Question

Exercise 1: Average daily hotel room rate (x) and amount spent on entertainment (y) is given in the following table for different cities. a.       Use these data to develop an estimated regression equation that could be used to predict the amount spent on entertainment for a given average daily hotel room rate. b.       What is the value of sample correlation coefficient? c.       Compute the coefficient of determination. What percentage of the variation in total amount spent on entertinment can be explained by room rate? d) Predict the amount spent on entertainment for a particular city that has a daily room rate of $89. City Room Rate ($) Entertainment ($) Boston 148 161 Denver 96 105 Nashville 91 101 New Orleans 110 142 Phoenix 90 100 San Diego 102 120 San Francisco 136 167 San Jose 90 140 Tampa 82 98

Answer 1

Answer a:

Using excel function Slope and Intercept we get the following:

Hence the regression equation is"

Entertainment $ = 17.4915 + 1.03341 * City Room Rent $

OR y = 17.4915 + 1.03341x

This can also be done by plotting scatter diagram with 'display equation' as follows:

Answer b:

Correlation coefficient = 0.8600 or 86%

Using excel function CORREL we Correlation coefficient as follows:

Answer c (i):

Coefficient of determination = R² = (Correlation coefficient) ² = 0.86 ² = 0.7396 or 73.96%

Coefficient of determination = 73.96%

Answer c (ii):

The coefficient of determination gives the proportion of the variation in amount spent on entertainment that is explained by explained by room rate.

Hence,

Percentage of the variation in total amount spent on entertainment can be explained by room rate = 73.96%

Answer d:

Entertainment $ = 17.4915 + 1.0334 * City Room Rent $

Amount spent on entertainment for a particular city that has a daily room rate of $89 = 17.4915 + 1.03341 * $89 = $109.47

Amount spent on entertainment for a particular city that has a daily room rate of $89 = $109.47