Question

Seth Wagerman, a former professor at California Lutheran University, went to the website RateMyProfessors.com and looked up the quality rating and also the "easiness" of the six full-time professors in one department. The ratings are 1 (lowest quality) to 5 (highest quality) and 1 (hardest) to 5 (easiest). The numbers given are averages for each professor. Assume the trend is linear, find the correlation, and comment on what it means. $$ \begin{array}{|c|c|} \hline \text { Quality } & \text { Easiness } \\ \hline 4.8 & 3.8 \\ \hline 4.6 & 3.1 \\ \hline 4.3 & 3.4 \\ \hline 4.2 & 2.6 \\ \hline 3.9 & 1.9 \\ 3.6 & 2.0 \\ \hline \end{array} $$

Name: Problem 25, Chapter 4: Essential Statistics: Exploring the World through Data
Uploaded: 2022-01-18T14:16:20-08:00
Duration: 2 min 5 s
Channel: Nick Johnson

   Seth Wagerman, a former professor at California Lutheran University, went to the website RateMyProfessors.com and looked up the quality rating and also the "easiness" of the six full-time professors in one department. The ratings are 1 (lowest quality) to 5 (highest quality) and 1 (hardest) to 5 (easiest). The numbers given are averages for each professor. Assume the trend is linear, find the correlation, and comment on what it means.
$$
\begin{array}{|c|c|}
\hline \text { Quality } & \text { Easiness } \\
\hline 4.8 & 3.8 \\
\hline 4.6 & 3.1 \\
\hline 4.3 & 3.4 \\
\hline 4.2 & 2.6 \\
\hline 3.9 & 1.9 \\
3.6 & 2.0 \\
\hline
\end{array}
$$

Essential Statistics: Exploring the World through Data

Robert Gould,… 3rd Edition

Chapter 4, Problem 25

Instant Answer

Solved by Expert Nick Johnson

01/18/2022

Step 1

The mean is calculated by summing all the values and dividing by the number of values. For the quality scores, we sum up all the values (4.8, 4.6, 4.3, 4.2, 3.9, 3.6) to get 25.4. Dividing by the number of professors (6), we get a mean quality score of Show more…

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Seth Wagerman, a former professor at California Lutheran University, went to the website RateMyProfessors.com and looked up the quality rating and also the "easiness" of the six full-time professors in one department. The ratings are 1 (lowest quality) to 5 (highest quality) and 1 (hardest) to 5 (easiest). The numbers given are averages for each professor. Assume the trend is linear, find the correlation, and comment on what it means. $$ \begin{array}{|c|c|} \hline \text { Quality } & \text { Easiness } \\ \hline 4.8 & 3.8 \\ \hline 4.6 & 3.1 \\ \hline 4.3 & 3.4 \\ \hline 4.2 & 2.6 \\ \hline 3.9 & 1.9 \\ 3.6 & 2.0 \\ \hline \end{array} $$

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Key Concepts

Pearson Correlation Coefficient

This is a statistical measure that indicates the extent to which two variables are linearly related. It takes values from -1 to 1, where values close to 1 indicate a strong positive relationship, values near -1 indicate a strong negative relationship, and values around 0 indicate no linear relationship. In this context, it quantifies how changes in one variable (quality) correspond to changes in another (easiness).

Linear Relationship

A linear relationship between two variables means that the change in one variable is proportional to the change in the other, which can be represented with a straight line on a scatter plot. Assuming a linear trend allows us to use tools like the Pearson correlation coefficient and linear regression to analyze the degree and direction of the connection between the variables.

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