Location analysis is an important decision in operations management of production and service industries. A critical decision for many organizations is where to locate a processing plant, warehouse, retail outlet, etc. A large number of business variables are typically considered in this decision problem.

The management of a large motel/inn chain is aware of the challenges in choosing new motel locations. The chain's management uses the "operating margin," which is the ratio of the sum of profit, depreciation, and interest expenses divided by total revenue, to make this type of decision. In general, the higher the "operating margin," the greater the success of the motel/inn.

The chain's management has collected data on 100 randomly selected of its current inns. By measuring the "operating margin," the objective is to predict which sites would likely generate more profit. Below is a description of the different variables considered in this analysis.

Location ID Number 2801 2608 3191 3210 3701 2547 2670 2664 2492 2649 3066 2193 2793 3620 2538 3730 3120 2389 3053 3304 3770 3380 2795 2315 2682 2789 2847 2372 3349 3704 2872 2570 2956 3098 3256 2486 3466 2912 3200 3208 3799 3450 2403 2555 3056 2331 2806 2802 2501 2636 3016 3581 2395 2365 3152 3071 2698 3026 2785 2973 2785 2834 2146 3625 3328 3358 2230 2662 3736 3227 2718 3675 2960 3405 2793 2675 2874 3467 3593 2596 3341 3479 2656 2617 2114 3287 3531 3562 3648 3569 3038 2663 2971 3116 2546 2118 2117 3794 2910 3504 

Operating Margin 39.3 49.5 49.0 45.1 41.9 43.5 40.3 42.8 57.3 52.1 25.1 54.4 47.3 57.4 38.4 56.5 35.2 39.3 47.3 44.2 54.4 51.5 46.2 49.8 41.1 51.1 52.2 49.9 39.8 43.5 45.4 58.5 46.0 81.5 41.0 46.0 48.8 53.5 54.1 34.3 50.2 43.3 40.8 49.0 52.0 51.2 52.7 35.7 40.0 60.1 48.2 36.8 55.4 33.8 51.2 42.9 36.1 47.5 33.2 54.2 32.4 54.1 49.0 46.3 41.6 43.2 54.4 42.5 45.0 33.5 35.9 38.1 44.0 71.2 37.8 43.7 40.2 55.5 44.9 38.8 52.6 53.0 58.0 54.2 60.5 47.6 36.9 34.5 30.8 49.0 45.5 51.4 49.6 31.9 53.4 48.8 39.2 43.4 41.0 49.6 

Number 3591 2726 2890 2172 3517 2910 2848 3003 2601 3140 1613 3234 2761 2687 3264 2045 3251 3159 2642 3471 2756 3069 2244 2859 3098 3227 2879 3255 3823 3198 2443 2210 2655 4214 3480 2341 2935 3285 2862 3548 3021 3383 2676 2826 3354 3082 3378 3591 3397 2619 2429 3006 2790 2810 2775 3838 2962 3080 2629 2484 3124 2432 1998 2554 2776 2724 3241 2403 3697 3657 2786 3568 2813 3567 2980 2915 3670 3203 3003 3330 3013 2844 2382 3018 2932 2751 2923 2730 3622 3759 2691 2640 3359 3422 2772 2825 2996 3597 2846 2922 

Nearest 2.0 1.2 2.4 1.4 2.9 1.4 2.5 2.2 3.1 2.2 1.7 3.2 3.4 0.9 2.7 1.5 1.7 2.7 1.8 2.2 3.2 3.3 3.6 1.7 2.3 1.9 2.1 2.2 3.6 1.8 0.1 2.7 1.1 2.4 1.9 2.3 3.9 2.0 2.9 2.5 1.7 2.2 3.3 4.2 2.0 1.5 3.3 1.4 1.6 2.9 2.3 2.5 1.6 2.8 2.5 2.4 0.9 1.9 1.4 2.8 1.6 2.9 3.6 2.1 2.1 1.2 2.2 1.0 2.1 1.5 1.9 2.3 3.8 2.5 3.2 1.6 2.8 4.2 0.9 2.7 3.7 3.5 3.2 3.1 1.8 3.0 1.2 0.3 2.3 2.9 3.2 3.8 1.6 3.3 0.8 1.1 1.3 3.9 3.1 1.9 

Enrollment 18.5 19.0 20.0 7.0 6.0 12.5 19.0 19.5 18.5 23.5 21.5 19.5 16.0 15.5 22.5 15.0 13.0 11.0 9.0 12.0 14.5 20.5 15.5 14.5 11.5 11.0 19.5 22.5 17.0 17.0 10.5 17.5 22.0 16.0 18.0 23.0 20.0 23.5 16.5 13.5 8.5 11.5 25.0 17.0 26.5 22.0 10.0 9.5 19.5 12.0 20.0 15.5 12.0 17.5 15.0 10.0 12.5 13.5 20.0 16.0 17.0 17.5 19.0 10.0 16.0 14.5 21.5 19.0 20.5 18.0 15.5 16.5 15.0 13.5 12.0 13.5 17.5 8.0 15.5 13.5 20.0 13.5 12.0 20.0 19.5 10.5 14.0 17.0 15.0 19.0 13.5 19.5 10.5 15.5 14.5 13.0 15.5 15.5 20.5 19.5 

Income 29 36 35 35 38 35 30 39 39 34 29 39 39 42 29 38 35 34 30 39 39 37 36 39 34 37 36 36 38 36 36 35 34 34 31 29 35 42 41 31 41 33 41 34 37 40 34 43 32 31 33 37 37 35 39 40 41 43 35 33 29 35 41 32 31 42 44 32 40 28 37 37 33 32 32 36 37 37 37 41 41 30 39 39 39 36 40 33 34 33 46 37 44 38 45 40 38 35 31 32 

Distance 7.6 9.3 2.6 9.2 9.1 1.8 8.4 12.0 11.0 3.7 4.1 8.3 6.6 6.9 10.4 4.3 4.3 0.2 4.8 5.4 7.9 7.7 5.9 3.0 7.7 6.0 2.9 8.7 4.8 4.6 7.5 2.7 8.1 5.6 11.0 7.4 6.1 2.9 11.8 8.3 5.5 9.5 5.1 1.2 7.2 11.2 7.6 5.0 3.1 6.8 7.6 4.2 9.1 14.4 5.6 2.9 8.6 8.1 7.2 0.6 7.3 10.3 4.9 9.9 7.3 0.3 5.1 8.2 9.0 3.5 8.5 3.7 11.8 9.1 6.6 5.3 9.9 2.7 10.2 4.0 14.1 10.8 1.3 8.2 6.1 9.1 7.6 4.3 7.6 10.8 5.7 7.6 2.6 12.1 11.3 9.0 8.5 13.2 8.8 4.4 

Quality 2 3 3 3 2 2 2 2 4 3 4 4 3 4 2 4 1 2 3 3 4 3 3 3 2 3 3 3 2 2 3 4 3 1 2 3 3 3 3 1 3 2 2 3 3 3 3 1 2 4 3 2 4 1 3 2 1 3 1 3 1 3 3 3 2 2 4 2 3 1 1 2 2 1 2 2 2 4 3 2 3 3 4 3 4 3 2 1 1 3 3 3 3 1 3 3 2 2 2 3 

High Speed Internet 1 2 1 2 2 2 1 1 2 2 2 2 1 2 1 2 1 1 1 2 2 2 1 2 1 2 2 2 1 2 2 2 1 1 1 2 1 2 2 1 1 2 1 2 2 2 2 1 1 2 1 1 2 1 1 1 1 1 1 2 1 2 2 1 1 2 2 1 1 1 1 1 1 1 1 2 1 2 2 1 2 2 2 2 2 2 1 1 1 2 2 2 2 1 2 1 1 1 1 1 

Gym 1 2 2 2 1 1 2 1 2 2 2 2 2 2 1 2 1 1 2 1 1 2 1 2 2 2 2 2 2 1 1 2 1 1 2 2 2 2 1 2 2 1 1 2 2 2 2 1 1 2 2 1 1 1 2 1 1 2 1 1 1 1 2 1 2 1 2 1 1 1 1 1 1 2 1 1 1 2 1 1 1 1 2 1 2 2 1 1 1 2 2 2 2 1 2 2 1 1 2 2 

Operating Margin New 39.3 49.5 49.0 45.1 41.9 43.5 40.3 42.8 57.3 52.1 - (There was no Value given here) 54.4 47.3 57.4 38.4 56.5 35.2 39.3 47.3 44.2 54.4 51.5 46.2 49.8 41.1 51.1 52.2 49.9 39.8 43.5 45.4 58.5 46.0 - (There was no Value given here) 41.0 46.0 48.8 53.5 54.1 34.3 50.2 43.3 40.8 49.0 52.0 51.2 52.7 35.7 40.0 60.1 48.2 36.8 55.4 33.8 51.2 42.9 36.1 47.5 33.2 54.2 32.4 54.1 49.0 46.3 41.6 43.2 54.4 42.5 45.0 33.5 35.9 38.1 44.0 - (there was no value given here) 37.8 43.7 40.2 55.5 44.9 38.8 52.6 53.0 58.0 54.2 60.5 47.6 36.9 34.5 30.8 49.0 45.5 51.4 49.6 31.9 53.4 48.8 39.2 43.4 41.0 49.6 

Part 1 (10 marks)

Using Minitab or any other statistical software, run a simple linear regression model to predictOperating Marginbased onDistanceand answer the following questions:

a)Using an appropriate graph, plotOperating MarginversusDistanceand comment on the relationship between these two variables.

b)Write down your estimation of the regression equation for predictingOperating MarginfromDistance. Draw the regression line on the plot in part a).

c)Assuming = 0.01, test whetherDistancehas statistically significant predictive power in estimatingOperating Margin. State the hypotheses, provide a test statistic and p-value, and state your conclusion. Show your calculations.

d)Interpret the values of the regression coefficients (slope and intercept).

Part 2 (6 marks)

Using Minitab or any other statistical software, now perform a multiple linear regression analysis ofOperating Margin(response variable) against all the remaining variables as predictors, excludingLocation ID Number.

a)Write down the regression equation and provide at least two summary measures of the fit of the model. Based on the summary measures, does the model provide a good fit for the data? Explain.

b)Plot the residuals against the fitted values and comment on whether the usual model conditions are met.

c)The variableOperating Margin Newin the dataset corresponds to theOperating Marginvariable from which some values have been recorded as missing values. Identify those missing values and explain what they are and why they were recorded as missing.

Part 3 (12 marks)

Using statistical software, run the same multiple linear regression model as in Part 2 above but this time usingOperating Margin Newas the response variable. Then, answer the following questions:

a)Briefly compare the resulting regression equation and fit with those obtained in Part 2.

b)Plot the residuals against the fitted values and comment on whether the model complies with the usual conditions for multiple linear regression.

c)Provide an interpretation for the model intercept and for the regression coefficients associated with variablesIncomeandDistance. Is an interpretation of the model intercept appropriate in this case? Compare the value of the regression coefficient forDistancewith the one obtained in Part 1 above and clearly explain any difference.

d)Do you see any justification for dropping any variable(s) from the model? Explain (hint: multicollinearity; the significance of predictors).

e)Run a final model usingOperating Margin Newas the response variable and including only the significant predictors (hint: those with a p-value 5%).

f)Test the overall significance of the final model in part e). Use a 1% significance level and follow all the steps for hypothesis testing indicated in theInstructionssection.

Part 4 (10 marks)

Based on your final model in Part 3 above, answer the following questions:

a)Test the marginal contribution ofQuality,assuming that the other variables in the model remain constant. Use a 1% significance level, and make sure you follow all the steps for hypothesis testing indicated in theInstructionssection. Show the computation of the t- statistics (i.e., the ratio used to compute it).

b)Calculate the 99% prediction interval for the actual operating margin of a new location with the same characteristics as those forLocation ID Number3098 in the data file. Check if the prediction interval includes the actual operating margin associated withLocation ID Number3098 and explain why it does or does not.

c)Calculate the 99% confidence interval for the mean operating margin of a new location with the same characteristics as those forLocation ID Number3098 in the data file. Explain any difference between the size of this interval and the one in part b) above.