Problem 12-17 (Algo) 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 PRII Sale 4 6 7 8 9 41.9 42.1 42.9 37.3 40.0 45.0 45.5 49.750.6 118.0 16.0 127.0 112.0 115.0 125.0 125.0 129.0 136.0 10 51.5 139.0 DipictureClick here for the Excel Data File a. Construct a causal regression model using PMI as the causal variable. How well does your model fit the data? (Enter r-squared as decimal(not percent). Round your answers to 2 decimal places.) Sales (1000) R (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. b-1. Construct a new regression model using this information. (Enter t-squared as decimal (not percent). Round your answers to 2 decimal places.) Sales (1000) R! (PMI) b-2. Is the fit of the new model better or worse than the model you made for parta? Better Worse c. Pick the best model from parts a and b, and create a forecast for sales given PMI = 48.9. (Round your answer to the nearest whole number) Sales (1000)