he datasetsales_forecastcontains information on monthly sales at the University Bookstore (sales is in $1000). As you can see, the sales show a seasonal pattern, with the greatest sales occurring when the college is in session (spring and fall) and decrease during the summer months. You've been hired as new sales manager, and one of your first tasks on the job is to forecast sales for the spring semester of 2019 (January - May, i.e. month 49 to 53).

Estimate the linear trend model;

Y_t= a + bt

Where Y_tis sales in the t^thmonth and t = 1, 2, ..., 48.

• Check the statistical significance of the intercept and slope coefficient.
• Forecast sales for Jan-May of 2019

Now re-estimate the model with a dummy variable D_t(=1 for spring and fall months and 0 for summer months).

Y_t= a + bt +cD_t

• Check the statistical significance of the intercept and slope coefficients.
• Forecast sales for Jan-May using this new model.

Accurate forecasting is crucial to preventing stockouts and associated costs.

• Discuss which of the two forecasts is more accurate. Explain why.
• What surprised you most by these forecasts?

Year Month Sales ($1000) t Dt

2015 1 196 1 1

2 188 2 1

3 192 3 1

4 164 4 1

5 140 5 1

6 120 6 0

7 112 7 0

8 140 8 0

9 160 9 1

10 168 10 1

11 192 11 1

12 200 12 1

2016 1 200 13 1

2 188 14 1

3 192 15 1

4 164 16 1

5 140 17 1

6 122 18 0

7 132 19 0

8 144 20 0

9 176 21 1

10 168 22 1

11 196 23 1

12 194 24 1

2017 1 196 25 1

2 212 26 1

3 202 27 1

4 180 28 1

5 150 29 1

6 140 30 0

7 156 31 0

8 144 32 0

9 164 33 1

10 186 34 1

11 200 35 1

12 230 36 1

2018 1 242 37 1

2 240 38 1

3 196 39 1

4 220 40 1

5 200 41 1

6 192 42 0

7 176 43 0

8 184 44 0

9 204 45 1

10 228 46 1

11 250 47 1

12 260 48 1