Linear regression is a modeling tool that is designed to be used to generate high-quality predictions. But prediction is different from recommendation/optimization, which are tasks that managers also need to do well in the context of data analytics. To illustrate, suppose we must decide how many automobiles to produce in March in order to satisfy uncertain demand in the month of April. Suppose for simplicity that inventory of vehicles at the start of April is zero vehicles. Suppose our linear regression model predicts that the expected demand in April will be 15, 855 vehicles with a standard deviation of 1, 118 vehicles. Should we decide to produce 15, 855 vehicles? More than 15, 855 vehicles? Fewer than 15, 855 vehicles? To address these questions, please answer the following: i)What might be some of the various costs associated with producing more vehicles than the actual demand during a month? Similarly, can you think of some of the various costs associated with producing fewer vehicles than the actual demand? ii) Suppose as above that vehicle inventory at the start of April is zero. In the context of automobile production, do you think the cost of overproduction for April demand is larger or smaller than the costs of underproduction for April? Given that our linear regression model predicts that the expected value of demand in April will be 15, 855 vehicles with a standard deviation of 1, 118 vehicles, should we decide to produce 15, 855 vehicles/more than 15, 855 vehicles/fewer than 15, 855 vehicles? iii) Can you think of ways to do prediction that might explicitly account for the differences between costs when the prediction is higher versus lower than actual demand