Question 8: Using regression results

The table below reports several regression forecasts of sales using hypothetical data. There were 3 years of monthly sales data, with the months running from January to December. There appeared to be some seasonal variation, with sales lower in the spring and higher in the fall. The first model is a simple linear regression with time in months as the explanatory variable. The second model coded August, November and December as High Sales Months.

1. Write out the equation for sales using model 1. What is the predicted value for month 37?
2. Run one more model. Looking at the data, August and September (hay fever season?) are always high sales months and March, April, May, June, and July (clear skies?) are low sales months. Create 2 dummy variables to represent this - 1 for August and September; 1 for March through July. The remaining months will be the omitted, or reference, category. Calculate the MAD for this model. Add this model to the table.
3. Write out the equation for model 3. What is the predicted value for month 37? What is the predicted increase in sales in August and September, compared to October thru February?
4. Which model worked the best, as judged by the MAD?

Table: Regression estimates of sales
	Model 1: Time only	Model 2: Time and Hi Sales	Model 3: Time and Sales divided into 3 groups
Variable	Coefficient Estimate	Coefficient Estimate	Coefficient Estimate
Intercept	3896*	3312*
Time in months	132*	95*
High Sales Month		5104*
AugSep
MarchthruJuly**
MAD	2956	2257
N	36	36	36
* indicates statistically significant at the 0.05 level **Omitted group is months October, November, December, January, and February.