Empirical Macro economists often use the natural logarithm of their input variables in order to assess things in terms of percent change. The standard is to use lowercase variables to denote the natural log of upper case variables (i.e. y = In(Y), p = In(P), and so on). When you download PS6_data, you'll see the annual unemployment rate (u) and annual Real GDP (Y) for Canada between 1961-2020. First thing you'll need to do is get Real GDP in- terms of rates of change, which can be done by taking the natural log of Y and subtracting the natural log of Yt-1, we call this Ay which is just the annual growth rate of Real GDP. Formally Ay = Ut - yt-1 = In(Yt) - In(Yt-1). (You don't need to show/submit this step, but it will be necessary to compute in order to answer the remainder of the question.) 1. Assume the natural rate of unemployment (u" )is just the average rate from 1962-2020, so n-1962(Un/58), and the natural rate of output growth (Ay) is just the average rate from 1962-2020, so _-1962(Ayn/58). Report u" and Ay. 2. Calculate cyclical unemployment (u -u" ) and the output gap (Ay - Ay) for each period and then graph these over time. Show your graph What do you notice?3. Now present :1 scatter plot of your reeuite with cyclical unemployment on the yaxie and the output gap on the Xexie. and put in :1 Linear trend line (A line of beet t]. How do you interpret you scatter plot