Note: Please answer this question only by typing your answers in the typing space available for this question (a) Explain the role of regression models (time series and otherwise) in forecasting. That is, how is trend projection able to forecast? Ho regression used for causal forecasting? [2 Marks] (b) A firm cleans chemical tank cars in the Bay St. Louis area. With standard equipment, the firm typically cleaned 70 chemical tank cars month. They utilized 10 gallons of solvent, and two employees worked 20 days per month, 8 hours a day. The company decided to switch larger cleaning machine. Last April, they cleaned 60 tank cars in only 15 days. They utllized 12 gallons of solvent, and the two employe worked 6 hours a day. [3 Marks] (i) What was their productivity with the standard equipment? (ii) What is their productivity with the larger machine? (iii) What is the change in productivity? (c) A firm has modeled its experience with industrial accidents and found that the number of accidents per year ( Y ) is related to the number employees (X) by the regression equation Y=3.3+0.049X. R-Square is 0.68 . The regression is based on 20 annual observations. The fir intends to employ 480 workers next year. How many accidents do you project? How much confidence do you have in that forecast? Marks]