The marketing manager of a transportation network company offering taxi services in a metro city wishes to improve customer service and taxi scheduling based on the daily levels of customers in the past 10 weeks. The numbers of customers during that period are given below:
| Week | Monday | Tuesday | Wednesday | Thursday | Friday | Saturday | Sunday |
| 1 | 334 | 499 | 262 | 232 | 435 | 351 | 223 |
| 2 | 170 | 249 | 203 | 268 | 329 | 168 | 293 |
| 3 | 110 | 179 | 240 | 114 | 266 | 99 | 90 |
| 4 | 155 | 234 | 81 | 253 | 314 | 93 | 278 |
| 5 | 95 | 164 | 225 | 99 | 264 | 107 | 283 |
| 6 | 270 | 183 | 308 | 125 | 194 | 255 | 129 |
| 7 | 223 | 132 | 239 | 268 | 143 | 323 | 332 |
| 8 | 212 | 369 | 390 | 369 | 218 | 495 | 320 |
| 9 | 479 | 540 | 414 | 590 | 390 | 460 | 663 |
| 10 | 549 | 739 | 734 | 684 | 642 | 866 | 832 |
i) Determine the seasonal indices for the given data using a 7-day moving averages.
ii) Obtain the deseasonalised values.
iii) Fit the appropriate trend for the deseasonalised data using the least-squares method by matrix approach that best describes the data.
iv) Project the number of customers on Wednesday of the 52th week.
v) Plot the original data, the deseasonalised data, and the trend values
### i) Seasonal Indices using 7-Day Moving Averages
To determine the seasonal indices using a 7-day moving average, we will first compute the 7-day moving averages for each week. Then, we can calculate the seasonal indices by dividing the actual values by the corresponding moving averages.
#### Step 1: Calculate the 7-day moving average
The 7-day moving average for a given day is the average of the daily customer values from that day and the 6 previous days. This provides a smoothed estimate for the expected number of customers, taking into account the fluctuations.
For instance:
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