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Many supply managers use a monthly reported survey result known as the purchasing managers' index (PMI) as a leading indicator to forecast future sales for their businesses. Suppose that the PMI and your business sales data for the last 10 months are the following:
Month:
1
2
3
4
5
6
7
8
9
10
PMI:
42.1
43.0
41.0
38.2
40.2
44.1
45.8
49.0
48.7
52.0
Sales (1000s):
121
123
125
120
118
122
127
135
136
a. Construct a causal regression model using PMI as the causal variable. How well does your model fit the data?
b. Suppose that the PMI is truly a leading indicator. That is, the PMI value in one period influences sales in the following period. Construct a new regression model using this information. Is the new model better or worse than the model you made for part a?
c. Pick the best model from parts a and b, and create a forecast for sales given PMI 5 47.3.
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