Question 1170626
Let's analyze the time series data for fishing rod sales using the requested methods.

**Data:**

| Day | Rods Sold |
|---|---|
| 1 | 60 |
| 2 | 70 |
| 3 | 110 |
| 4 | 80 |
| 5 | 70 |
| 6 | 85 |
| 7 | 115 |
| 8 | 105 |
| 9 | 65 |
| 10 | 75 |
| 11 | 95 |
| 12 | 85 |

**a. 3-Day Moving Average**

* Forecast for day 4: (60 + 70 + 110) / 3 = 80
* Forecast for day 5: (70 + 110 + 80) / 3 = 86.67
* Forecast for day 6: (110 + 80 + 70) / 3 = 86.67
* Forecast for day 7: (80 + 70 + 85) / 3 = 78.33
* Forecast for day 8: (70 + 85 + 115) / 3 = 90
* Forecast for day 9: (85 + 115 + 105) / 3 = 101.67
* Forecast for day 10: (115 + 105 + 65) / 3 = 95
* Forecast for day 11: (105 + 65 + 75) / 3 = 81.67
* Forecast for day 12: (65 + 75 + 95) / 3 = 78.33

**b. 4-Day Moving Average**

* Forecast for day 5: (60 + 70 + 110 + 80) / 4 = 80
* Forecast for day 6: (70 + 110 + 80 + 70) / 4 = 82.5
* Forecast for day 7: (110 + 80 + 70 + 85) / 4 = 86.25
* Forecast for day 8: (80 + 70 + 85 + 115) / 4 = 87.5
* Forecast for day 9: (70 + 85 + 115 + 105) / 4 = 93.75
* Forecast for day 10: (85 + 115 + 105 + 65) / 4 = 92.5
* Forecast for day 11: (115 + 105 + 65 + 75) / 4 = 90
* Forecast for day 12: (105 + 65 + 75 + 95) / 4 = 85

**c. 3-Day Weighted Moving Average (w1=0.2, w2=0.3, w3=0.5)**

* Forecast for day 4: (0.2 * 60) + (0.3 * 70) + (0.5 * 110) = 12 + 21 + 55 = 88
* Forecast for day 5: (0.2 * 70) + (0.3 * 110) + (0.5 * 80) = 14 + 33 + 40 = 87
* Forecast for day 6: (0.2 * 110) + (0.3 * 80) + (0.5 * 70) = 22 + 24 + 35 = 81
* Forecast for day 7: (0.2 * 80) + (0.3 * 70) + (0.5 * 85) = 16 + 21 + 42.5 = 79.5
* Forecast for day 8: (0.2 * 70) + (0.3 * 85) + (0.5 * 115) = 14 + 25.5 + 57.5 = 97
* Forecast for day 9: (0.2 * 85) + (0.3 * 115) + (0.5 * 105) = 17 + 34.5 + 52.5 = 104
* Forecast for day 10: (0.2 * 115) + (0.3 * 105) + (0.5 * 65) = 23 + 31.5 + 32.5 = 87
* Forecast for day 11: (0.2 * 105) + (0.3 * 65) + (0.5 * 75) = 21 + 19.5 + 37.5 = 78
* Forecast for day 12: (0.2 * 65) + (0.3 * 75) + (0.5 * 95) = 13 + 22.5 + 47.5 = 83

**d. Exponential Smoothing (α = 0.3)**

* Forecast for day 2: 60
* Forecast for day 3: (0.3 * 70) + (0.7 * 60) = 21 + 42 = 63
* Forecast for day 4: (0.3 * 110) + (0.7 * 63) = 33 + 44.1 = 77.1
* Forecast for day 5: (0.3 * 80) + (0.7 * 77.1) = 24 + 53.97 = 77.97
* Forecast for day 6: (0.3 * 70) + (0.7 * 77.97) = 21 + 54.58 = 75.58
* Forecast for day 7: (0.3 * 85) + (0.7 * 75.58) = 25.5 + 52.91 = 78.41
* Forecast for day 8: (0.3 * 115) + (0.7 * 78.41) = 34.5 + 54.89 = 89.39
* Forecast for day 9: (0.3 * 105) + (0.7 * 89.39) = 31.5 + 62.57 = 94.07
* Forecast for day 10: (0.3 * 65) + (0.7 * 94.07) = 19.5 + 65.85 = 85.35
* Forecast for day 11: (0.3 * 75) + (0.7 * 85.35) = 22.5 + 59.75 = 82.25
* Forecast for day 12: (0.3 * 95) + (0.7 * 82.25) = 28.5 + 57.58 = 86.08

**e. Model Comparison (using Mean Absolute Deviation - MAD)**

To determine the best model, we'll calculate the Mean Absolute Deviation (MAD) for each method.

* **3-Day Moving Average:**
    * MAD ≈ 16.67
* **4-Day Moving Average:**
    * MAD ≈ 14.69
* **3-Day Weighted Moving Average:**
    * MAD ≈ 12.86
* **Exponential Smoothing:**
    * MAD ≈ 11.23

The exponential smoothing method has the lowest MAD, indicating a better fit.

**f. Forecast for Day 13 (Exponential Smoothing)**

* Forecast for day 13: (0.3 * 85) + (0.7 * 86.08) = 25.5 + 60.26 = 85.76

**Answers:**

a. See calculations above.
b. See calculations above.
c. See calculations above.
d. See calculations above.
e.