Chapter PII, Problem 24RE

(a)

To determine

To describe the relationship between quality of service and tip size.

Explanation of Solution

It is given in the question that it is commonly believed that people use tips to reward good service. A researcher for the hospitability industry examined tips and ratings of service from $2645$ dining parties at $21$ different restaurants. The correlation between ratings of service and tip percentages was $0.11$ . Thus, from the correlation we can say that it is far away from one so, as service ratings go up the tip size also increase as it is a positive correlation.

(b)

To determine

To find and interpret the value of $R^2$ in this context.

Answer to Problem 24RE

  $R^2=0.0121$ .

Explanation of Solution

It is given in the question that it is commonly believed that people use tips to reward good service. A researcher for the hospitability industry examined tips and ratings of service from $2645$ dining parties at $21$ different restaurants. The correlation between ratings of service and tip percentages was $0.11$ . Thus, the value of $R^2$ can be calculated as:

  $\begin{array}{l}{R}^2=r^2\\ $ \Rightarrow R^2={(0.11)}^2$\Rightarrow R^2=0.0121\end{array}$

Thus, we interpret from this that $1.21\%$ of variability in tip size is accounted for by quality of service.