ is negative.

For weak correlation,

$0<\left|r\right|<0.5$

For moderate correlation,

$0.5<\left|r\right|<0.8$

For strong correlation,

$0.8<\left|r\right|<1$

Note that

The correlation between Rob's and Marc's scores is significant and positive.

Since the data involves the same $10$essays for both the teachers.

Moreover,

The points should be properly aligned in a straight upward-sloping line.

However,

Ascertain that Rob's scores are consistently lower than Marc's.

Assume that

Scores were in percentage.

Thus, The highest possible score is $100\%$