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:

a. Construct a causal regression model using PMI as the causal variable. How well does your model fit the data? The R2 shows that 65% of the variance in sales is explained by the PMI.
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? This new model is better because it explains 91% of the variance in sales.
c. Pick the best model from parts a. and b, and create a forecast if the PMI is 47.3.

Month 1 2 34 5 6 78 910 PMI Sales (1000s) 121 123 125 120 118 118 122 127 135 136 42.1 43.0 41.0 38.2 40.2 44.1 45.8 49.0 48.7 52.0