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 The solution will be briefly discussed in class (in the first session after the due date).

Chapter 7: Linear Regression

You have been invited to help Alexa, a former student in College of Business Administration at CSUSM,

who is studying the waiting time of clients at San Marcos DMV office. Total Waiting Time of a client starts

from the moment they check in with the receptionists until they fully receive the service and leave the

office. Before proposing any recommendations to the DMV officials, she needs to understand why some

clients need to wait longer. As part of her analysis, she would like to run multiple regression models to

predict Total Waiting Time based on some potential predictors. She has managed to find the waiting time

and some other information like appointment type, time of the day, number of workers, number of

customers waiting in the system, etc., for a sample of 150 customers (Refer to CH7 for the sample data).

1. Run a regression model to predict waiting time based on all the predictors provided in the file.

For categorical variables, please define appropriate dummy variables.

 Write down the resulting equation.

 What is the estimated impact of having appointment on the waiting time?

 How much of the variation in waiting time does your model explain?

 Check the multicollinearity and the necessary conditions for the residuals, and

comment on the significance of the predictors.

2. Now add the squared number of working staff (quadratic factor) as a predictor and run another

model with all predictors including the squared staff number.

 Write down the resulting equation.

 What is the estimated impact of appointment type on the waiting time?

 How much of the variation in waiting time does the new model explain?

 Check the multicollinearity and the necessary conditions for the residuals, and

comment on the significance of the predictors.

3. Now, remove all the non-significant variables, and run another model with only significant

variables.

4. Which model would you prefer and why? What is your prediction for the waiting time of a 60-

year old customer with special needs who also has a scheduled morning appointment for vehicle

registration, arriving at a time when 10 staff are working and 70 clients are waiting in the office.

5. Can you help her come up with more independent variables that can potentially explain clients’

waiting time?

Chapter 8: Time Series and Forecasting

The CSUSM Restaurant just finished its fourth year of operation. Through the great efforts of its manager

and staff, this restaurant has become one of the most popular and fastest-growing restaurants in the SD

County.

The manager has recently decided to improve the capacity planning process of the restaurant. To do so,

they need to come up with an effective forecasting procedure to predict the monthly sales of foods for up

to a year in advance (12 months). Data file CH8 shows the value of food sales ($100s) for the first four

years of operation.

You, as the new forecasting analyst, have been asked to propose a new forecasting procedure with a

summary of your method, forecasts, and recommendations. Include the followings:

1. A time series plot. Comment on the underlying pattern in the time series. What forecasting

technique(s) do you recommend based on your visualization?

2. Do you consider moving average as an effective method for forecasting the food sales of this

restaurant? Why?

3. Using dummy variables for seasonality effects, forecast sales for January through December of

the fifth year.

4. Add a trend effect to your forecasting model in (3) and forecast sales for January through

December of the fifth year again with the new model.

5. Which model is expected to give more accurate forecasts, (3) or (4)? Calculate MSE for both

techniques.

6. Assume that restaurant’s sales in January of the fifth year turn out to be $175,000. What was your

forecast (and what is the forecasting error)? How do you explain this error to the manager?

Sheet1

CustomerWaiting timeType of serviceSpecial NeedsTime of the dayAgeWalk-in/AppointmentNumber of working staffNumber of waiting customers
143DL ReturningNOMorning42Walk-in8133
253DL ReturningNOMorning16Walk-in8132
367Vehicle RegistrationNOMorning16Walk-in7156
467DL FirstTimeNOMorning58Walk-in7161
568Vehicle RegistrationNOMorning28Walk-in6118
676DL ReturningYESAfternoon83Walk-in6124
731Vehicle RegistrationYESAfternoon50Appointment599
855DL ReturningNOAfternoon41Walk-in10140
959Vehicle RegistrationYESAfternoon20Walk-in5104
1073Vehicle RegistrationYESAfternoon50Walk-in12152
1165DL FirstTimeNOMorning16Walk-in11113
1249DL ReturningNOAfternoon42Walk-in10229
1382Vehicle RegistrationYESMorning33Walk-in12109
1465DL ReturningYESAfternoon23Walk-in662
1528DL ReturningNOAfternoon66Appointment1294
1665DL ReturningYESAfternoon25Walk-in10227
1764DL ReturningNOAfternoon67Walk-in7212
1825DL ReturningNOMorning26Appointment792
1934DL ReturningNOMorning73Appointment6206
2026DL ReturningNOMorning22Appointment667
2138Vehicle RegistrationYESAfternoon86Appointment7167
2252DL ReturningNOMorning52Walk-in990
2316DL ReturningNOAfternoon58Appointment8106
2438Vehicle RegistrationNOMorning54Walk-in8103
2565DL ReturningNOMorning16Walk-in12233
2674DL FirstTimeYESAfternoon81Appointment5248
2722DL ReturningNOMorning43Appointment10244
2850DL ReturningNOAfternoon58Walk-in5246
2947DL ReturningYESAfternoon22Appointment965
3089Vehicle RegistrationYESAfternoon47Walk-in1094
3143Vehicle RegistrationNOAfternoon85Walk-in10143
3279DL ReturningNOAfternoon31Walk-in5228
3373DL ReturningYESMorning79Walk-in970
3459Vehicle RegistrationNOMorning68Walk-in9225
3564DL ReturningNOMorning54Walk-in10197
3677DL ReturningNOMorning22Walk-in12176
3741DL ReturningNOMorning40Walk-in10153
3837DL ReturningNOAfternoon29Walk-in8131
3947DL ReturningNOAfternoon32Walk-in7125
4050DL ReturningNOAfternoon47Walk-in551
4122Vehicle RegistrationNOMorning16Walk-in776
4237DL ReturningNOAfternoon86Walk-in657
4364DL ReturningNOAfternoon73Walk-in10185
4429Vehicle RegistrationYESAfternoon41Appointment10115
4553DL FirstTimeNOMorning16Walk-in8227
4649DL ReturningNOMorning35Walk-in6138
4734DL ReturningYESAfternoon16Appointment1287
4867DL FirstTimeNOAfternoon71Walk-in8114
4983DL FirstTimeYESAfternoon51Walk-in1179
5011DL ReturningNOAfternoon16Appointment8196
5161DL FirstTimeNOMorning80Walk-in7247
5210Vehicle RegistrationNOAfternoon16Appointment7131
5373DL ReturningYESMorning61Walk-in9184
5428DL FirstTimeNOAfternoon16Appointment11176
5544DL ReturningNOMorning30Walk-in12104
5653DL FirstTimeNOMorning16Walk-in5224
5722DL ReturningNOMorning16Appointment9144
5813Vehicle RegistrationNOMorning32Appointment871
5929DL ReturningNOMorning17Walk-in7171
6064DL FirstTimeYESAfternoon53Walk-in9168
6111DL FirstTimeNOMorning16Appointment9209
6259DL FirstTimeNOMorning32Walk-in11189
6325DL FirstTimeNOMorning21Appointment8207
6414Vehicle RegistrationNOAfternoon41Appointment1260
6556DL FirstTimeNOMorning75Walk-in11229
6628DL ReturningNOMorning33Appointment6107
6758DL ReturningYESAfternoon60Walk-in9165
6871DL FirstTimeYESMorning65Walk-in6129
6958DL FirstTimeNOMorning86Walk-in668
7037DL FirstTimeNOMorning28Walk-in9186
7158DL ReturningNOMorning30Walk-in8166
7253DL ReturningNOAfternoon55Walk-in1095
7320DL FirstTimeNOMorning16Appointment11166
7422DL ReturningNOAfternoon31Appointment10150
758DL ReturningNOAfternoon75Appointment12147
7628DL ReturningYESAfternoon65Appointment11234
7710DL ReturningNOAfternoon64Appointment979
7871DL FirstTimeYESAfternoon20Walk-in557
7926DL ReturningNOAfternoon46Appointment9205
8014DL ReturningNOAfternoon24Appointment10241
8144DL ReturningNOAfternoon81Walk-in5151
8238DL ReturningNOAfternoon85Walk-in12166
8341DL ReturningNOAfternoon36Walk-in12130
8446DL ReturningNOAfternoon61Walk-in6198
8541DL ReturningYESMorning16Appointment11221
8653DL ReturningNOAfternoon74Walk-in10194
8734DL ReturningNOMorning45Walk-in12116
8826DL ReturningNOAfternoon44Appointment9125
898Vehicle RegistrationNOMorning57Appointment961
9031DL ReturningYESMorning55Appointment5119
9116Vehicle RegistrationNOAfternoon16Appointment6168
9222DL ReturningNOMorning47Appointment12201
9343DL ReturningNOAfternoon84Walk-in8210
9455DL ReturningNOMorning24Walk-in11109
9555DL ReturningNOAfternoon80Walk-in10207
9680DL ReturningYESMorning67Walk-in5194
9747DL FirstTimeNOMorning16Walk-in1167
9832Vehicle RegistrationNOMorning62Walk-in6203
9947DL ReturningYESAfternoon16Walk-in9229
10055DL ReturningNOAfternoon29Walk-in12164
10146DL FirstTimeNOMorning39Walk-in1171
10228DL ReturningNOAfternoon69Appointment6194
10349DL ReturningYESMorning73Walk-in1086
10413Vehicle RegistrationNOAfternoon16Appointment11153
10568DL FirstTimeYESMorning74Walk-in1281
10611Vehicle RegistrationNOAfternoon61Appointment5170
10782DL ReturningYESAfternoon49Walk-in5200
10853DL FirstTimeNOMorning47Walk-in7141
10917DL ReturningNOAfternoon29Appointment11193
11037DL ReturningNOAfternoon28Walk-in564
11147DL ReturningNOAfternoon16Walk-in9233
11252DL ReturningNOAfternoon16Walk-in7231
11322DL ReturningNOAfternoon39Appointment598
11413Vehicle RegistrationNOMorning16Appointment5124
11511DL FirstTimeNOAfternoon41Appointment12247
11658DL FirstTimeNOMorning58Walk-in560
11714Vehicle RegistrationNOMorning16Appointment767
11838DL FirstTimeNOMorning21Walk-in11208
11968DL FirstTimeYESAfternoon61Walk-in5193
12056DL ReturningNOMorning74Walk-in9154
12159DL ReturningNOAfternoon16Walk-in6141
12264DL FirstTimeNOMorning16Walk-in6245
12350DL FirstTimeNOMorning80Walk-in10198
12429DL FirstTimeNOMorning85Walk-in12127
12547DL ReturningNOAfternoon85Walk-in694
12617Vehicle RegistrationNOMorning16Appointment7125
12755DL ReturningNOMorning16Walk-in1173
12843DL FirstTimeYESMorning42Walk-in7185
12967DL FirstTimeYESMorning21Walk-in1074
13041DL FirstTimeNOMorning16Walk-in891
13141DL FirstTimeNOAfternoon27Walk-in7195
13213Vehicle RegistrationNOAfternoon16Appointment7111
13355DL ReturningNOAfternoon55Walk-in9132
13450DL FirstTimeNOMorning74Walk-in9227
13532DL ReturningNOAfternoon16Walk-in1252
13649DL FirstTimeNOAfternoon16Walk-in9138
13713Vehicle RegistrationNOMorning46Appointment12164
13810Vehicle RegistrationNOMorning54Appointment5163
13917Vehicle RegistrationNOMorning79Appointment5181
14032Vehicle RegistrationNOMorning44Walk-in10194
14146Vehicle RegistrationNOMorning16Walk-in5184
14241DL ReturningNOAfternoon36Walk-in12173
14311Vehicle RegistrationNOAfternoon69Appointment754
14450Vehicle RegistrationNOAfternoon16Walk-in9196
14526DL FirstTimeNOMorning30Appointment7174
14653DL ReturningNOAfternoon16Walk-in958
14711DL FirstTimeNOMorning55Appointment7156
14823Vehicle RegistrationNOAfternoon59Appointment9233
14940Vehicle RegistrationYESMorning52Appointment6184
15032DL ReturningNOAfternoon86Walk-in554

Data

MonthSales
11331
21293
31276
4979
51012
6770
7798
8836
9605
10715
11836
121133
131447
141309
151359
161062
171062
18820
19864
20886
21671
22715
23919
241265
251551
261403
271458
281128
291155
30880
31913
32957
33693
34814
35952
361293
371651
381513
391558
401228
411255
42980
431013
441015
45798
46919
471052
481394

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