Prediction · Exercise 23

The maximum discount value of the Entertainment® card for the “Fine Dining” section, Edition ten, for various pages is given in

\begin{array}{|c|c|}\hline \text{Page number} & \text{Maximum value ($)} \\ \hline \text{4} & \text{16} \\ \hline \text{14} & \text{19} \\ \hline \text{25} & \text{15} \\ \hline \text{32} & \text{17} \\ \hline \text{43} & \text{19} \\ \hline \text{57} & \text{15} \\ \hline \text{72} & \text{16} \\ \hline \text{85} & \text{15} \\ \hline \text{90} & \text{17} \\ \hline\end{array}

(a) Decide which variable should be the independent variable and which should be the dependent variable.
(b) Draw a scatter plot of the ordered pairs.
(c) Calculate the least-squares line. Put the equation in the form of: ŷ = a + bx
(d) Find the correlation coefficient. Is it significant?
(e) Find the estimated maximum values for the restaurants on page ten and on page 70.
(f) Does it appear that the restaurants giving the maximum value are placed in the beginning of the “Fine Dining” section? How did you arrive at your answer?
(g) Suppose that there were 200 pages of restaurants. What do you estimate to be the maximum value for a restaurant listed on page 200?
(h) Is the least squares line valid for page 200? Why or why not?
(i) What is the slope of the least-squares (best-fit) line? Interpret the slope.

OpenStax, Introductory Statistics 2e · §12.5 Prediction · Exercise 23