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– Simple Linear Regression Applications
Interpretation and Use of Computer Output (Results)
(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) 0.1 0.1 0.2 0.3 0.4 0.4 0.5 0.6 …
Occupancy (%) 92 95 96 90 89 96 90 83 85
Continue
Distance (miles) 0.7 0.8 0.8 0.9 0.9
Occupancy (%) 80 78 76 72 75
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 + b (Distncy)
What is the estimated regression equation?
Type in your answer here
(b) Interpret the meaning behind the values you get for both coefficients b and b .
Type in your answer here
(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?
Type in your answer her
To answer the questions, we need to first obtain the computer output from the simple linear regression analysis. This output will provide us with the estimated regression equation and the coefficients of the regression model.
Here are the steps to obtain the computer output and answer the questions:
1. Input the data into a statistical software or spreadsheet program such as Excel or R.
2. Run the simple linear regression analysis, making sure to designate the occupancy rate as the dependent (explained) variable and the distance from the beach as the independent (explaining) variable.
3. The computer output will provide you with the estimated regression equation, which takes the form Occpnc = b + b (Distncy). Look for the values of b and b in the output.
Now let's interpret the values obtained from the computer output:
(a) The estimated regression equation:
The computer output will provide the values for b (intercept) and b (slope). To answer this question, you need to find the specific values for b and b from the output. Once you have those values, you can plug them into the equation Occpnc = b + b (Distncy).
(b) Interpretation of the coefficients:
- b (intercept): This coefficient represents the estimated average occupancy rate when the distance from the beach is zero. In other words, it represents the average occupancy rate when a hotel is located right on the beach.
- b (slope): This coefficient represents the change in the average occupancy rate for every unit increase in the distance from the beach. A positive coefficient indicates that as the distance from the beach increases, the average occupancy rate tends to decrease. A negative coefficient would indicate the opposite.
(c) Relationship between hotel occupancy rate and distance from the beach:
Based on the coefficient b (slope), we can conclude that there is a negative relationship between average hotel occupancy rate and the hotel's distance from the beach. This means that as the distance from the beach increases, the average occupancy rate tends to decrease. This relationship makes sense because hotels located closer to the beach are often more desirable for beachgoers and therefore tend to have higher occupancy rates.
Note: To obtain the exact values for b and b and provide more specific interpretations, you would need to run the regression analysis using a statistical software or spreadsheet program.