$11.$ Barbara Lynch is the product manager for a line of skiwear produced by HeathCo Industries and privately branded for sale under several different names, including Northern Slopes and Jacque Monri. A new part of Ms$.$ Lynch$\text{'}$s job is to provide a quarterly forecast of sales for the northern United States, a region composed of $27$ states stretching from Maine to Washington. A $10-$year sales history is shown:a$.$ Because Ms$.$ Lynch has so many other job responsibilities, she has hired you to help with the forecasting effort. First, she would like you to prepare a time$-$series plot of the data and to write her a memo indicating what the plot appears to show and whether it seems likely that a simple linear trend would be useful in preparing forecasts.SALES $=$a$+$b $($TIME$)$ Set TIME $=1$ for $2007$ Q $1$ through TIME $=40$ for $2016$ Q $4.$ Write the trend equation: SALES $=+1=($TIME$)($Circle $+$ or $-$ as appropriate$)$ c$.$ Do your regression results indicate to you that there is a significant trend to the data? Explain why or why not. d$.$ On the basis of your results, prepare a forecast for the four quarters of $2017.$ c$.$ A year later, Barbara gives you a call and tells you that the actual sales for the four quarters of $2017$ were: Q$1=334,271.$ Q $2=328,982,$ Q $3=317,921,$ and Q $4=350,118.$ How accurate was your model? What was the mean absolute percentage error $($MAPE$)?$