Prediction (Optional) · Exercise 22

The maximum discount value of the Entertainment^® card for the Fine Dining section, 10th edition, 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 ŷ = a + bx.
(d) Find the correlation coefficient. Is it significant?
(e) Find the estimated maximum values for the restaurants on page 10 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 there are 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, Statistics · §12.4 Prediction (Optional) · Exercise 22