Question

The following table gives the distance from Boston to each city and the cost of a train ticket from Boston to that city for a certain date. $$\begin{array}{lcc} \text { City } & \text { Distance (in miles) } & \text { Ticket Price (in \$) } \\ \hline \text { Washington,D.C. } & 439 & 181 \\ \hline\text { Hartford } & 102 & 73 \\ \hline \text { New York } & 215 & 79 \\ \hline \text { Philadelphia } & 310 & 293 \\ \hline\text { Baltimore } & 406 & 175 \\ \hline \text { Charlotte } & 847 & 288 \\ \hline\text { Miami } & 1499 & 340 \\ \hline \text { Roanoke } & 680 & 219 \\ \hline\text { Atlanta } & 1086 & 310 \\ \hline \text { Tampa } & 1349 & 370 \\ \hline\text { Montgomery } & 1247 & 373 \\ \hline \text { Columbus } & 776 & 164 \\ \hline \text { Indianapolis } & 950 & 245 \\ \hline \text { Detroit } & 707 & 189 \\ \hline \text { Nashville } & 1105 & 245 \\ \hline \end{array}$$ a. Use technology to produce a scatterplot. Based on your scatterplot do you think there is a strong linear relationship between these two variables? Explain. b. Compute $r$ and write the equation of the regression line. Use the words "Ticket Price" and "Distance" in your equation. Round off to two decimal places. c. Provide an interpretation of the slope of the regression line. d. Provide an interpretation of the $y$ -intercept of the regression line or explain why it would not be appropriate to do so. e. Use the regression equation to predict the cost of a train ticket from Boston to Pittsburgh, a distance of 572 miles.

          The following table gives the distance from Boston to each city and the cost of a train ticket from Boston to that city for a certain date.
$$\begin{array}{lcc}
\text { City } & \text { Distance (in miles) } & \text { Ticket Price (in \$) } \\
\hline \text { Washington,D.C. } & 439 & 181 \\
\hline\text { Hartford } & 102 & 73 \\
\hline \text { New York } & 215 & 79 \\
\hline \text { Philadelphia } & 310 & 293 \\
\hline\text { Baltimore } & 406 & 175 \\
\hline \text { Charlotte } & 847 & 288 \\
\hline\text { Miami } & 1499 & 340 \\
\hline \text { Roanoke } & 680 & 219 \\
\hline\text { Atlanta } & 1086 & 310 \\
\hline \text { Tampa } & 1349 & 370 \\
\hline\text { Montgomery } & 1247 & 373 \\
\hline \text { Columbus } & 776 & 164 \\
\hline \text { Indianapolis } & 950 & 245 \\
\hline \text { Detroit } & 707 & 189 \\
\hline \text { Nashville } & 1105 & 245 \\
\hline
\end{array}$$
a. Use technology to produce a scatterplot. Based on your scatterplot do you think there is a strong linear relationship between these two variables? Explain.
b. Compute $r$ and write the equation of the regression line. Use the words "Ticket Price" and "Distance" in your equation. Round off to two decimal places.
c. Provide an interpretation of the slope of the regression line.
d. Provide an interpretation of the $y$ -intercept of the regression line or explain why it would not be appropriate to do so.
e. Use the regression equation to predict the cost of a train ticket from Boston to Pittsburgh, a distance of 572 miles.

Added by Kelly M.

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