La Quinta M otor Inns is a moderately priced chain of motels located across the
ID: 3316903 • Letter: L
Question
La Quinta M otor Inns is a moderately priced chain of motels located across the United Sates. Its market is the frequent business traveler. The chain recently launched a campaign to increase market share by building new inns. The chain collected data on 100 randomly s elected inns belonging to La Quinta. The objective was to predict which sites are most likely to be profitable. To measure profitability, La Quinta used operating margin. After some discussion, four variables were selected that may impact profitabilit y. T hese are; Total number of m otel and hotel rooms within 3 miles, Number of miles to closest competitor, Office space in thousands of square feet in the surrounding community, and Median household income (in $thousands) in the surrounding community. A portion of the data is provided as follows:
Using this data, a multiple regression analysis was used to assess the effect of Number of rooms, Nearest competitor, Office Space, and Income on Operating Margin . The results of the analysis follow :
a. State the multiple regression equation?
b. Using a significance level of 1%, i s there a significant relationship of operating margin and the overall set of independe nt variables – support your answer ?
c. Determine the coefficient of multiple determination and interpret its meaning.
d. Is there evidence that multicollinearity is present – support your answer ?
e. What is the residual when (Number = 2,890, N earest = 2.4, Office Space = 254,0 00, and Income = $35,000)?
A second multiple regression model was fit , adding two more independent variables; College and university enrollment (in thousands) in a nearby university and/or college, and Distance (in miles) to the downtown core . The results are as follows:
f. Conduct a n F - test , using a level of significance of 5%, to jointly determine if these two additional variables have a significant e ffect on operating margin .
g. What is the coefficient of multiple determination between Number of miles to closest competit or and the remaining set of 5 independent variables ?
Margin Number Nearest Office Space Income 4.2 2.8 2.4 3.3 0.9 2.9 55.53203 33.8 2810 49.02890 31.9 3422 57.4 2687 49.03759 549 496 254 434 678 635 37 35 35 38 42Explanation / Answer
a) mutiple regression equation
Y = 41.273 - 0.0079*number + 1.654*nearest + 0.0196*office space + 0.399*income
b) Decision rule : p value < 0.01, then there is significant difference
Actual decision : p value = 0.000 < 0.01, then there a significant relationship of operating margin and the overall set of independent variable at 1%
c) coefficient of multiple determination = 0.506
It indicates 50.6% explained variation is accounted of margin on multiple explanatory variables
d) the value mutiticollinearty = sqrt(0.506) = 0.711
it indicates moderate positive mutiple correlation between margin and all independent variables in this study
(as per chegg guidelines, I provided 4 parts of first question)
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