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) 121 123 125 120 118 118 122 127 135 136 a. Construct a causal regression model using PMI as the causal variable. How well does your model fit the data? Sales (1000s) = ________________
R² =
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. [HINT: To create the new regression model, the PMI in one period influences the sales in the next period. So the PMI in period 1, 42.1 influences the sales in period 2, 123 and so forth.]
Sales (1000s) = ________________
R² = _____ ____________________ Is the new model better or worse than the model you made for part a?
c. Pick the model with the better R2 from parts a and b, and create a forecast if the PMI is 47.3.
Sales (1000s) = ____________________________