Question

8. The manager of a diner wants to re-evaluate his staffing needs depending on variations in customer traffic during the day. He collects data on the number of customers served along with four dummy variables representing the morning, afternoon, evening, and night shifts. The dummy variable Morning equals 1 if the information was from the morning shift and 0 otherwise. The dummy variable Afternoon equals 1 if the information was from the afternoon shift and 0 otherwise. The dummy variable Evening equals 1 if the information was from the evening shift and 0 otherwise. The dummy variable Night equals 1 if the information was from the night shift and 0 otherwise. Data is posted on Webcampus in excel file titled Shifts Data.

Estimate a regression model using the number of customers as the response (dependent) variable and the shift dummy variables as the explanatory (independent) variables.

1. What is the regression equation? Attach the Excel output.

2. What is the predicted number of customers during the morning shifts?

3. What is the predicted number of customers during the afternoon shifts?

4. What is the predicted number of customers during the evening shifts?

5. What is the predicted number of customers during the night shifts?

Answer 1

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ANSWER:

EXPLANATION:

data taken

Customers	Morning	Afternoon	Evening	Night
99	0	0	0	1
148	0	1	0	0
130	0	1	0	0
106	0	0	0	1
133	0	0	0	1
119	0	0	0	1
105	1	0	0	0
74	1	0	0	0
106	0	0	0	1
94	0	1	0	0
69	0	0	1	0
86	0	0	1	0
95	1	0	0	0
99	0	1	0	0
71	0	0	1	0
80	0	0	1	0
63	0	0	1	0
93	0	0	0	1
117	1	0	0	0
136	0	1	0	0
91	0	0	1	0
131	0	0	0	1
112	0	1	0	0
88	1	0	0	0
59	0	0	1	0
44	0	0	1	0
129	0	0	0	1
82	0	0	1	0
78	0	0	0	1
109	1	0	0	0
51	0	0	1	0
71	1	0	0	0
57	0	0	1	0
112	0	1	0	0
61	0	0	1	0
83	0	1	0	0
101	1	0	0	0
92	0	0	0	1
48	0	0	1	0
73	0	0	1	0
83	0	0	0	1
133	0	1	0	0
69	0	0	1	0
135	1	0	0	0
135	0	1	0	0
96	1	0	0	0
50	0	0	1	0
110	0	0	0	1
58	0	0	1	0
121	0	1	0	0
113	1	0	0	0
65	0	0	0	1
45	0	0	1	0
41	0	0	1	0
86	0	0	1	0
110	0	0	0	1
70	0	0	1	0
104	1	0	0	0
121	0	0	0	1
79	1	0	0	0
121	0	0	0	1
89	0	0	0	1
126	0	1	0	0
75	0	0	1	0
67	0	0	1	0
100	0	0	0	1
93	0	0	0	1
56	0	0	1	0
91	0	0	0	1
129	0	1	0	0
96	0	0	1	0
78	0	0	0	1
48	0	0	1	0
69	0	0	1	0
156	0	1	0	0
98	0	0	0	1
90	0	0	0	1
133	0	0	0	1
93	1	0	0	0
130	0	0	0	1
112	1	0	0	0
109	0	0	0	1
86	0	0	1	0
52	0	0	1	0
104	1	0	0	0
27	0	0	1	0
119	1	0	0	0
113	1	0	0	0
123	0	1	0	0
95	1	0	0	0
93	1	0	0	0
130	0	1	0	0
102	1	0	0	0
111	1	0	0	0
103	0	0	0	1
69	0	0	1	0
101	0	0	0	1
118	1	0	0	0
58	0	0	1	0
111	0	1	0	0

(a) Regression Statistics

Multiple R = 0.789459

R Square = 0.623245

Adjusted R Square = 0.601055

Standard Error = 17.03472

Observations = 100

ANOVA

	df	SS	MS	F	Significance F
Regression	4	46083.06	11520.77	52.93586	2.23E-23
Residual	96	27857.45	290.1818
Total	100	73940.51

	Coefficients	Standard error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	102.0435	3.551985	28.72858	6.17E-49	94.99284	109.0941	94.99284	109.0941
Morning	0	0	65535	#NUM!	0	0	0	0
Afternoon	20.19182	5.448496	3.705943	#NUM!	9.376636	31.007	9.376636	31.007
Evening	-37.7622	4.656692	-8.10924	1.67E-12	-47.0057	-28.5188	-47.0057	-28.5188
Night	1.920807	4.79377	0.400688	0.68954	-7.59475	11.43637	-7.59475	11.43637

Customers = 102.0435 + 20.19*Afternoon-37.7622*Evening+1.921*Night

(b)

In morning shift,

Customers = 102.0435 + 20.19*0-37.7622*0+1.921*0

Hence, the predicted number of customers = 102.0435

(c)

In afternoon

Customers = 102.0435 + 20.19*1-37.7622*0+1.921*0

Hence, the predicted number of customers = 122.23

(d)

In evenings

Customers = 102.0435 + 20.19*0-37.7622*1+1.921*0

Hence, the predicted number of customers = 64.28

(e)

In night shifts,

Customers = 102.0435 + 20.19*0-37.7622*0+1.921*1

Hence, the predicted number of customers = 103.9645

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