# Forecasting – Simple Linear Regression Applications

**Topics:**Regression analysis, Linear regression, Statistics

**Pages:**11 (2349 words)

**Published:**April 17, 2013

FINAL EXAMINATION

Forecasting – Simple Linear Regression Applications

Interpretation and Use of Computer Output (Results)

NAME

SECTION A – REGRESSION ANALYSIS AND FORECASTING

1) The management of an international hotel chain is in the process of evaluating the possible sites for a new unit on a beach resort. As part of the analysis, the management is interested in evaluating the relationship between the distance of a hotel from the beach and the hotel’s average occupancy rate for the season. A sample of 14 existing hotels in the area is chosen, and each hotel reports its average occupancy rate. The management records the hotel’s distance (in miles) from the beach. The following set of data is obtained:

Distance (miles)0.10.10.20.30.40.40.50.60.7

Occupancy (%)929596908996908385

Continue

Distance (miles)0.70.80.80.90.9

Occupancy (%)8078767275

Use the computer output to respond to the following questions:

a) A simple linear regression was ran with the occupancy rate as the dependent (explained) variable and distance from the beach as the independent (explaining) variable

Occpnc=b[pic]+b[pic](Distncy)

What is the estimated regression equation?

The regression model is: Occpnc = b[pic] + b[pic](Distncy) The estimated regression equation is: OCCUPNC = 99.61444 – 26.703 DISTNCY

b) Interpret the meaning behind the values you get for both coefficients b[pic] and b[pic]. b[pic]=99.61444, represent the y-intercept as well as the starting figure for the distance coverage. This is the amount of distance in miles that the hotel is from a beach. b[pic] = 26.703, represents the percentage of occupancy a hotel has depending on the distance of the hotel from a beach.

c) What sort of relationship exists between average hotel occupancy rate and the hotel’s distance from the beach? Does this relationship make sense to you? Why or why not? Both distance and occupancy have a direct relationship. This is true because closer the hotel is to the beach, the higher the chance that the hotel’s occupancy will be greater. If a person is going to stay at a hotel, chances are they are on vacation. People on vacation love to spend time on a beach for relaxation purposes, so it would only make sense that a hotel that is closer to the beach will have a higher occupancy rate.

d) Interpret the R-Square value in your computer output

R-Squared = 0.848195 = 84.8195

e) Predict the expected occupancy rate for a hotel that is (i) one mile from the beach in that area, (ii) one and half miles from the beach. i. OCCUPNC = 99.61444 – 26.703 (1)

= 99.61444 – 26.703 = 72.911

ii. OCCUPNC = 99.61444 – 26.703 (1.5)

= 99.61444 – 40.055 = 59.559

f) In your mind, what other variables contribute positively or negatively to hotel occupancy besides distance from the beach? Other variables that contribute positively or negatively to hotel occupancy besides distance from the beach include the distance of restaurants, shopping centers, and airport from the hotel. The closer theses variables are to the hotel the chances the occupancy rate will be higher. In addition, other variables may include what type of amenities that are offered by the hotel, customer service, and rating of the hotel.

g) At a level of significance, α = 0.01 or 1 percent test the following pair of hypotheses: H[pic]: b[pic]= 0

H[pic]: b[pic]≠ 0

On the model: Occpnc=b[pic]+b[pic](Distncy)

What is your conclusion and why that particular conclusion?

COMPUTER OUTPUT – PART 1

INTERNATIONAL HOTEL

REGRESSION FUNCTION & ANOVA FOR OCCPNCY

OCCPNCY = 99.61444 - 26.703 DISTANCE

R-Squared = 0.848195

Adjusted R-Squared = 0.835545

Standard error of estimate = 3.339362

Number of cases used =...

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