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The Wall Street Journal asked Concur Technologies, Inc., an expense-management company, to examine data from 8.38.3 million expense reports to provide insights regarding business travel expenses. Their analysis of the data showed that New York was the most expensive city. The following table shows the average daily hotel room rate (x)(x) and the average amount spent on entertainment (y)(y) for a random sample of 99 of the 2525 most visited U.S. cities. These data lead to the estimated regression equation y^=17.49+1.0334x\hat{y}=17.49+1.0334 x. For these data, SSE=1541.4\mathrm{SSE}=1541.4.

 Room Rate  Entertainment  City ($)($) Boston 148161 Denver 96105 Nashville 91101 New Orleans 110142 Phoenix 90100 San Diego 102120 San Francisco 136167 San Jose 90140 Tampa 8298\begin{array}{lrr} & \text { Room Rate } & \text { Entertainment } \\ \text { City } & {( \$ )} & {( \$ )} \\ \text { Boston } & 148 & 161 \\ \text { Denver } & 96 & 105 \\ \text { Nashville } & 91 & 101 \\ \text { New Orleans } & 110 & 142 \\ \text { Phoenix } & 90 & 100 \\ \text { San Diego } & 102 & 120 \\ \text { San Francisco } & 136 & 167 \\ \text { San Jose } & 90 & 140 \\ \text { Tampa } & 82 & 98 \end{array}

Predict the amount spent on entertainment for a particular city that has a daily room rate of $89\$89.

Question

Concur Technologies, Inc., is a large expense-management company located in Redmond, Washington. The Wall Street Journal asked Concur to examine the data from 8.3 million expense reports to provide insights regarding business travel expenses. Their analysis of the data showed that New York was the most expensive city, with an average daily hotel room rate of $198 and an average amount spent on entertainment, including group meals and tickets for shows, sports, and other events, of$172. In comparison, the U.S. averages for these two categories were $89 for the room rate and$99 for entertainment. The following table shows the average daily hotel room rate and the amount spent on entertainment for a random sample of 9 of the 25 most visited U.S. cities (The Wall Street Journal, August 18, 2011).

 City  Room Rate ($) Entertain  ($)  Boston 148161 Denver 96105 Nashville 91101 New Orleans 110142 Phoenix 90100 San Diego 102120 San Francisco 136167 San Jose 90140 Tampa 8298\begin{array}{lcr}\text { City } & \begin{array}{c}\text { Room Rate } \\ (\$)\end{array} & \begin{array}{r}\text { Entertain } \\ \text{ (\$) }\end{array} \\ \text { Boston } & 148 & 161 \\ \text { Denver } & 96 & 105 \\ \text { Nashville } & 91 & 101 \\ \text { New Orleans } & 110 & 142 \\ \text { Phoenix } & 90 & 100 \\ \text { San Diego } & 102 & 120 \\ \text { San Francisco } & 136 & 167 \\ \text { San Jose } & 90 & 140 \\ \text { Tampa } & 82 & 98\end{array}

a. Develop a scatter diagram for these data with the room rate as the independent variable.

b. What does the scatter diagram developed in part (a) indicate about the relationship between the two variables?

c. Develop the least squares estimated regression equation.

d. Provide an interpretation for the slope of the estimated regression equation.

e. The average room rate in Chicago is $128, considerably higher than the U.S. average. Predict the entertainment expense per day for Chicago.

Solution

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a) For this exercise, we are to develop a scatter diagram for the given table with the room rate as the independent variable.

Table 1. Given values.\small \text{Table 1. Given values.}

City Room Rate ($) Entertainment ($)
Boston 148148 161161
Denver 9696 105105
Nashville 9191 101101
New Orleans 110110 142142
Phoenix 9090 100100
San Diego 102102 120120
San Francisco 136136 167167
San Jose 9090 140140
Tampa 8282 9898

What is the relationship of the independent variable to the coordinates of point?

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