Regression Analysis

Twenty Motels’ location data over the operating margin is reported in Table 1 below.

Table 1- Twenty Motels’ location data over the operating margin

Motel	Competitor rooms	Distance to competitor	Office space	Distance to downtown	Operating Margin
M1	2967	1.4	529	55.5	44.60%
M2	2613	1.8	249	61.5	43.30%
M3	3222	1.1	425	51	43.60%
M4	2945	3.5	697	43.5	48.10%
M5	3843	1.3	631	64.5	45.70%
M6	2178	2	578	73.5	54.90%
M7	2802	2.8	542	51	42.40%
M8	2586	3.5	627	60	51.00%
M9	2887	1.2	488	37.5	49.50%
M10	3575	2.3	499	49.5	39.70%
M11	3447	1.9	137	66	32.80%
M12	3555	1.6	398	64.5	41.40%
M13	2964	1.1	622	49.5	47.90%
M14	2540	3.7	178	57	38.40%
M15	2920	3.6	410	60	41.00%
M16	2083	2.6	595	49.5	49.40%
M17	3303	2.5	478	70.5	44.70%
M18	1477	2.7	663	69	62.30%
M19	3052	1.9	691	69	47.10%
M20	2841	2	449	55.5	42.30%

Questions:

a. Determine and interpret which variable is the most highly correlated to the measure of operating margin. Would you describe this relationship as strong or weak?

b. Plot the data and write out the regression model for operating margin and distance to downtown. Interpret it clearly [6 marks].

c. Identify the slope, the intercept in (b), then interpret the values [6 marks].

d. What is the value of R-squared? Properly interpret its meaning. [6 marks].

e. What is a potential limitation if we only consider one independent variable in the regression analysis? Discuss, comparing directly with the results obtained using multiple regression. [7 marks].