The manager of a diner wants to re-evaluate his staffing needs depending on vari
ID: 3325524 • Letter: T
Question
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.
Estimate a regression model using the number of customers as the response (dependent) variable and the shift dummy variables as the explanatory (independent) variables. Hint: See our lecture about avoiding the Dummy Variable Trap when there are multiple dummy categories.
What is the regression equation? Attach the Excel or Minitab output.
What is the predicted number of customers during the morning shifts?
What is the predicted number of customers during the afternoon shifts?
What is the predicted number of customers during the evening shifts?
What is the predicted number of customers during the night shifts?
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 0Explanation / Answer
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 = 102.0435
c)
In afternoon
Customers = 102.0435 + 20.19*1-37.7622*0+1.921*0 = 122.23
d)
In evenings
Customers = 102.0435 + 20.19*0-37.7622*1+1.921*0 = 64.28
e)
Customers = 102.0435 + 20.19*0-37.7622*0+1.921*1 = 103.9645
SUMMARY OUTPUT 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 11.43637Related Questions
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